Universe Down to Earth
Essays on special topics in astronomy that evolved principally from invited talks and lectures delivered for introductory college astronomy classes at Columbia University, University of Maryland, and University of Texas. The book uses creative “household” analogies to help bring complex topics of the universe to the lay reader.
The methods of science hold their deepest roots in the origin of numbers. We owe it to the “number line” to give due attention to all numbers big and small. As one who studies the universe, however, you can expect that I have slanted the coverage toward the big ones.
The last time somebody asked you,
How big is a billion?, what was your response? If you had nothing much to say, then one can infer that you are probably not an astronomer. Of all the natural and physical sciences, astronomers dominate the “big numbers” market. Indeed, it is nearly impossible to conduct a conversation with an astronomer without greeting numbers that contain more zeroes than you would bother to count. This chapter may help you appreciate the evolution of this phenomenon.
It is generally agreed among historians that economics played a role in the birth of mathematics. For example, if I breed chickens and you breed sheep, and I want some of your sheep, it would be natural for us to swap chickens for sheep. But first we must answer the question: How many chickens equal one sheep? This seemingly simple question, in fact, requires the invention of a logical scheme for counting. Some of the earliest evidence for the ability to count comes to us on a 30,000-year-old wolf bone excavated in eastern Europe that was deeply etched with fifty-five notches in groups of five. But the ability to count, undeniably a sophisticated concept, is still not sufficient to deal with all our problems. Suppose I have only five chickens, but you think a sheep is worth ten. I cannot afford to “buy” a whole sheep. With this predicament, a revolutionary concept of numbers is needed to help us consummate our trade: the concept of a half a sheep. But we need not stop with only half a sheep. Suppose my unit of barter is not a chicken but a pea from my vegetable garden. Certainly five peas will buy much less than half a sheep—perhaps only one-thousandth of a sheep. Apart from the logistical difficulty of actually trading a fraction of a (living) sheep, it is clear that advanced barter requires one to be comfortable with numerical quantities borrowed from the world of fractions.
For most of the 5,000 years of recorded history, little scientific significance was attached to extremely small numbers. It was not until the late 1600s when the Dutch naturalist Anton van Leeuwenhoek introduced the microscope to the world of biology. With the desire to measure precisely the sizes of cells, protozoa, and bacteria, there proliferated tiny fractions of the measuring unit such as one-thousandth, one-millionth, and one thousand-millionth.
Meanwhile, astronomers actively explored in the opposite direction with the help of Galileo Galilei’s introduction of the telescope to the world of astronomy in the year 1610. The telescope heralded a new scientific era that allowed astronomers to worry about, and subsequently estimate the sizes of objects in the universe, and the distances to them. Equally bulky numbers then emerged, such as one million-billion, one billion-trillion, and one trillion-trillion.
Astronomers and biologists alike were faced with the same problem: how can one cleanly and neatly talk about extreme quantities of the universe without polluting the conversation with countless “-illions” or “-illionths”? And European travelers need not be reminded that a billion in England and most of Europe is a thousand times bigger than a billion in the United States and France. This numerical dilemma was compounded in the early 20th century after atoms and subatomic particles were discovered by the physicists J. J. Thompson, Ernest Rutherford, and James Chadwick at the Cavendish Laboratory of the University of Cambridge.
What follows is a journey through some awkward “-illionths” and “-illions” that once bedeviled the scientific community.
|one thousandth||one over one with three zeroes||This is the approximate radius of a peppercorn.|
|one millionth||one over one with six zeroes||The head of a human sperm typically has this radius.|
|one billionth||one over one with nine zeroes||A common radius for the tiniest bacteria.|
|one trillionth||one over one with twelve zeroes||Fifty three of these is the classical radius of the hydrogen atom.|
|one quadrillionth||one over one with fifteen zeroes||About three of these will get you the classical radius of the electron.|
|one quintillionth||one over one with eighteen zeroes||This slice of a sheep would not buy much in any economy.|
|one thousand||A one followed by three zeroes||This is about the number of times per minute that Earth is struck by lightning.|
|one million||A one followed by six zeroes||When counting people, there are about eight of these piled into New York City.|
|one billion||A one followed by nine zeroes||If you never go to sleep, it will take you 32 years to count this high. And cows are dismayed to learn that, when last checked, McDonald’s hamburger food chain has sold about one hundred of these. Laid end-to-end, this many hamburgers would go around the Earth 200 times, and, with what remains after you have eaten a few, would bridge three round trips to the Moon.|
|one trillion||A one followed by twelve zeroes||This is about how many seconds of time have passed since the Neanderthal roamed Europe, Asia, and northern Africa.|
|one quadrillion||A one followed by fifteen zeroes||If the human population ever reaches this number then everybody will have to stand in order to fit on the surface of the Earth.|
|one quintillion||A one followed by eighteen zeroes||This is the sum of all sounds and words ever uttered since the dawn of the human species. The tally does include congressional debates and filibusters. Coincidentally, this is also about the number of grains of sand on an average beach.|
|one sextillion||A one followed by twenty-one zeroes||This is the estimated number of stars in the universe.|
|one bezillion||In spite of what your friends may tell you, this number does not really exist.|
The scientific community, unhappy with such awkward terminology, was in need of a more elegant method of numerical organization. Hence, a sensible system of prefixes was formalized by the International Union of Pure and Applied Physics to be used in conjunction with the metric system. With such a scheme, physical quantities are described in units of thousands such that every three zeroes appended to a number yields a new prefix. Additionally, scientific notation was introduced so that writer’s cramp would not arise if, for some reason, you chose to write out the number. A large number like 2,000,000 (two million) would be written in scientific notation as 2.0 × 106, where the “6” in the “106” tells you how many places the decimal hops to the right. For a tiny number such as .000002 (two millionths), scientific notation represents it as a 2.0 × 10-6, where the “-6” in the “10-6” tells you how many places the decimal moves to the left.
The officially accepted prefixes are listed below.
From what appears to be a melodic quartet in pentameter, one just locates the correct prefix and appends it to whatever quantity is measured. Some common examples: centimeter (one hundredth of a meter), kilogram (one thousand grams), and megahertz (one million hertz).
A romp through the scientific offerings of the universe can occasionally tempt you to invent new units that will make measurement simpler for the intended task. This, of course, has already been done for the smallest to the largest length scales. The branch of physics known as quantum mechanics dictates that the structure of space, itself, is discontinuous on scales of what is called the “Planck length,” which is about 1.6 × 10-33 centimeters. The role of the German physicist Max Planck, in the dawn of quantum mechanics, is discussed further in Chapter 8. Atomic distances and wavelengths of visible light are commonly measured in units of “Ångstroms,” which is defined to be 10-8 centimeters. Yellow light has a wavelength of about 5000 Ångstroms.
Distances among planets in the solar system are conveniently measured in “astronomical units,” which is defined to be the average distance between Earth and the Sun—about 93 million miles. On this scale, for example, the average distance of Pluto from the Sun is just under 40 astronomical units. The distance that light travels in one year is enormous. This is the famous “light year,” which is about 5.8 trillion miles. It forms a convenient yardstick to measure distances between the stars. The nearest star to the Sun, Proxima Centauri, is about 4.1 light years away.
For obscure historical reasons, most astronomers use the “parsec” rather than the light year as the yardstick of choice. One parsec equals 3.26 light years. There is no widely used unit of distance that is larger than the parsec, although one could, in principle, define the size of the entire universe (about 14 billion light years in diameter) as a new yardstick, but it would not be very useful—what else could you find to measure with it?
In any adopted set of units, there is no doubt that astronomers monopolize the big numbers. But the biggest number of them all—the one that signifies the physical limit of measurable Nature—is a very clean, compact-looking number within which all of astronomy is contained:
This unsuspecting quantity represents the estimated number of atoms in the Universe, yet it has no name. How about totillion? If you are worried that each atom contains subatomic particles that can each stand up and be counted, then you needn’t worry too much. Over ninety percent of all atoms in the universe are hydrogen atoms. Hydrogen in its most common form contains no neutrons—only a single proton and a single electron. For a better estimate we should then double our newly named number: 2 × 1081.
Does this mean that we cannot discuss numbers bigger than 2 × 1081? Certainly not. We must simply remember that such numbers have no relationship with physically countable quantities in Nature. Let’s take 10100, for example. It is a one followed by 100 zeroes. This rounded, neat-looking number, which is ten quadrillion times larger than the number of atoms in the universe, actually has a name. It was christened a “googol” by a nine-year-old nephew of the mathematician Edward Kasner. Though it is a worthy, even lovable number, it is not my favorite. That distinction goes to the number ten raised to the googol power:
10(googol) = 1010100
It has the immortal name of the “googolplex.” This number was originally supposed to be a one followed by as many zeroes as it would take for someone to get tired of writing them. Since different people obviously get tired at different rates, the googolplex was redefined in terms of the googol. Thus, a googolplex is so big that it cannot be written without the aid of scientific notation. It has more zeroes than can fit in Universe. Actually, this is not surprising since a googolplex is a one followed by a googol zeroes, and a googol is a number bigger than the sum of all particles in the Universe. Even if you could write your zeroes small enough to place one on every existing atom, the googolplex still could not be written out in the space of the Universe. It is sobering to see the dynamic range of astronomy humbled by the imagination of a nine-year-old just as it is enlightening to realize that one’s imagination can extend beyond the limits of astronomical perspectives.
Just for the record, there exists a named number that dwarfs even the googolplex. This is Skewes’ number, written as:
It is said that this number gives mathematicians information about the distribution of prime numbers. Skewes’ number can also be discussed abstractly even though it obviously has no measurable application to Nature. For example, the mathematician G. H. Hardy pointed out that if the entire Universe were a giant cosmic chessboard, and the interchange of protons between any two atoms were legal, then Skewes’ number would represent the total possible number of moves!
Is this the whole story of science and numbers, or can there be another level of investigation? One cloudy night, when I had nothing better to do, I decided to look more closely at our revered international system of metric prefixes.
In these days of inflated modifiers, a thank-you note might get more attention if you signed it “Thanks × 109,” provided, of course, you really do mean “Thanks a billion.”
What happens if you are 10-6 biologist? That must make you a microbiologist.
How about if you just read a copy of 2 × 103 Mockingbird? That must have been Harper Lee’s undiscovered classic novel, Two Kilo Mockingbird.
If you have ever played 10-12 boo with a child, then it was probably the metric version called pico-boo.
If the facial beauty of Helen of Troy was sufficient to launch a thousand ships, then the “10-3 Helen,” better known as the “milli-Helen,” must be the beauty required to launch just one ship.
Suppose you owned 101 cards? That would be your personal deka-cards.
What happens if you live in a 106 lopolis? This is none other than a megalopolis.
And finally, if you just had a 10-2 mental journey to the googolplex, what kind of journey was it?
This chapter might possibly belong at the end of the book as a glossary, but our discussion of the methods of science would be incomplete without paying homage to the invention, development, and usage of jargon. An academic discipline that is sufficiently mature will have normally assembled for itself a jargon-filled lexicon. But before you get indignant about this, consider that academic researchers are not exclusively guilty. When was the last time you understood your car mechanic when you were duly informed of what was wrong with your car? And if baseball were not your passion, then the following plausible scenario would sound completely meaningless:
The DH, who had homered in each of his first two at-bats, reached first on a pitcher’s balk, and two outs later advanced to third on a ground-rule double. He then scored to win the game on a payoff pitch to a batter who laid down a bunt for the squeeze-play with two outs in the bottom of the tenth. Yes, we all have our jargon, and we all use it to communicate with others in our field. But in my (possibly biased) opinion, astronomy has the most entertaining jargon of any discipline—enough to warrant a chapter of its own.
Terms of Entearment
To a botanist, the North American rose is a Rosa nutkana. To a marine biologist, a household goldfish is a Carassius auratus. To a medical doctor, a bruise on your jaw is a mandibular contusion. To a sociologist, your next-door neighbor is your residential propinquitist. These professions, and many others, are replete with polysyllabic terms that are precise yet devoid of romance. To Juliet Capulet (of Romeo and Juliet fame),
…a rose by any other name would smell as sweet. But what Juliet neglected to mention is that a rose by a five syllable term would make its way into much less poetry.
Astronomers, however, get the award for creating the most diverse set of terms ever assembled to communicate science. There are romantic-sounding words, words that mean something different from what they say, words that are intentionally misspelled, words that sound like diseases, words that are historical relics, and most importantly, household words that mean exactly what they say. Consequently, terms of astronomy can be enlightening as well as mind-scrambling, but never boring.
Some Terms That Mean Exactly What They Say
- Red Giants:
- This is what we call big red stars. It is an evolutionary phase through which nearly all stars pass.
- White Dwarfs:
- This is what we call little white dead stars. Only rarely is “dwarfs” spelled as “dwarves.” Not to be confused with “dwarf” stars, which are main sequence stars such as the Sun, that burn hydrogen for fuel in their core.
- Black Holes:
- This is what we call gravitational holes in space and time that look black. A black hole’s surface gravity is so high that the speed one needs to escape from them is greater than the speed of light. Since light, itself, cannot escape then all hope would be lost for you if you happened to stumble upon one. Unlike a simple hole in the floor, you can fall into a black hole from any direction. Yes, the properties of black holes would make good script material for a sci-fi horror story.
- Big Bang:
- This is the technical term we use to describe the beginning of the universe. It must have been a really big explosion, even if nobody was around to watch or listen. It is estimated to have occurred about 15 gigayears (15 × 109 years) ago.
- Missing Mass:
- This refers to material in the universe that we have good reason to believe ought to be out there, but we cannot see it. We are still looking for it.
- Star Cluster:
- This is a cluster of stars that are held together by their collective gravity. One variety of cluster contains relatively few (up to 1,000) stars, and has an open appearance. We call these open clusters. Another variety is globular in appearance, and can contain up to hundreds of thousands of stars. We call these globular clusters.
- Star Formation:
- This is the official term we use when we discuss the formation of stars.
Some Famous Names that Precisely Describe the Object’s Appearance
- Jupiter’s Red Spot:
- There is a large circular red region on Jupiter’s cloudy surface. It is a raging anti-cyclone several times larger than Earth, which was discovered by Galileo over 350 years ago. It is officially called the Red Spot. Incidentally, the planet Neptune has a big (dark) spot of its own, which is officially called Neptune’s Dark Spot.
- On the Sun’s visible gaseous surface there are small areas that are cooler than the surrounding regions. Relative to the rest of the Sun these spots look dark. Ignoring the fact that they are periodic magnetic storms that move in pairs across the Sun’s disc, we simply call them sunspots.
- Ring Nebula:
- The tenuous outer envelope of what was formerly a red giant star has escaped into interstellar space. It is nebulous and it looks like a ring. We call it the Ring Nebula.
- Crab Nebula:
- There are no claws, no roaming eyeballs, and no antennae, but this nebulous explosive remnant of the famous supernova of AD 1054 resembles what an impressionist artist might draw as a crab.
- Horsehead Nebula:
- In a corner of the constellation Cygnus there is a dark cloud that obscures part of an illuminated gaseous region behind it. The dark cloud bears a remarkable resemblance to the silhouette of a horse’s head.
- Milky Way:
- If thoroughfares of ancient times were called streets instead of ways then our galaxy might have been named Milky Street. Without a telescope, the billions of stars that compose our galaxy are distant enough, and dim enough, to blend together in what resembles a milky path across the sky. The milk theme exists in the word galaxy itself—the Greeks called the Milky Way the galaxias kuklos, which translates to milky circle.
Some Terms That Sound Mysterious
- Pronounced al-bee-dough. It is a measure of how much light a surface reflects. A perfectly white surface will reflect all light and have an albedo of exactly 1.0, while a perfectly black surface will absorb all light and have an albedo of 0.0.
- Zone of Avoidance:
- The solar system is embedded in the star-filled, gas-rich and dusty disk of our Milky Way galaxy. We must look above and below this galactic pancake to see other galaxies and the rest of the universe. A map of all objects in the sky will readily show that galaxies seem to “avoid” this zone where our own galaxy’s disk is in the way.
- Event Horizon:
- This is the boundary between what is in our universe and what is not in our universe. For example, it is the horizon that separates us from the undetectable galaxies that recede with the speed of light at the “edge” of the universe. Additionally, the event horizon of a black hole is what separates us from the region where light (and anything else) cannot escape. Indeed, the size of black holes and the size of the universe are defined by their event horizons.
- Roche Lobe:
- In the mid-19th century, the astronomer E. Roche studied the detailed gravitational field in the vicinity of a binary system. The Roche lobe is an imaginary, dumbell-shaped, bulbous envelope that surrounds any two orbiting objects. What makes the Roche lobe special is that if material from one object passes across its own envelope, then the material is no longer gravitationally bound. This peculiar-sounding event is actually common among binary stars where one star swells to become a red giant as it overfills its Roche lobe. The material then spirals toward the second star, which adds to its mass, thereby hastening its evolution. When the second star becomes a red giant, the mass-transfer will reverse thus creating a modelling nightmare for binary star theorists.
Some Terms That Sound Like Names One Might Give to an Alien
- For anything in orbit around a galaxy (inclusive of another galaxy), it is the point of closest approach. The farthest orbital point is, of course, apogalacton.
- What at first sounds like the name given to residents of planet “Boso,” is actually the collective name given to particles with a specific quantum mechanical property in common. This includes all photons (massless particles of light), and all mesons (elementary particles with masses that fall between that of the electron and proton). Bosons are named for the Indian physicist Jagadis Chandra Bose.
- Another group of particles. These are neutrons and protons and all heavier particles that decay to become them. From the Greek barus meaning heavy.
- Omega Centauri:
- Surely there must have been a person, place, or thing on the Star Trek television and film series that was an “Omega Centauri.” In astronomy, however, it is the name given to the titanic globular cluster of stars that appears in the southern constellation Centaurus.
Some Terms That Look Like Typographical Errors
- A vertical stick in the ground (not in the mud) that was used by the ancients to measure the angle of the Sun above the horizon. By knowing the height of the stick, and by measuring the length of the shadow, one can determine the altitude of the Sun with great precision. It is the same term used for the raised pointer of a sundial. A gnomon is useless on a cloudy day.
- If you place marks on the ground at the top of your gnomon’s shadow at exactly the same time of day, for every day of the year, then the pattern of marks will trace a figure “8”. This is a simple demonstration that the Sun does not always return to the same spot in the sky at the same time each day. The figure “8” is called an analemma, and is often inscribed in sundials, or drawn on globes of the Earth—usually somewhere in the Pacific Ocean.
- This is the less-than-elegant term to describe the moment when three cosmic bodies have aligned. For example, during full moon and new moon, the Earth, Moon, and Sun are in syzygy.
- A faint glow seen in the nighttime sky 180 degrees away from the sun. It is the reflection of sunlight back to Earth from particles in the plane of the solar system. Gegenschein translates from the German as simply “reflection.”
- The American physicist George Gamow suggested this name for the high-temperature primordial cosmic soup that preceded the big bang. George Gamow is no longer with us, and neither is his word.
- Any mechanical model of the solar system where planets can actually revolve around the Sun. The better models also display the various moons that revolve around the planets.
Some Terms That Carry Emotional or Intellectual Stigma
- Mean Sun:
- Here mean means average. Because of Earth’s elliptical orbit, and because the Sun does not traverse the sky along the celestial equator, the Sun does not always take 24 hours to reach its highest point in the daytime sky. Sometimes it takes less, sometimes it takes more. Also, atmospheric refraction makes the Sun appear to move through the sky more slowly than it otherwise would. To render the Sun more friendly to time keepers, we define the average Sun as simply the one that moves uniformly through the sky so that it always takes 24 hours to reach its highest point. All the clocks of society are set to the mean Sun and grouped, for convenience, into time zones.
- Inferior Planet:
- Any planet that is found between Earth and Sun (i.e. Mercury and Venus).
- Superior Planet:
- Any planet that is found beyond Earth’s orbit (i.e. the rest of the planets).
- Major Planet:
- Any of the nine (i.e. Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto).
- Minor Planet:
- Any asteroid.
- Unstable isotope:
- One of the few properties of atomic nuclei that is modified with a word that is also used by psychopathologists. The identity of a chemical element is set by the number of protons in its nucleus. The number of neutrons, however, can vary. Each variation in the number of neutrons is called an isotope of that element. But deep in the world of atomic nuclei, life is not always tranquil. Some elements have isotopes that are decidedly unhappy about the number of neutrons they contain. These elements can transmutate (decay) into another element by converting one of their neutrons into an electron and proton pair. Such disgruntled elements are quite sensibly referred to as “unstable isotopes.”
- Great Circle:
- This is, quite simply, the shortest distance between two points on the surface of a sphere. There is nothing especially great about it, and it normally refers to only a segment of a circle, such as the path an airplane might take between two cities.
- The term eccentricity is the mathematical measure of the shape of an orbit. A perfect circle has zero eccentricity. An ellipse can have an eccentricity anywhere between zero and one. A parabola has eccentricity equal to one, and a hyperbola can have any eccentricity greater than one. Eccentric orbits are easier to understand than eccentric people.
- Degenerate Star:
- Any star that is supported from collapse by an inter-particle pressure that prevents electrons from getting too close to one another. This electron degeneracy supports all white dwarfs from further collapse. Neutrons can also support a star from collapse by a similar mechanism. This neutron degeneracy supports all neutron stars (inclusive of pulsars). White dwarfs and neutron stars contain some of the densest known matter in the universe.
- Greatest Brilliancy:
- Used almost exclusively for the planet Venus, it refers to the moment when the planet, in its orbit around the Sun, is brightest as viewed from Earth. When this happens, Venus is likely to be near the horizon and brighter than any airplane in the sky. Since Venus is not “coming in for a landing” people who do not know better tend to call police departments to claim they see a glowing and hovering UFO.
Some Terms That Sound Like Diseases
- Inferior Conjunction:
- When an inferior planet passes between Earth and the Sun. This is not a very interesting event because it is the other side of the planet that is illuminated with sunlight.
- Superior Conjunction:
- When a planet (inferior or superior) passes to the other side of the Sun from Earth. If for no other reason, inferior and superior conjunction are worth noting because they are the moments in a planet’s orbit that signals the transition between when a planet is visible in the evening sky and morning sky. For both inferior and superior conjunctions, the Sun, Earth and the planet are in syzygy.
- When a foreground object passes in front of a background object. The term is typically used when an asteroid or the Moon passes in front of either a planet or a star. Strictly speaking, a solar eclipse is an occultation.
- Obliquity of the Ecliptic:
- This is simply the tilt angle of Earth’s axis. More complicatedly put: when the plane of the solar system (the ecliptic) and Earth’s equator are each projected onto the sky, they will intersect at an angle called the obliquity of the ecliptic.
- Bok globules:
- What sounds like malignant tumors is actually the name for small, opaque regions of gas and dust in the Galaxy that are the sites of upcoming star formation. They are named for the pioneering Dutch astronomer Bart Bok.
Some Terms That Resemble Rock Groups
- Shadow Bands:
- These are fleeting ripples of shadows that are noticed during a solar eclipse just before and just following totality. With the Sun as a skinny crescent, the atmospheric optics are ideal for revealing the fluctuations in density within Earth’s lower atmosphere.
- Kirkwood Gaps:
- Regions in the asteroid belt between the planets Mars and Jupiter where orbits are unstable and almost no asteroids are found. Named for the 19th century American astronomer Daniel Kirkwood, who first explained the effect. A gap with similar dynamical origin is found in the rings of Saturn, except that it is called Cassini’s division, after the 17th century Italian astronomer Giovanni Domenico Cassini.
- A region of a star’s spectrum that has a strong absorption feature from the presence of the two-atom molecule, carbon hydride (CH) in the star’s atmosphere.
- Atmospheric Band:
- A region of a star’s spectrum that has a strong absorption feature from the presence of the oxygen molecule (O2) in Earth’s atmosphere. All starlight that is observed from Earth’s surface must pass through the atmosphere. Consequently, this band sneaks into the spectrum of every star.
Some Terms That Have Too Many Syllables
- In the Germanic tradition of slapping together word parts to make an even bigger word, magnetohydrodynamics is the study of the effects of a magnetic field (magneto) on the behavior and motion (dynamics) of a fluid (hydro) that is hot enough for electrons to be separated from their host atoms. Such a gas is called a plasma and is often considered to be the fourth state of matter.
- Thermonuclear Fusion:
- It takes very high temperatures (thermo) to merge (fusion) positively charged atomic nuclei (nuclear) against their natural force of repulsion to create heavier atomic nuclei. The core of the Sun merges hydrogen atoms to form the heavier helium atom with an enormous energy dividend. This nuclear reaction powers the Sun and, in a less-contained way, also powers H-bombs.
- A device that solar astronomers use to observe the Sun in a narrow part of the spectrum. Often the intent is to isolate a single emission or absorption feature.
- Orthoscopic ocular:
- One of many different varieties of telescope eyepieces. This one is relatively expensive and is good if you want excellent image quality. It is also one of the few eyepieces that work well with bespectacled observers.
Some Terms that Sound Like Romantic Places
- Coudé Room:
- It sounds romantic as long as the English translation of the French coudé is not revealed. Some telescopes have secondary and tertiary mirrors that can swing into places that considerably extends the path of starlight before it comes to what is then called the coudé focus. En route to the detector, the starlight is directed out of a hole in the telescope’s side and focuses in a separate room—the coudé room—where high resolution spectra are recorded.
- Ascending Node:
- The spot in space where a tilted orbit crosses a pre-established plane going north. When the orbit crosses the plane going south the node is descending. It is a common term when planet orbits and binary stars are discussed.
- Lagrangian Point:
- What ought to be the name of one of those erogenous spots on the human anatomy is actually any one of five points in the vicinity of two orbiting bodies where all centrifugal and gravitational forces balance. It is named for the 18th century French mathematician J. L. Lagrange. One of the five Lagrangian points, L-5, was adopted as the name of a space exploration society that seeks to promote, among other things, the construction of a space station at this location of the Earth-Moon system.
If you are still wondering, the English translation of coudé is elbow.
Some Terms that are Historical Relics
- Spectral Lines:
- In the old days of astronomy, when photography was the standard means of detection, it was common to publish photographs of stellar spectra. A typical stellar spectrum produced by a prism or a diffraction grating will display an elongated rectangle of light that is marked with narrow emission and absorption features, which indicates (among other things) the chemical composition and temperature of the star’s atmosphere. In a photograph, these features look like lines that segment the rectangle—hence the term spectral lines. Nowadays, with modern digital detectors, spectra are commonly published as graphs of intensity versus wavelength (or something equivalent to wavelength). In these displays the word line loses its descriptive meaning. The emission features look like peaks and the absorption features look like crevasses—but they are still called lines. It is not a singular tragedy, however. There are plenty of examples where word meanings have changed due to technology. For example, some people still call the refrigerator an “ice-box” and many people still say they “dial” a telephone number even though they are simply pushing buttons.
- Can lead to confusion if taken literally. Formerly two separate words, it soon became hyphenated. In its current use, redshift has finally lost its hyphen. When used among astronomers who study galaxies, it refers to the shift in spectral features (absorption or emission lines) toward longer wavelength that is the consequence of a galaxy’s motion away from us. In an expanding universe, where distant galaxies recede faster than nearby galaxies, the redshift is frequently taken to be an indicator of distance. All the spectral lines that were first used to measure this shift had shorter wavelengths than red light. A measured red shift therefore had the unambiguous meaning that the spectral features shifted toward the longer wavelengths of the red part of the spectrum. Yet infrared, microwaves, and radio waves have longer wavelengths than red light. A feature in these parts of the spectrum, if it experienced what is called a redshift, would still shift to longer wavelengths. But to do so will move the feature away from the red part of the spectrum, not toward it. A non-confusing (though non-historical) name might be longshift.
Some Famous Acronyms
- Laser, like scuba and radar, is one of those acronyms that has achieved greater status than the words for which the letters stand. Certain atoms and molecules, when excited, can be made to emit photons of visible light upon being stimulated by photons of the same energy. The remarkable result is an amplified coherent pulse of photons with all the same energy. With a specially designed cavity, this unusual property can be exploited to sustain a narrow beam of coherent photons. The process was dubbed Light Amplification by Stimulated Emission Radiation or laser, for short.
- Identical to a laser except microwave light is emitted rather than visible light. The molecules OH (hydroxyl), H20 (water), and SiO (silicon monoxide) have each been discovered to be a source of maser energy in gaseous regions of our galaxy.
- Quite obviously, a pulsing star. Many types of stars pulse. The term pulsar, however, is reserved for rapidly rotating neutron stars where their magnetic field axis is tilted from their axis of rotation. As the magnetic pole sweeps past our field of view we detect pulses of radiation. Not all neutron stars have the favorable geometry to be called pulsars, yet all pulsars are neutron stars.
- A loose assembly of letters from the phrase quasi-stellar radio source. With few exceptions, quasars look like ordinary stars on ordinary photographs. Their enormous redshifts and their staggering energy production make them some of the most curious objects in the sky. The first of these quasi-stellar objects to be discovered were strong radio sources. Later discoveries showed that some were radio weak. To be fair to these quasars, the radio source was changed to object to now read quasi-stellar object, or QSO, for short.
Some Terms That Have Nothing to do With Punctuality
- Early Galaxy / Late Galaxy:
- Early-type galaxies are elliptical and late-type galaxies are open-pattern spirals. The original “tuning-fork” galaxy classification diagram of Edwin Hubble displayed elliptical galaxies on a tuning fork’s handle (extending to the left) with normal spiral galaxies placed along one tine, and spiral galaxies with a bar-pattern in their center placed along the other tine (each extending to the right). The spiral pattern became less tightly wound as you moved along the tines. Hubble postulated an evolutionary sequence among the galaxy shapes but it was later found that no obvious connection exists. If you will have difficulty remembering early from late, then imagine you are a snail on a page where the tuning-fork diagram is drawn. If you started a left-to-right page trek you would pass the elliptical galaxies early and the spiral galaxies late.
- Early Stars / Late Stars:
- Early-type stars are hot and late-type stars are cool. The original Hertzsprung-Russell (HR) diagram plots luminosity versus temperature with the hotter part of the scale on the left and the cooler part of the scale on the right. Our page-trekking snail, moving once again from left-to-right (across an HR diagram), will pass the hot stars early and the cool stars late.
Some Terms That Have Nothing to do With Texture
- Soft X-rays:
- Low energy X-rays. Nobody has ever squeezed them to verify that they are indeed soft.
- Hard X-rays:
- High energy X-rays. Considerably more deadly than soft X-rays.
Some Terms That Have Nothing to do With Distance
- Near infrared:
- If our peripatetic snail actually lived on the visual interval of a map of the electromagnetic spectrum (violet-indigo-blue-green-yellow-orange-red), and if our snail wanted to visit the infrared part that was just beyond the red, then it would consider the destination to be near.
- Far infrared:
- The snail would have to go far if it wanted to go beyond the near infrared to the part that was on the border with microwaves. Far infrared photons have much lower energy and longer wavelength than near infrared and visual photons.
Some Terms That Have Nothing to do With Etiquette
- Proper motion:
- This is the motion of a relatively nearby star when measured against the background of “fixed” stars.
- Peculiar velocity:
- For a star, this is the velocity that is left over after you have accounted for the larger scale motion of the Milky Way galaxy’s rotation. For a galaxy, it is the velocity that is left over after you have accounted for the larger scale motion of the expanding universe. There is nothing peculiar about either of these.
A Term That Has Nothing to do With Jesus Christ
- Right Ascension:
- As lines of longitude are used to locate east-west positions on Earth, so is right ascension used to locate positions of stars east-west on the sky.
Some Terms That Lie to You
- Contrary to the tenets of a chemist, metals to an astronomer are all elements other than hydrogen and helium in the Periodic Table of Elements. There is actually a practical utility to this scheme. The big bang endowed the universe with primarily hydrogen and helium. Everything else is “pollution” that was forged in the thermonuclear furnaces of stellar cores. Furthermore, in most environments that are astrophysically interesting (such as stars), the temperatures are so high that elements are vaporized and ionized into the free floating charged particles of the stellar soup we call plasma. The traditional laboratory concept of a metal loses its meaning and significance.
- Hydrogen Burning:
- This term is used by nearly all astronomers to describe energy production in the Sun’s core. Conventional usage of the word burn refers to the breakup and rearrangement of molecular bonds with a release of chemical energy. But nothing actually burns in the Sun. Not that all your possessions wouldn’t vaporize if you tossed them there. It’s just that the thermonuclear fusion of hydrogen in the Sun’s core has no resemblance to any traditional understanding of the word burn. Hydrogen fusion unleashes what is aptly called nuclear energy, which is not normally released in your household fireplace.
- Planetary Nebulae:
- Everybody (who owns a telescope and has looked skyward with it) knows that stars do not look much different through a telescope than with the unaided eye—they are simply twinkling points of light. Planets, however, look like points of light only with the unaided eye. Through a telescope they become distinctive circular disks. The sky also contains fuzzy-looking things like galaxies, star clusters, and genuine gaseous nebulosities. One variety of nebulosity, (the lost, over-puffed spherical envelope of a dead red giant star) often appears disk-like through a telescope. The visual resemblance to planets led to the unimaginative and misleading term planetary nebulae.
- Amateur Astronomer:
- If you put the word amateur in front of most professions you would probably doubt whether a person with such credentials would be of any use to you. For example, it is not likely that an “amateur” neurosurgeon, or an “amateur” attorney could attract much business. Amateur astronomers, however, are indispensable. Let it be known that the average amateur astronomer knows more about the appearance of the sky than the average professional astronomer. Furthermore, in almost all cases, the professional astronomer who knows the sky probably started as an amateur. The advantage to knowing what the sky looks like is that you also know when it looks different. Many supernovae, most comets, and nearly all asteroids are discovered by amateur astronomers upon noticing that a familiar region of the sky has a visitor.
What do You Call Something That is Big?
In the business of astronomy, if you dare call something big or bright you are at risk of exhausting your vocabulary of superlatives if you discover something even bigger or brighter. With open arms, astronomers have welcomed the word-prefix super into the dictionary of cosmic jargon. It endows astronomers with the power to create terms like super-giant, super-cluster, super-bubble, and super-nova, and it gives physicists terms such as super-collider, super-symmetry, super-string, super-conductivity, super-fluid, super-sonic, and super-luminal.
This penchant for using the word super has adequate precedent in 20th century society. Comic book characters with trans-human powers were always called super heroes. There are markets and supermarkets. There are highways and super highways. There are ordinary bowls, and then there is the Super Bowl. The engines of some cars are charged while those of other cars are super charged. And we can credit Walt Disney’s Mary Poppins for the “super” version of cali-fragil-istic-expi-ali-docious. A notable exception to this trend was the Boeing 747, which was spared being “super” in favor of the alliteration offered by Jumbo Jet.
In astronomy, giant stars are called giants. But when even bigger giants were discovered we were forced to call them super-giants. These are objects that we now know to be the bulbous evolutionary fate that awaits high mass stars. Normal main sequence stars such as the Sun, are officially called dwarfs, which is clearly what they would look like to a giant—dwarf stars have a million times smaller volume than many giants. Yet let us not confuse normal dwarfs with the hot degenerate stellar corpses that we call white dwarfs, which have a million times smaller volume than normal dwarfs.
Note the rapid loss of descriptive adjectives at the “dwarf end.” I am convinced that it is the result of the relative scarcity of English words that describe what is smaller than normal when compared to words that describe what is bigger than normal.
The day that “super” becomes an insufficient modifier, astronomers will be armed and ready. We have reserved “super-duper” for the occasion.
Astronomers have always had a penchant for lettering things. Ever since Joseph Fraunhofer lettered major features in the solar spectrum in the early 1800s, astronomers have been lettering things from stellar surface temperature to galaxy shapes. Some of Fraunhofer’s nomenclature is still used today to identify the strong absorption features: atmospheric “A” and “B” bands, sodium “D”, calcium “H & K”, and the “G” band of calcium hydride.
As is detailed in Chapter 9, the lettering tradition continued across the turn of the century when Annie Jump Canon at the Harvard Observatory classified and sequenced stellar spectra according to the strength of an absorption feature due to hydrogen. The stars with the strongest features were lettered “A”, the stars with the next strongest features were lettered “B”, and so forth. It was later found that a temperature (color) sequence revealed more stellar physics than a spectral line strength sequence. Some lettered categories were discarded. Others were combined. What remains is the famous spectral classification sequence that is still used today to classify all stars. In order of decreasing temperature we have: O B A F G K M. This sequence has occupied, and will continue to occupy, the minds of mnemonic writers for decades.
Star that vary in luminosity are no strangers to lettering schemes. Omitting A through Q, the first variable star discovered in a constellation is noted by R followed by the genitive of the constellation name. Clearly, only a few variable stars can be discovered before one exhausts the alphabet. By convention, after Z comes RR, then RS, and so forth, all the way to RZ. If that’s not enough, then the scheme resumes at SS, then ST, and so forth all the way to SZ. This continues until ZZ. If the constellation is big, and has many stars, then it may need even more letter combinations than those up to ZZ. When this happens, the scheme continues at AA, then AB, through to AZ. Next comes BB, then BC, through to BZ. The last possible lettered variable star is QZ, because afterwards you would hit RR, which was already used after Z. This naming scheme, for no particular reason, insures that the first letter is always earlier in the alphabet than the second letter—unless the letters are the same. One final criterion is that the relatively modern letter “J” is never used. If you were counting, then you should have obtained 334 combinations.
If a constellation has the audacity to exhaust this many letters and letter-pairs then stars are simply numbered (not from one, but from the number that is appropriate if all previous variables in the constellation were numbered instead of lettered) with a prefix of “V” for variable. For example, the star V471 Tauri is a well-studied variable that can change its brightness abruptly. If a variable star is discovered to be the prototype of a new class of variable stars then the entire class is named for that star. The famous star RR Lyrae, (discovered after, of course, Y Lyrae and Z Lyrae), in the constellation Lyra, defined the properties of what are now called “RR Lyrae” variables.
Letters are also used to convey shapes. In 1925, the American astronomer Edwin Hubble classified the appearance of galaxies in a lettering scheme that still bears his name. It is this lettering scheme that one follows as you move from early galaxies to late galaxies along Hubble’s tuning fork diagram. Preserving the I-call-them-as-I-see-them tradition of astronomers and baseball umpires, Hubble identified elliptically-shaped galaxies with the letter “E”; the most round among them was labeled E0 (pronounced “E-zero”), while the most elongated among them was labelled E7. Hubble labelled flat, spiral-shaped galaxies with an “S”. If the spiral arms were connected by a straight bar-like section in the middle of the galaxy (as is true for nearly half of all spiral galaxies), then a “B” was appended to the “S”. Some spirals were so puffy-looking that they resembled elliptical galaxies. These became their own category called S0 (pronounced “S-zero”). Tightly wound spirals were sub-labelled “a”. Intermediate spirals “b”. Loosely wound spirals “c”. In modern times, this three tiered scale was expanded to describe really loose spirals, which are sub-labeled “d”. And of course, irregularly shaped galaxies were labelled “I”. If you are curious, the family photo of the Milky Way galaxy and its nearest neighbors would show: Milky Way–Sbc (a cross between types b and c); Large Magellanic cloud–I; Small Magellanic cloud–I; Andromeda Galaxy–Sb; and NGC205 (a satellite galaxy to Andromeda)–E5; Hubble’s original scheme is now extended to describe all sorts of galaxy morphology. My favorite among them is the letter “p”, which you add to the classification if, no matter how you describe it, the galaxy just looks peculiar.
The first asteroid or comet or supernova discovered in a year is designated by the year followed by the letter “a”. For example, the famous supernova that was discovered in the Magellanic Clouds in 1987 was the first supernova to be discovered in 1987. Its official name is SN1987a. Subsequently discovered supernovae are assigned, in sequence, the rest of the twenty six letters of the alphabet. When the alphabet runs out (as it does frequently with asteroids and supernovae) you simply double-up. The twenty-seventh supernova of 1991 was named SN1991aa. The twenty-eighth was named SN1991ab. Earth had a close encounter with a 200 million ton asteroid 1989fc; the hundred and fifty-ninth asteroid discovered in 1989. Unlike supernovae, which keep their lettered identification forever, asteroids and comets graduate to “name” status after their orbits and identities are confirmed. They can be named by their discoverer after any person, place, or thing.
Roman Numeral Soup
There are Type I and Type II supernovae; there are Seyfert galaxies of Type I and Type II; there are Population I and Population II stars; and there are stellar luminosity classes of Type I through VII. There is nothing mysterious about these classifications. They are the product of a humble attempt to distinguish more than one variety of object in a given category.
All supernovae have at least one property in common: a star explodes. If you wish to understand supernovae in detail, however, then further classification is warranted. Type I supernovae have weak hydrogen absorption features in their optical spectrum while in Type II supernovae these features are strong. Recently, Type I supernovae, based on closer examination of the class, have been split into two categories, Type Ia and Type Ib. This schism helped to reveal that Type Ib and Type II owe their origin to the explosive death of an isolated high mass star. A Type Ia supernova, however, is the consequence of mass transfer in a binary system where a white dwarf recipient explosively unbinds from a thermonuclear runaway.
Seyfert galaxies are normal-looking spiral galaxies with remarkably luminous nuclei. Carl Seyfert first identified the class in 1943 as part of a larger survey of spiral galaxies. Once again, the class subdivision is based on the appearance of hydrogen in the spectra. Type I Seyfert galaxies have much stronger hydrogen emission than Type II Seyferts.
The light from elliptical galaxies is dominated by old red stars while the light from spiral galaxies is dominated by young blue stars. This simple observation leads to the idea that ellipticals and spirals have different stellar populations. The most recently formed stars are called Population I. They have been enriched (or polluted, if you prefer) by heavy elements that have been scattered through space by previous generations of supernovae. The oldest stars, however, were born before significant enrichment could occur—they are called Population II. Ellipticals are generally considered to be Population II while spirals have a mix of Population II and Population I. The population concept is only a convenience that actually clouds the reality of transitionary populations within spiral galaxies. To confuse matters further, note that Type II supernovae are found only among Population I systems.
Luminosity class is one of the few intuitive Roman numeral classification schemes. In basic terms it is an indicator of how big a star is. Class I are super-giants. These are stars that can get as big as the orbit of Mars. (That’s why they are called super-giants.) Class III are normal red giants, and Class V are main sequence “dwarf” stars, like the Sun. The smallest are among Class VII, which are exclusively white dwarfs. The three other classes are intermediate in size: Class II contains sub-supergiants, Class IV contains sub-giants and Class VI contains sub-dwarfs.
The 88 constellations in the sky have their brightest stars lettered in order of brightness. The squiggly-looking, lower case, 24-letter Greek alphabet (α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ϑ ϒ ϖ) has been endowed with this honor. The brightest star in any constellation is named with the first Greek letter α (alpha) followed by the genitive case of the constellation name. Dimmer stars are named in sequence down the alphabet. Some famous stars are α Centauri in the southern constellation Centaurus, which happens to be the closest star system to the Sun, and β Cygni, which is also known as Alberio, a beautiful double star system in the northern constellation Cygnus. The well-known science fiction television and film series Star Trek borrowed this nomenclature and appended a Roman numeral to indicate a planet’s number according to its distance from a star. One of their better known planets is α Ceti-V to where Khan (the bad guy) was banished.
The astronomer’s cosmic laboratory contains billions of stars and galaxies. It should be no surprise that catalogues proliferate the profession. There are three basic naming formats. One scheme uses somebody’s name followed by a number, like Messier 101, or Arp 337. These are objects that have simply been collected together in a list, and then numbered. The Messier catalogue happens to be a list of fuzzy objects in the sky that was originally intended to prevent confusion with what might otherwise be a newly discovered comet. The Arp catalogue is a list of peculiar-looking galaxies, most of which are gravitationally disturbed by a near neighbor. Occasionally, an astronomer (or an institution) will publish more than one freshly-numbered lists. These objects require an extra identifier. For example, II-Zwicky-70 (a compact, irregular galaxy) is the seventieth object on Zwicky’s second list of compact objects, and 3C273 (the brightest and first confirmed quasar) is the two hundred and seventy-third object in the third University of Cambridge catalogue of radio sources.
Another basic scheme uses a name followed by the approximate coordinates of the object on the celestial sphere. For example, IRAS 1243+30 is simply an object located at 12 hours 43 minutes in right ascension and +30 degrees in declination that was discovered by the Infrared Astronomical Satellite. Cosmic objects that are not fortunate enough to make it into anybody’s list are simply noted with their coordinates preceded by the letter A for “anonymous.” Among astronomers, this coordinate designation is affectionately referred to as the object’s telephone phone number.
The third basic scheme is a hybrid of the first two. Here, all objects are listed in order of increasing right ascension and are numbered in this order. Famous (enormous) catalogues like the New General Catalogue of Non-stellar Objects (NGC) and the Smithsonian Astrophysical Observatory Star Catalogue (SAO) are well-known examples. Incidentally, NGC 224 is the Andromeda galaxy and SAO 000308 is Polaris, the North Star. And if you see a star labeled BS 1457 don’t be alarmed, it’s just a star (in the constellation Taurus) from the Yale Bright Star Catalogue.
Among its varied and numerous duties, it is the job of the International Astronomical Union (IAU) to establish rules of naming and nomenclature. In many cases, however, these rules are established after a naming scheme or term has already been widely used by professional astronomers. Consequently, typical rules of the IAU are simply the formal recognition of a naming trend. This approach to the jargon of a discipline tends to preserve the history, spontaneity, and novelty of the language of scientific discourse. These ingredients are likely to ensure that the discoveries of astronomy will forever remain attractive and accessible to the general public. It is also no surprise that astronomy, the second oldest profession, is the most frequently tapped discipline for science fiction, literature, and films. The subject, as well as the terms themselves, seem to capture the imagination and romance of scientific exploration.
May the terms be with you.
One of the greatest triumphs of 18th and 19th century physics was the formal understanding of heat energy and its interchangeability with mechanical energy. Out of these efforts was born the branch of physics called thermodynamics, which was pioneered through the efforts of many scientists, including the Scottish engineer James Watt (born 1736), who perfected the modern condensing steam engine; the American physicist Benjamin Thompson (born 1753, later Count Rumford), who first proposed that heat is a form of energy; the French engineer Nicolas Léonard Sadi Carnot (born 1796), who provided the first analysis of heat engines; the British physicist James Joule (born 1818), who performed careful experiments to prove that heat is, indeed, a form of energy; and the British physicist William Thompson (born 1824, later Lord Kelvin), who helped to formulate a consistent physical theory.
Modern society owes its industrial success primarily to the invented machines that allow work to be accomplished from energy that is not supplied by the physical labor of humans or of other animals. It is no accident that the 19th century industrial revolution coincided with the development of thermodynamics. A curious 20th century analog is that computers allow certain computational tasks to be completed without the intellectual labor of humans, so that society can now substitute machines for both our body and our brain. Meanwhile, back in the rest of the cosmos, the conversion of one form of energy to another plays a major role in stellar evolution, stellar orbits, and in the fate of the universe itself.
There are many different types of energy, although not all of them manifest themselves in everyday life. Among those that do, there is one type of energy that kills more people per year than any other. It is the energy you have by simply being in motion, which is known in the world of physics as your kinetic energy.
When you start your car and accelerate to 50 miles per hour onto the freeway and drive for a few hundred miles, you may notice that there is less fuel in your tank than when you started. During your trip, you converted the stored chemical energy of the gasoline into heat energy from the friction of the car’s internal moving parts, and into the kinetic of your entire car plus its occupants. When you apply your brakes to return to zero miles per hour, your car’s kinetic energy must go somewhere. It transforms to heat by way of the friction between your brake pads and your wheels, and if you skid, between your rubber tires and the road.
In a head-on collision, you also slow, for example, from 50 miles per hour to zero miles per hour, except that this does not happen with the help of your brakes. The kinetic energy of car-plus-driver at 50 miles per hour must go somewhere. It becomes the sole source of energy for the deafening sound of the collision, the crunch of the car’s front end, the smashed face and skull of any unseatbelted passenger, the damaged guard rail alongside the road, and any toppled lamp posts. The kinetic energy wielded by an object depends on its mass and on its velocity. But it only takes a small change in velocity to induce a big change in the kinetic energy. More precisely stated, the kinetic energy depends on the mass and on the square of the velocity
Kinetic Energy = ½ × mass × velocity2
This formula, translated into a proverb, would read “speed kills.” A sobering example is that at 70 miles per hour, you have nearly twice the kinetic energy of what you had at 50 miles per hour. In other words, if you were to drive 70 miles per hour rather than 50 miles per hour, then every aspect of a car accident would be twice as worse. Not only would the sounds be louder, but, on average, the damage to your car would be twice as costly, and you would be twice as likely to die. Yes, speed does kill.
While departments of transportation try to help people stay alive on the highways, the United States Department of Defense tries to find ways to kill people. Using the principle that speed kills, a rifle was invented that fires a relatively small bullet (0.22 caliber), but achieves a muzzle velocity of 3,250 feet per second, which is about three times the speed of sound—you would be hit with the bullet before you hear the rifle fire. This weapon is the M-16 assault rifle designed by Eugene Stoner in 1959, which was widely used by the American forces in the Vietnam War. It replaced the Thompson sub-machine gun that was used throughout the Korean War, which fired relatively slow-moving, fat (0.45 caliber) bullets. Stoner realized that high muzzle velocity is more important than massive bullets. This physical principle had not escaped the Russian weapons designer Mikhail Kalashnikov. His AK-47 rifle, the Russian high velocity counterpart to the M-16, was widely used by the North Vietnamese. It is the kinetic energy of the bullet, obtained from the stored chemical energy of explosive powder, that transfers to the target, which in the case of human flesh can be quite devastating. A letter home from Vietnam, written by Army Corporal George Olsen in 1969 contains the following passage
…we crawled within six feet of one group [of the North Vietnamese Army] and then charged, and all hell broke loose…One [of them] went down fighting; [he] shot our point man in the ankle at fistfighting range, [but] then was blown apart by the sergeant leading us. I won’t go into detail, but it is unbelievable what an M-16 will do to a man—particularly at close range. The only conceivable comparison is swatting a bug with a chain-mail glove. Enough said—perhaps too much.
[Our point man’s] wound, of itself, wasn’t serious, but the power and shock of a modern rifle bullet is absolutely unbelievable and within two minutes of being hit he was fighting for his life in shock…1
Chemical energy is not the only way to set something into motion. Gravity is well known for this ability. For example, if you set a pan of freshly baked peach cobbler to cool on the narrow sill of your open window on the 8th floor of an apartment building, and if, by chance, it accidentally flies out of the window, it will increase speed (gain kinetic energy) all the way to the ground. Unless you have lived in the basement all your life, this airborne fate of your peach cobbler comes as no surprise. What was the source of energy that became the kinetic energy of the cobbler? It was not gasoline. We presume it was not gun powder. It was you (or your elevator). You carried the peaches. You carried the flour. You carried the brown sugar. You carried the eggs. You carried all ingredients from the ground level to the 8th floor against the will of gravity. This common consequence of a shopping trip endows your food with the potential to recover the work you did against gravity. In genuine terms of physics, the food was given gravitational potential energy simply by being lifted to some height above the ground. The higher above the ground the food is taken, the more potential energy it gains, and the faster it will hit the ground after it flies out of the window. What then happens to the kinetic energy? It promptly explodes the food in a manner that is commonly described with the word “splat.” It also may damage the ground.
On an average day, Earth plows through about 1,000 tons of meteors. As they fall toward Earth’s surface, most of these meteors lose all their kinetic energy in a spectacular way as friction with the atmosphere makes them burn. They become what we all identify as “falling” stars in the nighttime sky. Some of the larger meteors actually survive the trip through Earth’s atmosphere, and hit the ground with tremendous kinetic energy. What then happens to the kinetic energy? It digs holes. The 25,000 year old Barringer crater near Coon Butte, in Coconino County, Arizona, is an impressive example of a hole “dug” by the impact energy of an iron meteor. It is 14 football fields in diameter and about 500 feet deep.
When astronauts re-enter Earth’s lower atmosphere from orbit, their heat shields get hot. What is not widely appreciated is that these shields are the thermal repository for the loss of the spacecraft’s kinetic energy. Heat shields do not simply serve as protection, they are a way of slowing down. One might even call them “airbrakes.”
Spongy objects such as foam, springs, and car airbags, make excellent kinetic energy absorbers. If a pole vaulter chooses to land on a slab of concrete after a 20 foot vault, then the kinetic energy of the fall would be used to fracture bones and rupture body tissue upon impact. This is the splat effect that the peach cobbler experienced. Organizers of track and field events wisely place fluffy things near the pole vault and high jump to absorb the kinetic energy of impact. The task of absorbing the kinetic energy is now passed from the human body to these spongy pillows, which is why pillows are normally preferred to concrete. What then becomes of this absorbed energy? It is converted immediately to heat within the absorbers and then dissipated to the atmosphere. Springs, however, take longer to convert kinetic energy into heat. If our pole vaulter landed on springs, then the kinetic energy would swap back and forth with the mechanical potential energy of the spring. You would watch the vaulter bob up and down until the energy was converted to heat within the springs.
Children’s toys are no exception to these rules. When you shove the clown of a jack-in-the-box back into its box, you are providing energy that is stored in the inner spring. When the lid is released and the clown pops out, the spring converts its stored mechanical energy into the kinetic energy of the clown. Only when the bobbing stops has the spring converted all available energy into heat, which dissipates to the atmosphere. Many toys require that you “wind up” some sort of device that stores mechanical potential energy. The stored energy is then converted to kinetic energy, such as a truck that rolls, a robot that walks, or perhaps even a baby doll that pees. In other toys, this mechanical potential energy is converted to sound energy as the robot or doll speaks to you. The only difference between toys that use batteries and toys that need to be wound is that batteries use stored chemical energy obtained from the battery manufacturer, and wind-up toys use stored mechanical energy obtained from you.
The conversion of gravitational potential energy to kinetic energy is a fundamental ingredient in star formation and stellar evolution. In the final collapse of a gas cloud to form a star, there is a precipitous rise in the kinetic energy of the individual atoms of the cloud. Because the cloud is gaseous, the individual atoms cannot fall straight to the cloud’s center. Instead, the increase in kinetic energy is revealed through an increase in atomic collisions and an associated increase in temperature. Some of this kinetic energy is also converted to photons of light, which escape into space. Eventually, if the gas cloud contains enough mass, the core temperature will become high enough to trigger thermonuclear fusion.
A similar mechanism allows us to discover the presence of compact cosmic objects with high mass such as neutron stars and black holes. Unlike the Sun, most stars in the Galaxy do not travel though space alone. It is not uncommon to find binary, triple, or even quadruple star systems with all members in mutual orbit. If one star first collapses to become a black hole, and another star passes through the red giant phase, then the red giant may fill its Roche lobe and dump matter across its Lagrangian point onto the black hole. Rather than fall straight in, the gaseous matter is likely to spiral toward the black hole’s event horizon, like water that runs down a toilet bowl. Friction between the inner, fast-spinning regions and the outer slower-spinning regions heats the gas to enormous temperatures. As a consequence, the funneling gas emits copious quantities of ultraviolet light and X-rays, which is the calling-card of a massive, yet compact object. Such high energy emission would be uncharacteristic of an ordinary star. Once again, the gravitational potential energy is converted to the kinetic energy of atomic collisions rather than to the kinetic energy of descent.
There are many astrophysical systems where mechanical energy is not rapidly lost to heat. In clusters of galaxies, for example, where there are no galactic airbags or fluffy pillows, galaxies orbit the cluster center with a relatively constant average kinetic energy. For large clusters of hundreds or thousands of galaxies, this average kinetic energy is a direct and reliable measure of the total gravity, which remains the primary means by which the total mass of a galaxy cluster is determined. The same principles of energy and gravity are also invoked to compute the total mass of the larger open star clusters and of all globular star clusters. This method, however, derives total masses for galaxy clusters that are systematically higher (in some cases, by a factor of one hundred) than what you get if you summed the mass of each individual galaxy. The discrepancy was discovered in 1936 by the California Institute of Technology astrophysicist Fritz Zwicky, and it festers to this day as the infamous “missing mass” problem in the universe.
In the reverse of a collapsing gas cloud that gets hotter, the entire universe cools for every moment that it expands. The overall density of energy drops continuously. The temperature of the radiation that permeates all of space, which is the frigid remnant of a hot big bang, is now just under 3 kelvins. If the universe expands forever, then its contents will ultimately greet a cold and dark death as all the stars burn out and as the background temperature nears absolute zero.
How much energy does it take to throw a tomato straight up so that it never returns? It may surprise you to learn that the adage “what goes up must come down” is more a statement of human weakness than of the laws of physics. There is, in fact, a particular velocity that an object must have for it to leave Earth and never return. It is called, quite sensibly, the escape velocity. In the absence of atmospheric resistance, Earth’s escape velocity is about seven miles per second from the surface, which is 250 times faster than the fastest pitches thrown in professional baseball.
With rockets, or other launch apparatus, however, if you propel a tomato with at least Earth’s escape velocity, then you have endowed it with sufficient kinetic energy to leave the force of Earth’s gravity forever. Earth’s gravity does manage to slow the tomato down somewhat, but you have given it more kinetic energy than it would gain had it fallen to Earth from the edge of the universe. In genuine descriptive terms of physics, the escaping tomato has sufficient energy to climb out of Earth’s gravitational potential “well.” On this subject, an acquaintance once penned
Some of what goes up,
If launched with great ferocity,
Will never return—
It reached escape velocity.
Some of what goes up,
If propelled both high and far,
Burns upon return
To become a “falling star.”
The rest of what goes up,
Tossed slowly from the ground,
Started the old saying,
“What goes up, must come down!”
Comets that move with speeds near the local escape velocity of the solar system are only loosely bound to the Sun, and may be considered one-time events. Such comets are not uncommon and are often more spectacular than famous ones that are tightly bound such as Halley’s Comet. Earth is treated to one or two of the one-timers per decade.
There are four types of orbits that an object can have in a simple gravitational field. If all four varieties are given the same closest approach to the central object, then sequenced by increasing total energy (potential plus kinetic) they are the circle, the ellipse, the parabola, and the hyperbola. If an object’s speed is less than the escape velocity, then its orbit will be bound and assume the shape of a circle or of an ellipse. If an object’s speed equals the escape velocity then it will be unbound with a parabolic trajectory. If an object’s speed exceeds the escape velocity then its trajectory will be hyperbolic. The colloquial cool-down phrase, “Don’t get hyper!” does have genuine astrophysical relevance. And if “Don’t get hyper!” is too strong for your needs, then you can always substitute, “Don’t get parabolic!” or “Don’t get elliptical!”
For elliptical orbits, or more generally, for any orbit where the orbit distance varies, there is a continual exchange between an object’s kinetic energy and its gravitational potential energy. As the orbiting object moves closer, gravitational potential energy gets converted to kinetic energy—the object moves faster. This is precisely what happened with our defenestrated peach cobbler. In orbit, however, the object gets to move farther away again as some of its kinetic energy is converted back to gravitational potential energy. Amusement park roller coasters are living physics experiments on the conversion of gravitational potential energy to kinetic energy. In a typical gravity-driven roller coaster, the connected cabs are first dragged up to the highest point in the entire ride, which supplies the requisite gravitational potential energy to avoid getting stuck somewhere between two hills. Now comes the physics experiment: the cabs roll down-and-up and down-and-up and down-and-up in a continual exchange of potential energy with kinetic energy. If there were no friction between the cabs and air and between the cabs and the track, then the roller coaster ride would continue forever. But the roller coaster owner depends on this friction to convert your kinetic energy into heat. The successive hills must therefore get shorter and shorter, until a short final hill just before the ride ends. If you are a roller coaster enthusiast, then all other things being equal, the roller coaster with the single highest hill will also be the longest and the fastest in the world.
Sunlight is, perhaps, the most pervasive form of energy on Earth. Nearly every form of energy that one encounters on Earth can be traced back to the Sun. A car that runs on roof-top solar panels is, in principle, no different from a car that runs on potatoes. Both use energy derived from the Sun. Wood for your fireplace (or wood in general) can burn because it contains a lifetime of energy that a tree absorbed from the Sun. From the point of view of energy, sitting before a toasty fireplace is no different from sitting before a hearth of sunlight, except that burning logs pollute the atmosphere. Hydroelectric plants derive their energy from falling water, usually through ducts in a dam. They exploit the extra gravitational potential energy that water in the dammed lake has over water in the valley below. But how did the water get from sea level up to the lake in the first place? It is the Sun’s energy that helps to evaporate ocean waters, while convection in the atmosphere, which is also caused by the Sun, brings this moisture inland, where it falls out of the sky as rain—hydroelectric energy is really a form of solar energy.
We can also attribute the complexity of life, itself, to solar energy. There are countless organic and inorganic chemical reactions on Earth that thrive in the presence of the Sun’s abundant energy. How else do you think an acorn becomes an oak tree? If the Sun were to disappear tomorrow, then all flora and fauna would eventually “wind down” until the chemical reactions that sustain life ceased. In addition, all motion would stop as mechanical energy irreversibly converts to heat energy. With the Sun as a rather impressive source of external energy, however, almost anything is possible. And the self-organization of complex forms of matter is expected.
For similar reasons, there can never be an isolated “perpetual motion machine,” unless you feed it energy, in which case it would be simply be a battery operated “temporary motion machine.” This is not a statement of inadequate engineering, it is a fundamental axiom of the physics of systems that do not tap an external source of energy.
Calories are a direct measure of heat energy. This simple fact seemed to elude the makers of a well known peanut-filled candy bar in the mid 1980s. The print on the wrapper featured the following absurd claim, “High in energy, Low in calories!” An equally absurd statement might be, “High in weight, Low in pounds!” The human body uses calories derived from food as a means to maintain body temperature and as a source of mechanical energy to do things such as walk, talk, run, circulate blood, and climb stairs. For example, if you just ate a T-bone steak, then the calories you consumed came from the loin of somebody’s cud-chewing cow, and the cow was assembled from farm-feed such as grass and grain, which was grown with the Sun as a source of energy. Credit the Sun, once again.
An under-appreciated aspect of eating cold food is that its net calorie content is always less that what is advertised on the label. Do you want to lose a fast forty calories? Just drink a liter of ice water. Water is often advertised to have zero calories, but by the time it emerges from your body it will have been heated to your body temperature at the expense of your own stored energy. The cost? About forty calories. You get to subtract even more calories for treats such as frozen desserts. Ice cream, for example, is commonly consumed at temperatures well-below freezing. Its calorie correction would be quite large. The only disadvantage is that unlike a liter of water, a tub of premium ice cream packs two or three thousand calories. For this reason, we should not expect the “ice cream diet” to emerge as the latest fad.
Insight to the correspondence between mechanical energy and heat energy was obtained experimentally by the 19th century British physicist James Joule. He revealed that only a small change in temperature results from the dissipation of an enormous amount of mechanical energy. A similar correspondence exists between the food calories that the body consumes and the mechanical energy that is derived from them. In a now famous experiment, Joule stirred a jar of water by the action of falling weights. The gravitational energy of the weights was transferred into the water. Joule describes the experiment:
The paddle moved with great resistance in the can of water, so that the weights (each of four pounds) descended at the slow rate of about one foot per second. The height of the pulleys from the ground was twelve yards, and consequently, when the weights had descended through that distance, they had to be wound up again in order to renew the motion of the paddle. After this operation had been repeated sixteen times, the increase of the temperature of the water was ascertained by means of a very sensible and accurate thermometer…
I may therefore conclude that the existence of an equivalent relation between heat and the ordinary forms of mechanical power is proved … If my views are correct, the temperature of the river Niagara will be raised about one fifth of a degree by its fall of 160 feet.3
In a possibly more relevant example than the Niagara Falls, the calorie content from the stored chemical energy in a single McIntosh apple is more than enough for a 150 pound person to climb, against gravity, every step from the ground to the top floor of the tallest building in the world. In over-fed nations such as the United States, “calorie” is often taken to be a bad word. However you choose to view it, “calorie” still means energy, even when your body stores excess quantities of it as layers of fat on your tummy.
The calorie content of an apple is not nearly as impressive as the heat content of the world’s oceans. The ocean may feel cold when you swim in it, but if you were to add up the vibration energy of every water molecule, then you would get an enormous total quantity of heat. In household example, a standard five gallon fish tank at room temperature contains over 60 times the total heat energy that is found in an eight ounce cup of hot tea. Yes, the cup of tea is hotter, but it contains many fewer water molecules. The tremendous capacity for oceans to store heat energy and influence the local climate it is what keeps the England from becoming a major cross country ski resort; the entire nation is located farther north than the northern tip of the state of Maine. The warm North Atlantic Drift current of the Atlantic Ocean encircles the British Isles, warms the air, and ensures a relatively temperate climate throughout the year.
Photons of all varieties are also a form of energy. The energy created in the core of the Sun emerges as photons from the solar surface. These photons, however, do not come from chemical energy, or gravitational energy. They are the by-products of thermonuclear fusion, which converts raw matter into energy. Four hydrogen atoms assemble under high pressure and temperature to become a single helium atom. The mass of the helium atom is slightly less than the combined mass of the four hydrogen atoms. The lost mass transforms to energy as described by Albert Einstein’s famous formula,
Energy = mass × (speed of light)2
which may be more recognizable when written with its familiar symbols
where c stands for the speed of light, which we learned from Chapter 3 to be a very large number. A small amount of lost mass, after being multiplied by the square of the speed of light, becomes an enormous amount of energy. For example, just one ounce of matter, converted to energy, could power a 100 watt light bulb for over 800,000 years. This simple and profound fact is why tiny humble atoms can serve as the energy source for nuclear power plants, nuclear bombs, and for every living star in the universe.
There are three ways that heat energy can move from one place to another. One is through conduction, which is what happens when you hold the fireplace poker too long with the tip embedded among the burning embers. Heat from the fireplace induces faster vibration in the poker’s atoms. These vibrations are communicated systematically up the poker from atom to atom until the top of the poker burns your unsuspecting hand. Conduction is the primary way that solid objects transfer heat.
Another method of heat transfer is radiation, which simply means energy is transferred directly by photons. Quite independent of your burning hand on the fireplace poker, infrared photons that are emitted from the fire will strike you directly. The human body senses this infrared energy as heat, which is why your exposed skin feels warm when you turn toward a raging fire, yet your skin immediately feels cooler when somebody blocks your view. Photons also travel by radiation from the Sun to Earth along a 500 second journey through interplanetary space. If you had a melt-proof 93 million mile long fireplace poker, then you could poke the Sun and tap solar energy by conduction if you felt so inclined, but it is much simpler to wait for the Sun’s photons to arrive.
A third method of heat transfer is convection. This is how a gaseous or liquid fluid manages to move heat when conduction is ineffective. Returning to our fireplace, the air nearest the burning embers is at a much higher temperature than the air anywhere else in the room. Much of this hot air convects up the chimney as it is replaced with cooler air along the floor of the room. Unfortunately, the frigid outside air then seeps into your home to replace the hot air that went up the chimney. There is no doubt that a fireplace is a toasty addition to any domicile because of the direct infrared photons it provides. Convection, however, insures that it does a poor job of raising a room’s air temperature.
A pot of water on the stove that is being heated to boil normally sits atop a very high flame or a very hot electrical coil. Rather than communicate this high heat through slow conduction from the bottom of the water to the surface, blobs of steam and pockets of water physically move from the bottom to the top. If this were all that happened, then the water would jump out of the pot and float to the ceiling, which would be in conflict with culinary experience. In fact, blobs of water at the surface descend to the bottom to replace the volume that was previously occupied by the rising blobs. When water behaves this way, it is common to say that the water is “boiling.” Raisins make excellent tracers of convecting blobs. Just toss one into a pot of boiling water, and you can entertain yourself for hours as you watch it circulate up and down. If you could toss a flame-proof raisin into the Sun, you would discover that convection is the major means by which energy traverses the outer gaseous layers before it is released as photons from the surface.
A few thoughts about these precious solar photons might possibly help you through the work-day without caffeine. The next time your energy level is low, or the next time the elevator is broken and you must walk up the steps to your destination, remember that you possess stored chemical energy from the food you have eaten, and that the energy content of the food owes its origin to sunlight. You thus have permission to declare to yourself that you are (indirectly) powered by thermonuclear fusion.
- 1 From Dear America: Letters Home from Vietnam, 1985, ed. Bernard Edelman (W. W. Norton: New York), pp. 64–65.
- 2 From Merlin’s Tour of the Universe, 1989, Neil deGrasse Tyson (Columbia University Press: New York), p 230. Used with permission of the author.
- 3 From a letter to the editor of Philosophical Magazine (1845) vol. 27, p 205, reprinted in Great Experiments in Physics, ed. Morris H. Shamos. (1959) (Dover: New York), p 170.
There are 88 keys in a piano and there are 88 constellations in the sky. The 88 piano keys make music. The 88 constellations make a zoo. The tally: one insect, two crustaceans, five fishes (with a pair among them), five reptiles, nine birds, three women, twelve men (with twins among them), five canines (inclusive of a hunting duo), fourteen other mammals, five mythical-magical creatures, and thirty inanimate objects that include three boat parts, ten scientific instruments, one musical instrument, two crowns, a flat-topped mountain, somebody’s hair, and a river.
To supplement your nighttime viewing, here is some under-publicized information that a well-informed star gazer should know.
From a species point of view, the following constellations are in the record-book of celestial creatures:
|Tallest:||Camelopardalis, the Giraffe|
|Heaviest:||Hydra, the Whale|
|Smallest / Lightest:||Musca, the Fly|
|Most Poisonous:||Scorpius, the Scorpion|
|Fastest:||Pegasus, the Winged Horse|
|Prettiest:||Pavo, the Peacock|
|Ugliest:||Medusa’s snake-ensnarled bloody severed head as displayed by Perseus|
From a connect-the-dots point of view, the constellation Orion has the rare combination of large size, bright stars, and an outline that resembles the hunter he is purported to be. His neck, shoulders, waist (belt), knees, sword, and shield are all clearly defined. Unfortunately, he hasn’t much of a head—there is a big empty space above his neck. There is some controversy about whether Orion is left-handed or right-handed. Early drawings and woodcuts from the 15th, 16th, and 17th centuries show the back of Orion’s head, his rear end, and the rest of his loin-cloth-drapped body as he faces away from you. The star pattern requires that he wield his wooden battle-club with his left hand, which makes Orion the world’s largest and most famous lefty. Illustrated globes of the celestial sphere from the same period (an excellent collection may be found at the Musée National des Techniques, Paris) also depict Orion from the rear, even though the constellations are intended to be viewed from the “other side” of the sky, and thus should be drawn in reverse. More recent sketches of Orion (probably drawn by righties) show him facing you as he wields his club in his right hand.
Orion’s sword is commonly illustrated over a short string of stars that hangs from his belt and dangles between his legs. I have never hunted with a sword and club, but of all the places on my anatomy that I might carry a sword, it seems to me that between-the-legs would be low on my list. Such is the cost of connecting the dots.
The stars in Pegasus, the flying horse, are not quite as bright those in Orion, but they are just as majestic. Clearly visible are four stars of a “Great Square” that form the horse’s body. Front legs drape below it. Extending forward is a slightly bent line of stars that resembles the curve of a horse’s neck and head. You must rely on your imagination for its wings. It is not commonly discussed that Pegasus is only a half a horse. You must invoke your imagination if you wish to picture Pegasus’ rear end, because the constellation Andromeda occupies the region that would otherwise complete the horse. By coincidence of configuration, the interior of the Great Square of Pegasus is remarkably devoid of visible stars—the square is as impressive for its near-square geometry as it is for its emptiness. And unbeknownst to our empty bellied winged steed, Pegasus flies through the sky upside down as viewed by residents of the northern hemisphere.
The award for most exotic star names must go to the otherwise undistinguished constellation Libra, the Scales. Its two brightest stars are officially named Zubenelgenubi and Zubeneschamali.
The most boring constellation in the sky is no doubt Triangulum Australis, the Southern Triangle. A detailed photograph of its three brightest stars shows—you guessed it—a triangle. Since nearly any three stars in the sky form a triangle, Triangulum gets the award for the most unimaginative constellation name. To be fair to Triangulum, there are several dimmer stars in and around the triangle. But since the constellation is simply the “Southern Triangle”, these stars do not participate in the designated pattern.
The greatest stretch of the imagination occurs with Apus, in the southern hemisphere. It is a constellation with three prominent stars near the south celestial pole that is supposed to be a fully plumed bird-of-paradise.
Some stars grow in the mind. The most famous of these is Polaris, the North Star. In an informal poll I once asked passers-by,
What is the brightest star in the nighttime sky? Three fourths of them unwittingly proclaimed,
The North Star! Let it be known that the North Star is not even in the celestial top forty. In addition, its reputation puts it at the point in the sky that is directly over the Earth’s North Pole. In the real sky, however, Polaris is nearly one degree from the north celestial pole—about twice the width of the full moon. I do not wish to upset anybody, but in 12,000 years, due to the wobbling of Earth’s axis, Polaris will be over 45 degrees from the celestial pole. Perhaps our north star should be renamed Somewhere-near-the-pole-aris. In spite of all this, residents of the northern hemisphere should not complain. Currently, the region of sky that surrounds the south celestial pole is practically blank. The nearest star with a brightness similar to that of Polaris is over twelve degrees away.
For the record, the brightest star of the nighttime sky is Sirius (Alpha Canis Majoris) in Canis Major, the Big Dog. It is nearly thirty times brighter than the North Star and commonly depicted as the Big Dog’s eyeball. Indeed, Sirius is affectionately known as the “Dog Star.” Sirius is quite recognizable as it lurks below and to the left of Orion. Sirius is also visible from nearly the entire inhabited Earth during one season or another, but it is best viewed in December and January when it rises at sunset and sets at sunrise. A corny joke between star gazing astronomers occurs when, after hearing an unbelievable story, one asks the other,
You can’t be serious! The response is likely to be,
No, I am not Sirius, I am Zubenelgenubi! At the end of July, Sirius rises just before the morning Sun, as though the Sun were walking its dog into the summer sky. This annual celestial ritual thus heralds the onset of the hot-and-steamy “dog days” of August.
The appearance of Sirius just before sunrise was historically well-timed with the annual rise of the Nile River through Egypt, and thus became a harbinger of a renewed agricultural cycle. So important was (and is) the rising Nile to life in Egypt that the five thousand year old Egyptian calendar uses the appearance of Sirius just before sunrise as the first day of the year.
Sirius is actually a double star. The dimmer of the pair, now called Sirius B is an extremely dim degenerate white dwarf. Its existence was not telescopically confirmed until 1862, when Alvan G. Clarke, an ace observational astronomer, revealed its presence buried within the glare of Sirius A.
The nearest star to Earth, as conclusively established by extensive astronomical research, is the Sun. It is often quoted that the nearest star to the Sun is Alpha Centauri, the brightest star in the southern constellation Centaurus and the third brightest star in the night sky. Alpha Centauri is, however, a double star system, not a single star, and that neither star in the pair is the closest star to the Sun. That privilege goes to the dim star Proxima Centauri, which is near enough to the Alpha Centauri pair to complete an orbiting triple star system. All three stars compose the front hoof of the Centaur as he straddles the Southern Cross. At one hundred times dimmer than the detection limit of the naked eye, Proxima Centuri makes a rather demure nearest neighbor.
The constellation with the greatest hype is Crux Australis, the Southern Cross. There are songs written about it, and it appears on the national flags of Australia, New Zealand, Western Samoa, and Papau New Guinea. What they do not tell you is that the constellation is small, (it is the smallest of all 88—your fist at arms length would eclipse it entirely), and its four brightest stars outline the corners of a crooked square, or a kite. In geometric terms it is nearly a “rhombus”, (although “Southern Cross” conveys more romance than “Southern Rhombus.”) There is not even a star in its middle that could represent the center of a cross. The Southern Cross is best used as a signpost to find other, more interesting celestial objects. For example, the Southern Cross is thirty degrees north of the star-starved south celestial pole, and ten degrees south west of the titanic naked-eye globular cluster Omega Centauri. The Galactic equator, (also known as the “Milky Way”), also passes directly through its middle.
Two relatively recent additions to the celestial menagerie are the southern constellations Telescopium and Microscopium, the Telescope and the Microscope. Unlike Triangulum Australis, which is simply boring, each of these two constellations are boring and undistinguished. The brightest stars in Telescopium and Microscopium are over one hundred times dimmer than Sirius. These constellations date not from the ancients but from Abbé Nicolas Louis de La Caille of the middle 18th century. With decidedly less imagination that the ancients, La Caille identified fourteen new groups of stars from the poorly-charted southern celestial sphere. He honorably named them for the principal instruments (hardware) of the arts and sciences. As noble as all this sounds, La Caille had no excuse, and thus is never to be forgiven, for naming two of the least distinguished constellations in the heavens after two of the most important scientific instruments of our times.
A constellation that was simply too big for its neighborhood was the sprawling southern hemisphere constellation Argo Navis, or Argo the Ship. Its length spanned nearly one fifth of the entire sky. Mythology holds that this is the same ship made famous by Jason and his fifty Argonauts, who set sail from Iolchis in Thessaly to Aea in Colchis to search for the golden fleece. The disproportionate size of Argo Navis led our friend Abbé Nicolas Louis de La Caille to cut up the constellation into four smaller patterns while preserving the boat theme. Thus was born Carina the Keel, Puppis the Stern, Pyxis the Compass, and Vela the Sail.
Enduring favorites for the three quarters of the world population that live in Earth’s northern hemisphere are the Big and Little Dippers. They are officially asterisms which simply means that they are interesting subsets of otherwise uninteresting constellations. The Big Dipper’s seven stars form a convincing kitchen saucepan in the sky: three stars form the slightly curved handle, four stars form the pot. Incidentally, the two stars of the saucepan’s front edge are reputed to point towards Polaris, but they miss their target by nearly three degrees. Hanging off Polaris is the Little Dipper. Its handle is curved the other way when compared with the Big Dipper. It looks very much like a cauldron ladle with Polaris at the handle’s tip.
The Big and Little Dippers are actually parts of the constellations Ursa Major and Ursa Minor, the Big and Little Bear. They are reported to be rather chubby bears (as bears are wont to be) with long bushy tails that form the handles of the saucepan and ladle. But these long tails are actually part of cosmic tales because tails of terrestrial bears are only nubby stubs.
Keeping with the kitchen theme, we go to an asterism in the constellation Sagittarius. Sagittarius is a centaur-archer who is part man and part horse (the front end is the half man). In spite of this legendary description, the brightest stars bear a remarkable resemblance to a stove-top tea kettle. It is short and stout—complete with a handle and a spout. This asterism is especially revered in England because the band of light from our Milky Way galaxy appears to pass through the tea kettle’s spout. In England, they always take a spot of milk in their tea. In China, however, milk was never a popular beverage. The Chinese know the Milky Way as “Yin-hur”, or Silver River. Aside from its kitchen-accessory status, Sagittarius is deservedly famous because it contains the center of the Milky Way galaxy—located about three degrees west of the spout.
The most misidentified asterism in the sky is the Pleiades. This little bunch of seven stars has a vague resemblance to a dipper. Since it is little (your thumb held at arm’s distance would cover all visible stars) many people mistakenly call it the Little Dipper. The Pleiades is above and to the right of Orion’s missing head. In Greek legend the seven stars of the Pleiades represent the seven daughters of Atlas: Alcyone, Maja, Merope, Taygete, Asterope, Electra, and Celeno. While a simple telescope shows dozens of stars, the naked eye sees only six. Celeno is missing. To reconcile this numerical error the 4th century Alexandrian-Greek commentator Theon the Younger surmised that Celeno, which is the dimmest of the group, must have been struck by lightning.
To experienced star gazers, the constellation with the most convincing resemblance to a letter of the alphabet is Cassiopeia, queen of Ethiopia. She owes her celestial existence to five bright stars in the sky that form a “W” which, according to some legends, is her throne. The “W” is somewhat lopsided, like a chair that is ready to collapse—it is rumored that she gained weight in her later years. Cassiopeia is near enough to the “pole” star Polaris that for most of the Northern Hemisphere she never sets. At various times of the night and at various times of the year she can be found above, below, and to each side of Polaris. The “W” will sometimes be a “Σ” (the upper case Greek letter sigma), sometimes an “M”, and sometimes a “∃.” This merry-go-round behavior is not a fitting fate for a queen, but Cassiopeia once said she was more beautiful than the Nereids (the Water Nymphs). The Gods did not take kindly to this boasting and (among other things) condemned her to swing eternally around the pole.
As we will detail in the next Chapter, the constellations with the greatest irrational following are the twelve of the zodiac: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. One is often led to believe that the zodiacal constellations are prominent in the nighttime sky. But astrologers do not tell you that Aries, Cancer, Virgo, Libra, Capricorn, Aquarius, and Pisces, are underwhelming constellations that are barely recognizable as coherent patterns in the nighttime sky. Astrologers do not tell you that the constellations are not the same size so that the Sun does not move across them at equal one-month intervals. Astrologers do not tell you that the correspondence of the zodiac with calendar months is shifted backwards by an entire constellation due to Earth’s ongoing precession on its axis. Astrologers do not tell you how much money they make from gullible people.
The fact remains: all you ever see in a clear night sky is a few thousand dots of light. If you would like to see a real menagerie, and you cannot hallucinate like the ancients, then visit your nearest zoo. You will see real (tailless) bears, real (wingless) horses, real scorpions, and no centaurs. These animals will look exactly as nature intended. And the zoo-keeper will not tell you about your financial life, home life, or love life.
The Sun is among hundreds of billions of stars in the disk of our own Milky Way spiral galaxy. The stars in the Sun’s vicinity comprise what is politely called the solar neighborhood. Some stars emit copious amounts of light while others emit much less. Some are near and some are far. Yet all stars present the illusion that they are firmly embedded in the “dome” of the night sky. Any two stars form a line. Any three stars form a triangle. Imagine the endless shapes and patterns that can be envisioned among the six thousand stars visible to the unaided eye.
Over five millennia ago, in the days before evening television, the Babylonians and Chaldeans kept accurate records of the night sky. They assigned icons of the local mythology to the planets and the various star patterns. Between AD 127 and AD 150, the Greek philosopher Ptolemy catalogued many of the familiar names upon these skeletal star patterns that are otherwise known as constellations. Thrust upon these patterns were not only the names of animals and gods but their quirky behavioral traits as well.
Over five millennia after Ptolemy, in the days of space travel, recombinant DNA, and microwave popcorn there are people who believe that planets and star patterns influence their life’s events in ways derivable from the mythology of sleepless and TV-less Babylonians.
The basis for modern day astrology is quite simple. Its premise is that the relative positions of the Sun, Moon, planets and constellations affect you and the events in your life—especially your social and financial life. Note that in a free, capitalistic society these aspects can be the totality of one’s life. All planets of the solar system orbit the Sun in roughly the same plane. Consequently, it makes sense that when viewed from Earth, the motion of the planets, Moon, and Sun appear to be restricted to a relatively narrow band across the entire sky. The exact path of the Sun is centered in this band and is known as the ecliptic. As Earth orbits the Sun we see the Sun travel eastward along this ecliptic until one year has passed when the Sun returns to its initial position. If Earth’s rotation axis were not tilted, the ecliptic would coincide with the projection of Earth’s equator on the celestial sphere. Our 23 ½ degree tilt, however, creates what is tongue-twistingly called the “obliquity of the ecliptic.” This obliquity grants two special points to the Sun’s yearly journey across the sky. They are where the ecliptic crosses the projection of Earth’s equator. They are commonly called the first day of spring (vernal equinox) and the first day of autumn (autumnal equinox). The first day of spring is referred by astrologers as the “first point of Aries.” This officially begins the Sun’s journey through the 12 constellations of the zodiac. If your astrological sign is Aries, this means the Sun was passing through the constellation Aries when you were born. Following Aries on the calendar are Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpius, Sagittarius, Capricornus, Aquarius, and Pisces.
Many astrologers say they can predict your behavior and personality based on your sign in conjunction with the signs that the planets and Moon happen to be in when you were born. It would be wrong to say that the planetary positions in the sky have no effect on human behavior. Planets do reflect light from the Sun and do have gravitational forces. Both factors (the only quantities measurable from Earth) have the potential to affect objects at a distance. But before we jump to conclusions you should know that if we calculate the force of gravity of Mars on you when you were born you will discover that the force of gravity from the obstetrician or midwife who delivered you was 150 times greater than that of Mars.
This leaves light as a last hope for the effects of Mars on your birth. If we presume optimum conditions—you were born on a clear night by an open window in a hospital that happened to have Mars in the sky in view from the delivery table—then we may discuss the effects of its light. We discover here that the six high intensity lamps over your delivery table produce 160 billion times more light on you than the light from Mars. It is not clear why national cults never emerged that would predict your fate based on how the obstetrician was positioned at your birth, or whether GE bulbs were used instead of Westinghouse bulbs.
Astrologers generally agree that the most important astrological effect is the Sun’s location on the zodiac at your time of birth inasmuch as it defines your “sign.” But those who believe in the Sun’s positional influences will have to contend with a sobering fact: the first point of Aries today no longer coincides with the first day of spring. This is a far-reaching twist of the same magnitude as if Alex Haley, author of his well-known genealogy Roots, had later discovered that he was an adopted child. The Sun at the vernal equinox is currently in the constellation Pisces and will soon be in Aquarius. Among people who read their daily horoscope it is not widely known that Earth wobbles on its axis. This is normal behavior for any oblate, spinning, tilted top under the influence of an external gravity so we should not be surprised that the spinning tilted Earth also wobbles on its axis under the influence of the Sun and Moon. The time for one complete Earth wobble is about 25,700 years and its effects are manifested by the drift of the vernal equinox through the entire zodiac over a 25,700 year period. Ptolemy named the constellations about 2,000 years ago. We see that since then, the equinox has traveled nearly one-twelfth the way around the zodiac—one complete sign. What this means is that if you thought you were an Aries, you are really a Pisces; if you thought you were a Pisces, you are really an Aquarius, and so forth. Matters are worsened upon learning that the boundaries of the constellations do not split the zodiac evenly—some astrological signs “last” longer than others. Matters are worsened further upon recognizing that seven of the twelve constellations are feeble skeletal excuses for the animals and objects they are purported to be.
An amusing addition to the above hijinks is that the zodiac contains fourteen constellations, not twelve. The Sun, after leaving the constellation Scorpius, enters the constellation Ophiuchus. It then stays in Ophiuchus for a longer period of time than Scorpius, the sign that is advertised to precede Sagittarius. The confusing conclusion is that most Scorpions are actually Ophiuchans and all Scorpions and Ophiuchans are currently Librans. The fourteenth constellation in the set is Cetus. It is a large constellation that dips into Pisces. The Sun passes through Cetus briefly as it ambles through Pisces but you are not normally informed of this in the horoscope pages.
Some astrologers (typically the expensive ones) are actually aware of these astronomical truths. A common response, when confronted with the facts, is the assertion that the effects of the stars were set 2,000 years ago, and still apply today. I once tested a daily (syndicated) horoscope from the newspaper on the 50 students in one of my introductory astronomy classes. Rather than have the students read their horoscope and decide whether it applied to that day’s dilemmas, I picked one of the twelve horoscopes at random and read it to the class. I then asked all students to declare whether it was “unlikely”, “possible”, or “likely” that I had just read the their own horoscope. Fully one third (17) of the class declared that the horoscope was “likely” to be their own. The class was astonished to learn that the horoscope I read belonged to none of these people. Of the ten people who responded “unlikely”, the horoscope actually belonged to three of them. Controlled experiments such as this one, consistently demonstrate that daily horoscopes would do no worse if they were laid on the page at random, yet horoscope casting in the United States remains the most lucrative industry among the pseudo-sciences.
A subject of fascination and confusion for many people is the effect of the full Moon on human behavior. It is commonly thought that more babies are born during full moons than during any other phase. It is also thought by many people that the full moon has some mystical effect on the human psyche that forces people to behave strangely, to commit crimes, or to transmutate into a howling and hairy canine. Literature abounds with stories of werewolves and other moon-induced human behavior. I have heard some people explain these phenomena with the tidal effects of the Moon on the brain:
…since the oceans are water and are duly influenced by the lunar tides, then the large water content of the human body should also be affected.
Before we jump to cosmic conclusions, consider the following: 1) If the oceans were 100 percent nitroglycerin (or 100 percent anything else) they would still exhibit tides. 2) Tidal forces of the Moon are, indeed, large during full moon. But they are also large two weeks later during the new moon. This phase of the moon cannot be observed. Nobody sees it. Nobody writes lycanthropic stories about it. 3) Tidal forces of the Moon are measured by the difference in gravity between the side of Earth closest to the Moon and the side of Earth farthest from the Moon. If your skull were 7,000 miles across (the size of Earth) then the lunar tides would, indeed, give you an oblong-shaped head, with untold consequences on your mental facilities. But since your skull is only about eight inches across, the tidal force that you “feel” is quite small. Indeed, the weight of a down-filled bed pillow placed upon your head will produce a force that is seven trillion times larger than that of the Moon’s tidal force on your head. The next time somebody tries to blame a bio-cosmic-lunar connection for irresponsible behavior, perhaps we should first blame the influence of creative literature. And then possibly the pillow.
Let us return to the birth rates during the full moon. The average human gestation period is about 267 days†, which is an excellent match with the 265 ½ days in nine cycles of lunar phases. What this means is that babies who are born during a full moon are very likely to have been conceived during a full moon. And nobody will argue the romantic effects of a moon-lit evening.
In a free society, intellectual enlightenment is your best defense against misguided claims in the name of science. Only then can society, as a whole, cultivate a scientifically literate public.
- † You get this from a commonly invoked, yet convoluted formula: Add seven days to the first day of your last menstrual cycle before becoming pregnant. Count backwards three months, and then add a year. If we assume a 28 day menstrual cycle, and conception during ovulation, then this formula will give you 267 days.
University astronomy departments and planetariums, especially those near large population centers, typically receive hundreds, sometimes thousands of daily telephone calls per year from the general public with questions about cosmic phenomena. Some of the calls are induced by heavily publicized events such as lunar and solar eclipses, or planet-Moon conjunctions, while other telephone calls are simply the consequence of people with curious minds who should have otherwise been busy at their jobs. In all cases, however, the array of questions reveals a genuine interest in celestial happenings that serve as a daily reminder to professional astronomers that in the absence of telescopes and computers and theories, one can still be awed by just looking up.
It is often said that Earth’s axis is tipped in space. But in space, there is no uniform up or down, so being tipped can only have relative meaning. We can draw on a sheet of paper the slightly flattened circle of Earth’s eccentric orbit, and ask whether Earth’s axis points straight out of the page. It does not. Earth’s axis is tipped slightly more than one fourth of the way towards the plane of the page. When measured in angle, it amounts to about 23 ½ degrees. That the round Earth rotates on a tipped axis and revolves around the Sun required millenia of the worlds greatest thinkers to unravel. So there is no need to get upset if this circus of motion has ever left you confused.
It is sometimes convenient to think of the sky above you as the inner surface of an inverted salad bowl, which forms what is otherwise known as a hemisphere. Following this analogy, the entire sky as seen from Earth, is known as the celestial sphere. By helpful coincidence, the North Pole of Earth’s axis points near a star “on” the sky, which is, of course, called the North Star. The South Pole points to a big empty area that is not too far from the Southern Cross. If we continue this cosmic correspondence, we can also project Earth’s equator onto the sky. With this simple exercise, we have identified three places: the North Celestial Pole, the South Celestial Pole, and the Celestial Equator. In a layout that is analogous to Earth’s longitude and latitude, there exists coordinates for the sky called right ascension and declination.
Contrary to popular belief, Earth rotates on its axis once in 23 hours and 56 minutes, not 24 hours. In other words, a star, or any other spot on the sky, will return to the same location above you every 23 hours, 56 minutes. On average, however, the Sun reaches its highest spot on the sky every 24 hours. For daily scheduling, people tend to respect, honor, and obey the Sun—not the rest of the stars in the sky. Most of human civilization has therefore chosen to set clocks against the 24 hours of the Sun. Astronomers, however, conduct business in star time. All time-keeping devices that are set to the stars are called sidereal clocks, where midnight sidereal time equals midnight Sun time only once a year on the first day of autumn, which falls on or near September 21st. Thereafter, for every day of the year, the sidereal clock will lose 4 minutes against the Sun clock because Earth must rotate an extra 4 minutes just to return the Sun to the same location as the day before.
Earth’s orbital motion insures that day-to-day the Sun’s position in the sky will migrate across the background of stars1. There is nothing complex about this. If your name were Fido, and you were tethered to a pole, and if you decided to run in circles around it, then you would systematically observe the pole to appear in front of every part of your surroundings. Earth is tethered to the Sun by gravity, and Earth moves in unending circles around the Sun. The only important difference is that Earth is not likely to strangle itself.
Longitude on Earth is measured in degrees, yet right ascension, the corresponding cosmic coordinate, is measured in hours. Where does right ascension begin? In the same place that longitude begins, at the Royal Greenwich Observatory in Greenwich, England. Using an accurate clock—sidereal of course—the time in Greenwich is the right ascension of the star that happens to be crossing a line through the zenith that connects due north and due south. For anybody in the world, this line is called a meridian, but for Greenwich it is exaltedly known as the Prime Meridian—not by cosmic mandate, but by international convention. Zero degrees longitude, the Earth boundary between east and west, is also defined to go through Greenwich. Incidentally, there is no cosmic reason why the Prime Meridian could not have been Eddie’s Steak House in Kalamazoo, Michigan. Except that Eddie would be obligated to supply right ascensions to the world astronomical community for all stars in the sky. He could, however, start a catchy ad-campaign, “Enjoy your Prime Rib on the Prime Meridian!”
Sometimes simple longitudes, latitudes, and meridians are not enough. I once received a telephone call at my office from a practicing Muslim, who was new to the New York City area. The caller needed to know the exact direction that points toward the shortest distance to the sacred Kaaba in Mecca, Saudi Arabia (not to be confused with Mecca, California or Mecca, Indiana). It is this direction that one uses when it is time to pray toward Mecca. The solution is a non-trivial problem in spherical trigonometry that begins with a straight line that connects New York City to Mecca through the Earth, and then projects the line up to Earth’s surface. The result is what is called a great circle, which is normally the most desirous path for airplanes to fly. I computed the direction and told the caller. And like the proverbial boy scout who helps old ladies cross the street, I logged it as a public service deed for the day.
As you might expect, the annual path that the Sun appears to take against the background stars is obliquely tilted from the celestial equator at the same 23 ½ degree angle as the tilt of Earth’s axis from a direction that is straight out of its plane of orbit. There can only be a solar or lunar eclipse when the Moon is very near the Sun’s path. Reflecting this requirement, the Sun’s path has been and officially named the ecliptic. The ecliptic and the celestial equator form tilted rings across the entire sky that intersect at two nodes. The angle of the tilt is mouth-fillingly called the obliquity of the ecliptic.
The Sun is south of the celestial equator for half the year and north of the celestial equator for the other half. Therein lies the origin of the variation in daylight through out the year and the origin of the seasons. By definition, spring begins when the center of the Sun’s disk crosses the celestial equator from south to north—the ascending node. This is why newspapers report the particular minute of the day when spring begins. They could, if they felt so inclined, report the beginning of spring to the fraction of a second. By definition, summer begins when the Sun has climbed the farthest north of the celestial equator. This is where the two tilted rings have their greatest separation. As is true with spring, summer occurs at a particular moment that could be reported to the fraction of a second if there were public demand for such precision.
The important spots along the rest of the Sun’s path can be readily deduced. The first moment of autumn is when the Sun crosses the celestial equator going south—the descending node—and the first moment of winter is when the Sun has descends the farthest south of the celestial equator before it resumes its journey northward. Two thousand years ago, on the first day of every summer, the Sun was superimposed on the constellation Cancer. The first day of summer is the only day of the year where the people on Earth who live at a latitude of 23 ½ degrees north get to have the noon-day sun directly overhead.
Not surprisingly, this band on Earth’s surface can be identified on most maps and on all globes as the Tropic of Cancer. Equivalently the first day of winter historically found the Sun to be superimposed on the constellation Capricorn. Only then can the residents along 23 ½ degrees south latitude enjoy a midday sun that is directly overhead. On Earth, this latitude is identified as the Tropic of Capricorn. At no time of any day in the year do Earth residents outside of the region between 23 ½ degrees south and 23 ½ degrees north have a midday sun that is directly overhead. More bluntly stated, most of the population of the world has never seen the Sun directly overhead. They can only envy those who have traveled to the “tropics” or who just happen to live there.
The Sun begins its journey north along the ecliptic toward the celestial equator after the first day of winter. It begins to make larger and larger arcs across the daily sky, and thus stays in the sky longer and longer for northern hemisphere dwellers. If you have ever paid attention to the daytime sky then you might have noticed that the winter sun rises far south of east and sets far south of west. The daily path is a low arc across the sky. In the summer, the Sun rises far north of east and sets far north of west. The daily path is a relatively high arc across the sky. During your lunch-break, you can discover this for yourself if you measure the height of your shadow at noon on the first day of winter, and again at noon on the first day of summer.
A more revealing experiment, if you have nothing better to do for every one of your lunch breaks over the next year, is to stand in the same place every day at exactly 12 noon and put a mark on the ground where top of your shadow falls2. After a year of missed lunches you will notice that your marks on the ground will grow longer and longer as December 21st approaches. The length of your shadow will pause for a day or two, and then by Christmas, you will see it get shorter and shorter again for the six months up to June 21st. Beginning June 21st, your shadow length will once again pause for a day or two before it begins to get longer and longer for the six months that lead back to December 21st. You already know June 21st to be the first day of summer and December 21st to be the first day of winter. Your experiment showed that for each of these days, the change in the length of your noon shadow stopped. If we deduce the Sun’s behavior from your markings on the ground, we conclude that the noon-day Sun reached its highest point on June 21st and its lowest point on December 21st. In each case, before the Sun turned around, it appeared to stop for a day or two. This phenomenon is endowed with its own name: solstice from the Latin sol = sun, and stitium = stationary. The terms summer solstice and the winter solstice are no less common than the “first day of summer” and the “first day of winter.”
Had the descent of the Sun not stopped on December 21st, then each day your shadow would continue to lengthen as the noon Sun gets lower. Eventually, the length of your shadow would become infinite just before the noon Sun fails to appear above the horizon as you are abandoned in eternal darkness. One could make a horror movie about this. In the days of pagan rituals, the rebound of the Sun after December 21st was heralded as a joyous occasion. There were celebrations and festivities. When Christianity began to spread, and the uncertain birth date of Jesus Christ needed to be set, a time near this pagan Sun ritual (December 25th) was selected to help promote the new religion with a minimum of resistance.
If you were extraordinarily precise during the year-long adventure in shadow etchings, and each measurement was taken at exactly 12 noon, then you will notice that your marks on the ground will trace a figure “8”. Because Earth’s speed in its eccentric, oval-shaped orbit is not constant, and because the Sun seasonally finds itself above and below the celestial equator, the 24 hours of Earth rotation does not always return the Sun to its highest spot on the sky. Sometimes the Sun gets there in a few minutes less than 24 hours, and other times it gets there in a few minutes more than 24 hours. This alternating speedy and tardy Sun is what causes the figure “8”. On average, the Sun gets to its highest point in 24 hours, which is why household clocks needn’t worry about such antics, even though sundials do. The figure “8” is also known as an analemma, which occasionally makes a guest appearance—sideways and afloat—in the middle of the Pacific Ocean as drawn by globe-makers. Perhaps there is no place else for them to place it.
The longer and shorter daytime arcs of the Sun are the cause of longer and shorter days. When I was a child, however, I was terribly confused. I knew that a solar day was always 24 hours, and that the rotation rate of Earth could be trusted, so I did not understand what people meant when they declared,
In the summer the days get longer. When I finally figured out that people were referring to the duration of daylight, I was still confused. Daylight hours begin to grow just after the first day of winter (the shortest day of the year). And they continue to grow through all of winter and all of spring until the first day of summer (the longest day of the year), at which time daylight begins to shorten again. So let it be known among the confused children of the land that winter is the season where days get longer and summer is the season where days get shorter. Perhaps British children are less likely to get confused since the first day of summer in the United Kingdom is called mid-summer, and the first day of winter is called mid-winter.
On the first day of spring and of autumn, the Sun crosses the celestial equator. These are the only days of the year where every Earth resident experiences daylight of equal duration to the night. These two days are more commonly called the vernal (spring) and the autumnal (autumn) equinox from the Latin æqui = equal and noct = night.
The lengthening of the daytime hours from winter to spring is accompanied by sunlight that is more direct, and consequently more intense on Earth’s surface. The slow and continued day-to-day increase in sunlight heats the hemisphere as the season changes from winter to spring. At any moment of the year, the opposite transition is happening in the southern hemisphere. What does this say for the equator? Being caught exactly in the middle, its residents experience no seasons. On the equator, every day is equivalent to an equinox. There are also no deciduous trees, no hibernating animals, and no canceled school days from snow storms. What does this say about the poles? Beginning at 66 ½ degrees latitude, (which, by the way, is the 90 degree latitude of the pole minus the 23 ½ degree tilt of Earth’s axis) and heading toward the pole, there will always be at least one day where the arc of the Sun is so broad that it is, in effect, broader than the entire horizon, and the Sun does not set. The 66 ½ degree north latitude is unimaginatively called the Arctic Circle while the 66 ½ degree south is called the Antarctic Circle. Nearer and nearer to the poles, the number of days in a year grows for which the Sun does not set. This event is known as the “midnight sun” in many places, but they could just as accurately, though less romantically, call it the “11:30 p.m. Sun” or the “1 A.M. Sun.” By the time you get to the poles, you will notice that the Sun rises just once a year and, of course, sets just once a year. The consequence: a six month day and a six month night.
I once received a telephone call from an orthodox Jew who was planning a summer trip to Alaska. He needed to know the exact setting time of the Sun for the Fridays of his trip, which signals the onset of the Jewish Sabbath3. I told him he had better keep out of the Arctic Circle, and I gave the caller sunset times for more southern latitudes in Alaska.
From the point of view of an observer perched “above” the solar system, northern hemisphere summer is where the north pole of Earth’s axis is tipped toward the Sun. Six months later, with Earth on the other side of the Sun, the same tilt of the axis now points away from the Sun. As noted in Chapter 12, just as a spinning and tilted top will wobble, so does the spinning and tilted Earth. Since a full wobble takes about 25,700 years to complete, you need not worry about getting tossed off the surface of the Earth. One of several cosmic consequences is that one half a wobble from now (the year AD 15,000) Earth will be tipped the other way. Polaris, the North Star, will become Polaris, the ex-North Star. The constellations that are normally identified with the nighttime winter sky will have shifted to become summer constellations, and the summer constellations will have shifted to become visible in the winter. In other words, the celestial grid, complete with its celestial equator, the path of the Sun, their nodes of intersection, and the celestial poles, will be projected onto a backdrop of stars that is offset from before.
Indeed, Earth has wobbled enough already so that the position of the Sun against the backdrop of stars on the first day of summer no longer falls in the constellation Cancer—the name Tropic of Cancer is technically no longer appropriate. The current backdrop is the constellation Gemini. Additionally, the Sun on the first day of winter now has the constellation Sagittarius as a backdrop, not Capricorn—the name Tropic of Capricorn is also no longer appropriate.
Either by tradition or by a mandate from frustrated map and globe makers, the Tropic of Cancer and the Tropic of Capricorn have retained their names in spite of this early-breaking news. Two thousand years from now, perhaps you can lobby the map-makers to introduce the names of the next constellations to get the Tropic of Taurus and the Tropic of Scorpius.
After its 500 second journey, light from the Sun must cross from the vacuum of interplanetary space to Earth’s atmosphere. Upon traversing the boundary between these two regions of different density, the speed of light will drop, which beacons an under-unappreciated fact of physics: the speed of light through anything other than a vacuum will always be less than it is in a vacuum. When light penetrates at oblique angles, then the direction of motion changes as well. This phenomenon is known as refraction, and is the principle that allows eye glasses, and of course eyeballs, to focus light. The deeper into Earth’s atmosphere the light travels, the more it refracts as the atmosphere gets denser an denser. What all this means is that the Sun is not where you think it is in the sky. At sunset, as our precious orb of glowing hydrogen poses prettily upon the horizon, the refraction of its light is greatest. Indeed, the unrefracted Sun has already set. Don’t tell your lover, but every romantic memory of a sunset (or sunrise) in your life is the consequence of a refracted image of the Sun, and not the Sun, itself. Of course, the same is true for the Moon since its light also originates from outside of Earth’s atmosphere. The song that contains the lyric, “It’s only a paper moon,” could easily be re-worded to, “It’s only a refracted image,” with no loss of relevance to the song’s content.
People who go fishing with a bow and arrow know all about refraction. Do not aim where you see the fish—you will miss. The fish you see is a refracted image, which is formed as the light from the real fish bends upon crossing the boundary from water to air. Those who are experienced know that to nab the fish you must aim at the correct angle beneath it. In honor of this talent, maybe people who fish with a bow and arrow should be called “anglers.”
Earth’s moon holds a special place in my heart. It was a view of the first quarter Moon (the phase that many people call “half”) through binoculars at age 11 that triggered my career path to study the universe. The mountains and valleys and craters were revealed in detail that I could not have imagined from a simple glance with the unaided eye. With greater academic sophistication, I soon began to appreciate other aspects of the Moon that are just as ogle-worthy: 1) the Moon is the only satellite in the solar system that has no name; 2) the Moon is in predictable gravitational orbit around Earth; 3) the orbit of the Moon sometimes gets in the way of our view of the Sun, which spawns one of Nature’s greatest spectacles—a total solar eclipse; 4) on occasion, the Moon ambles into Earth’s shadow, which extends nearly a million miles into space, and spawns yet another spectacle—a total lunar eclipse; 5) the Moon is in a gravitational tidal lock with Earth, which prevents the far side of the Moon from ever facing Earth; and 6) the Moon is made of rocks and not some variety of smelly exotic cheese.
You can actually observe the Moon’s motion in orbit around Earth, although it is not much more exciting that watching the hour hand on a clock. The next time you spot the Moon at night, take notice of the pattern of stars that surround it, and of the Moon’s position relative to them. Go back inside for about three hours, and then return to see the Moon. You will see that it moved east relative to the background stars by an amount equal to its own diameter. The cumulative effect of this daily orbital motion is for the Moon to rise about 52 minutes later and set about 52 minutes earlier each day. This slow, steady and systematic motion continuously changes our view of the illuminated Moon relative to the Sun. We see the Moon “wax” (grow) from a thin crescent, which sets shortly after the Sun, to a first quarter, commonly known as a “half moon”, which sets at about midnight. The Moon phase continues to wax until it is full. Full moons rise just after sunset, and set just before sunrise. The portion of the Moon’s illuminated surface that faces Earth next wanes to last quarter, which sets at 12 noon, and then to crescent, which sets just before sunset. The phase between the waning and waxing crescents is called the “new moon.” It is the only unobservable phase because the entire far side of the Moon receives complete illumination.
In a clash of terminology, I once received a telephone call from someone who wanted to know when the next new moon was to occur. This is, of course, a single moment in time as the Moon passes between the Sun and Earth. I gave the caller the information, but then the caller asked when this new moon would be visible from New York City. I knew, at the time, that Ramadan was near. This is the ninth month of the Muslim calendar that is traditionally a period of daily fasting—it begins and ends with the sighting of what is called the new moon. But what the Muslims, and almost any other religious or social culture refers to by the “first sighting of the new moon” is the first sighting of the waxing crescent in the early evening sky towards the west, just after sunset. For this to happen, the Moon must emerge from the new phase to be far enough away from the Sun in the sky so that you obtain a crescent-shaped glimpse of the illuminated half. This normally takes a day or two beyond the new moon.
The phases of the Moon (as well as tons of other information) are tabulated in a book called the Astronomical Almanac, formerly the Astronomical Ephemeris and Nautical Almanac, which is published annually by the nautical almanac offices of the United States Naval Observatory, in Washington, DC, and of the Royal Greenwich Observatory in Greenwich, England.
The word almanac also appears in the title of the annually published book The Old Farmer’s Almanac, where weather predictions were traditionally made from a secret formula—devised by the founder—which is contained in a black tin box located in Dublin, New Hampshire. One particular occasion, a caller to my office wanted to plan a honeymoon vacation around the full moon. When I told the caller that my source for the Moon’s phases is the Astronomical Almanac, the response was,
…then predicting the phase of the Moon must be like prediction the weather, you really cannot know for sure what it will be the next day. I did not know whether to compliment the caller on such healthy skepticism of the weather predictions from The Old Farmer’s Almanac, or whether to chide the caller for never having noticed the daily, predictable changes of the Moon. Actually, I did both, and then explained that with the exception of rare typographical errors, the Astronomical Almanac is 100% correct, every day of every year. And that it contains no horoscopes, folk remedies, or cute human-interest stories.
For many people in the world, the rising full moon is one of the top wonders of Nature—especially if the horizon is dotted with trees or buildings as the Moon emerges from behind. This wonderment often includes a full case of the “Moon on horizon illusion,” where the orb appears unnaturally large as it rises or sets. While there is still no agreement among Moon-on-horizon experts, it is almost certainly related to a confusion in your depth perception induced by familiar objects on your horizon. A full moon, and the presence of identifiable buildings or trees adds considerably to the illusion. Sales brochures for romantic cruises notwithstanding, moonrise over an expanse of ocean—where there are few horizon depth cues—provides a relatively poor moon-on-horizon moment. It is rumored that if you observe the rising moon through your legs while bent over, then the moon-on-horizon illusion will also be significantly lessened because the trees and buildings are no longer registered as recognizable icons. Feel free to attempt the experiment when nobody is looking.
The human fascination with the Moon on the horizon is powerful. I once received a phone call from a cinematographer of a film in production by Francis Ford Coppola. The cinematographer wanted to obtain genuine footage of the full moon as it rose over the Manhattan sky line. The film clip would be edited into the film to establish the urban “night mood.” I was asked to provide the best time, date, and location for this task. Only after the telephone call did it occur to me that the full moon’s photogeneity is what gets it artificially selected for appearances in feature films. The other moon phases, which are also cosmically legitimate, tend to be neglected.
I was also concerned that Coppola’s clip was going to feed the misconception that the Moon only comes out at night. Please tell your friends that the Moon is visible in the broad daylight on about 24 of the 29 ½ day cycle of phases. The film clip may also feed the idea that the full moon is common. But the Moon spends 10 of its 29 ½ day cycle being a crescent, and another 10 days being that funny-looking intermediate phase between quarter and full, which is officially called gibbous.
Perhaps I am biased. Nights with full moons are the most avoided nights of the year among the world’s professional astronomers. The full moon is so bright (it is over five times brighter than the combined light of two side-illuminated “half” moons) that the number of detectable objects in the night sky drops precipitously. The full moon is not even interesting through binoculars. Being front illuminated as seen from Earth, there are no shadows among the mountains, hills, and valleys, that would otherwise reveal surface texture and depth. A professional portrait photographer would never illuminate someone from directly in front; the person’s face would look flat, dull, and lifeless. Lights are typically placed at some oblique angle to provide shadows among the facial features. Although, if the person has a serious case of acne pimples, then detailed facial texture may not be what is sought.
It is not fully appreciated that the Apollo astronauts on the Moon’s surface could always communicate with mission control. As seen from the near side of the Moon, Earth is always in the sky, which can only be true if the Moon rotates on its axis in exactly the same amount of time that it takes for the Moon to orbit Earth. Indeed, the Moon is in a tidal lock with Earth such that it always shows the same face. Yes, there is a near side, and a far side of the Moon, but since all parts of the Moon receive sunlight at different times in its monthly orbit, there is no such concept as the dark side of the Moon. It may require a century of effort among astronomy educators to undo the influence of the popular rock group Pink Floyd, whose 1973 album title The Dark Side of the Moon misled an entire generation of Americans.
The Earth-Moon tidal lock is not a cosmic coincidence. It is the natural consequence of strong tidal forces on a nearby rotating object. A similar condition exists for the large planets (Jupiter, Saturn, Uranus, and Neptune) with their inner satellites and for the Sun with Mercury. The Moon’s tidal forces are at work on Earth which, among other things, act to slow Earth’s rotation rate. Eventually the rotation rate of Earth, itself, will equal the time it will take for the Moon to complete one orbit. The result: Earth will show only one face toward the Moon the way the Moon shows only one face toward Earth. This will take several hundred billion years, so you needn’t worry about it just yet. In the meantime you can “watch” it happen as the occasional leap seconds are introduced to the calendar year by the International Earth Rotation Service.
The Moon’s orbit around Earth is tipped about five degrees from the path of the Sun against the background stars. As a consequence, the Moon crosses the ecliptic twice for each complete orbit. If the Moon’s phase is new when it crosses the ecliptic, then Earth, Moon, and Sun are aligned in syzygy, and earthlings are treated to a total solar eclipse. No, not all earthlings. Just the ones who are lucky enough to have the narrow Moon shadow pass over their town, or the ones who are rich enough to travel to the shadow’s path. The dark cone of the Moon’s shadow, the umbra, just barely reaches Earth in a fast-moving dark circle that is typically 100 miles wide. The range among eclipses extends from zero to about 200 miles. In what would otherwise be broad daylight, the Sun disappears behind the Moon. Strictly speaking, any time one cosmic object passed in front of another, as in a total solar eclipse, the event is known as an occultation.
On Earth, the Moon and Sun appear roughly the same size in the sky. They are each about ½ degree in angle. An excellent protractor, for those emergencies when you must measure an angle in the sky, is your fist at arms length. It spans about 10 degrees for the average human. If you align the bottom of your fist with the horizon, then nine fists (your left and right fist alternatively stacked) should leave you straight overhead at a 90 degree angle from where you started. If you have big fists then you probably also have long arms, which insures that your fist still spans 10 degrees at arms length. (For this method to fail you would need the arm-to-fist proportions of an orangutan.) At ½ degree, the Sun and Moon each span less than one-fourth the width of your finger at arms length.
The near-match in angular size between the Sun and Moon allows the outer atmosphere of the Sun, known by the poetic term corona, to be revealed during the few minutes of totality. If you know which way the Moon’s umbra will approach, then a glance toward the horizon in that direction during the few seconds before totality will reveal a fast-moving column of darkness that looks as though the sky were being parted. In the precious few minutes of totality, the entire sky darkens, the stars become visible, the solar corona glows with gentle radiance, the air temperature drops, and animals behave strangely—especially humans. Humans temporarily leave their job to spend wads of money traveling to exotic spots on Earth’s surface via car, plane, and ocean liner. They spend millions of dollars on eclipse memorabilia. And they suffer great mental trauma if clouds appear on the day of the eclipse.
I was one of these strangely behaving humans when I saw the seven minute total solar eclipse of June 30, 1973—one of the longest on record, with a moon shadow on Earth that was 185 miles wide. I was on board a large ocean liner that sailed into the path of the Moon’s shadow in the Atlantic Ocean, off the coast of north west Africa. Ocean liners give you the option to sail to a spot with a good weather forecast so I did not risk mental trauma. There was one woman on the ship, however, who did not act strangely. What was shocking about her behavior was that she seemed to function in an alternative reality—only by not acting strangely did her behavior look strange. During totality, everybody else on the ship (myself included) rattled off dozens of photographs while grunting assorted primitive syllables such as “ooooh” and “aaahhhh.” Meanwhile, in a vision equally as surreal as the total eclipse, this woman was knitting a sweater while comfortably seated on a deck chair. This was my first lesson that perhaps the marvels of universe do not induce awe in everyone.
The eccentric orbit of the Moon around Earth brings it within 220,000 miles and as far as 255,000 miles. Similarly, the eccentric orbit of Earth around the Sun brings it as close as 91,500,000 miles and as far as 94,500,000 miles. The apparent size of the Sun and the Moon in the sky changes accordingly.
There are some solar eclipses where not only is the Earth-Moon distance is larger than average, but the Earth-Sun distance is smaller than average. Under these circumstances the dark cone of the Moon shadow does not reach Earth’s surface. From Earth’s point of view, the Moon’s size in the sky is not large enough to cover completely the size of the Sun in the sky—as the eclipse proceeds, a ring of sunlight encloses the Moon the way a hungry amoeba encloses its dinner. These eclipses have been dubbed annular eclipses for the annulus of sunlight that remains during mid eclipse.
During all solar eclipses, the Moon shadow blazes across Earth’s surface between two and three thousand miles per hour—it will most certainly out-run you. As lyrical as it may otherwise sound, you will never be casually followed by a moon shadow.
If the Moon’s phase is full when it crosses the ecliptic, then once again, Earth, Moon, and the Sun are in syzygy, but earthlings are now treated to a total lunar eclipse. The Moon, in its orbit, crosses the 850,000 mile-long shadow cone of Earth’s umbra. At the distance to the Moon, Earth’s umbra is over three times as wide as the full moon, so the entire eclipse takes many hours. An unsuspecting glance at the eclipse in progress looks as though the Moon spontaneously decided to cycle through phases, with Earth’s umbra taking bigger and bigger bites. During totality, when the Moon has completely entered Earth’s umbra, the Moon all but disappears without much spectacle or fanfare. Unlike the narrow path of a total solar eclipse, nearly everyone on the same side of Earth as the full moon will bear witness to a lunar eclipse. So while they are not more common than solar eclipses, far more people get to view lunar eclipses from their own backyard, or roof. Compared with total solar eclipses, total lunar eclipses are long and, quite frankly, boring.
Nights during or near the full moon, known as “bright time” by astronomers, are the least desirable nights to observe the universe because the sky is hopelessly contaminated with moonlight. To the unaided eye, the number of detectable stars drops from over 3,000 during new moon to about 300 during full moon. And nebulous extended objects such as galaxies are decidedly less impressive. Nearly all discoveries of dim galaxies at the edge of the universe have occurred during or near new moon, or “dark time,” at the world’s major observatories. On May 25, 1975, there was a total lunar eclipse for which a group of astronomers at the California Institute of Technology, in Pasadena, California deemed enough of an excuse to hold an evening party. When the eclipse began, it was noticed that a particular astronomer did not show up for the gathering. One of those in attendance recalled that the missing astronomer had suspiciously requested time on the 200-inch Palomar telescope during the full moon to observe a very dim object. By mid eclipse it simultaneously occurred to all assembled that the missing astronomer was clever enough to request observing time during the full moon—knowing that it was to be eclipsed—knowing that the observing conditions during a totally eclipsed full moon rival the darkest skies of a new moon.
If there exists a cosmic ballet, it is among the solar system’s planets, as they wander against the background stars with orbits and paths that are choreographed by the forces of gravity. With an occasional cameo appearance by the Moon, the planets, (especially the five visible to the unaided eye: Mercury, Venus, Mars, Saturn, and Jupiter) assemble in different combinations at different times of the year to create striking photo opportunities. The planets, in their orbits, have enchanted star gazers for centuries. In the days before computer simulations, people even built orreries, which are mechanical working models of the solar system. They served as a teaching tools and as toys to play with on a cloudy nights.
All planets in the solar system orbit the Sun in roughly the same plane. The observational consequence is that the ecliptic is shared by all other planets. It is a veritable planetary freeway of the sky. Perhaps it should, instead, be called a highway. One should expect many occasions each year where several of these objects are found in the same region of the sky. Indeed, when two or more objects can fit within the field of view of ordinary binoculars, then we say they are in conjunction. In an opinion I have, which is shared by many, the most photogenic conjunctions occur when one or more planets assemble with the crescent moon against the deeply colored curtain of the twilight sky. This can happen during dusk with the waxing crescent moon, or, as those who work the “graveyard shift” know, it can happen during the early dawn with the Moon as a waning crescent.
If Earth’s lower atmosphere is more turbulent than usual, then the path of starlight becomes severely disrupted as it refracts unpredictably across the different air densities. When this happens, stars begin to “twinkle.” When it gets bad, even planets will twinkle. All this may sound poetic, and look pretty during a conjunction, but it represents the worst possible seeing conditions that an astronomer can encounter. (Actually, total cloud-cover is slightly worse.) The well-publicised Hubble Space Telescope was lifted into orbit primarily to escape the degraded image quality and poor resolution that the lower atmosphere imposes on observations of all objects. Arguably, the world’s most famous painting that portrays stars is Starry Night by the 19th century Dutch impressionist Vincent van Gogh. These stars are drawn as large circular undulating yellow-white blobs in the sky. If this is what the Vincent actually saw, assuming his eyeballs did not suffer from a bad case of astigmatism, then it must go down in the annals of astronomy as the worst seeing conditions ever recorded for a clear night.
In my early years of high school I attended a summer camp for kids who knew they wanted to grow up to become astronomers. It was located in the cloudless skies of the Mojave Desert of southern California where we lived nocturnally for two months. The camp was equipped with a bank of over a dozen telescopes of various sizes, each equipped for a particular scientific purpose. A friend of mine at the camp received a letter from home that said all the usual tender things that letters from home say. Except that the letter ended with an unwittingly declared curse from hell:
…and we hope that all your stars are twinkling!
Sometimes a twinkling planet in the twilight sky can be quite striking, especially if it is Venus. Because of its proximity to Earth, and because of its high albedo from a thick white cloud-cover, Venus is often the brightest object in the sky. At its brightest, it is nearly 20 times brighter than Sirius, the brightest star in the nighttime sky. When it is low on the horizon, a turbulent atmosphere can sometimes behave like a prism and display quite a show of twinkling colors. For these reasons, Venus is occasionally mistaken for a UFO that hovers over the horizon. For some people, a UFO means a flying saucer that is commandeered by hostile aliens. To other people, a UFO is simply an object that they cannot identify. In general, it is safer to admit uncertainty and to inquire further than it is to invoke extraordinary imagination—particularly if you are otherwise unfamiliar with that evening’s schedule of cosmic conjunctions.
For example, in some urban settings the sky is unfamiliar to many people. I submitted the following recollection to the New York Times, which was printed in their “Metropolitan Diary” of Wednesday, July 12, 1991.
Dear Metropolitan Diary,
An elderly sounding woman with a strong Brooklyn accent recently called my office at Columbia University’s Department of Astronomy to ask about a bright glowing object she saw “hovering” outside her window the night before. I knew that the planet Venus happened to be bright and well-placed in the west for viewing in the early evening sky, but I asked more questions to verify my suspicions. After sifting through answers like,It’s a little bit higher than the roof of Marty’s Deli,I concluded that the brightness, compass direction, elevation above the horizon, and time of observation were indeed consistent with her having seen the planet Venus.
Realizing that she has probably lived in Brooklyn most of her life, I asked her why she called now and not at any of the hundreds of other times that Venus was bright over the western horizon. She replied,I’ve never noticed it before.You must understand that to an astronomer this is an astonishing statement. I was compelled to explore her response further. I asked how long she has lived in her apartment.Thirty years.I asked her whether she has ever looked out her window before.I used to always keep my curtains closed, but now I keep them open.Naturally, I then asked her why she now keeps her curtains open.There used to be a tall apartment building outside my window but they tore it down. Now I can see the sky and it is beautiful.
The path of the planets through the sky is not as simple as that of the Moon or the Sun. Yes, the planets orbit the Sun. And yes, if you looked from night to night you would see them move against the background stars.
But what complicates this simple picture is that we observe planets that orbit the Sun while riding on a planet that orbits the Sun. The resulting planetary paths confounded centuries of the worlds greatest thinkers before there was agreement that the Sun was the center of planetary motion.
All planets orbit counter-clockwise4 when viewed from “above” the Sun. When viewed from Earth, a general trend emerges for planets to move from west to east against the background stars. The inner two planets, (Mercury and Venus), complete their orbits around the Sun faster than Earth. The outer planets, however, (Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) take longer than Earth to complete their orbits around the Sun. A simple and direct observational consequence is that there will always arrive a time interval when the relative motion between Earth and each of the other planets makes them appear to move in “reverse”, from east to west, against the background stars. If you do not put the Sun at the center of planetary motion, you will have an extraordinarily difficult time explaining what you see. In spite of this, the historical bias towards an earth-centric view of the universe was strong. When the 16th century Polish astronomer Nicolaus Copernicus wrote De Revolutionibus, (a treatise that placed the Sun, rather than Earth, at the center of planetary motion), an anonymous foreword was inserted at the time of publication without Copernicus’ knowledge or permission. It was later revealed to be written by the Lutheran theologist Andreas Osiander, who had helped to supervise the printing. The foreword included the following disclaimer:
To the reader Concerning the Hypothesis of this Work
There have already been widespread reports about the novel hypothesis of this work, which declares that earth moves whereas the sun is at rest in the center of the universe… For these hypothesis need not be true or even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough…
The concept of backward apparent motion should be easy for modern humans. The next time you visit an amusement park, give close attention to the dizzy people on the rides that go in circles. (Ignore the people doing energy experiments on the roller coaster.) In an analogous scenario to orbiting planets, you will notice that when the riders are near you on these nausea-inducing machines they might cross your field of view from left to right, yet when they are on the other side of the machine the reverse is true—you will see them pass from right to left. Similarly, these people see you, as you wait patiently in line for the next ride, shift across their field of view alternatively from left to right and then from right to left.
Planets that appear to move backwards are commonly said to be in retrograde, which has even found its way into Shakespearean literature. In the first scene of the first act of the comedy All’s Well that Ends Well, Helena displays a sharpness of wit as she comments on the valor of Parolles.
HELENA: Monsieur Parolles, you were born under a charitable star.
PAROLLES: Under Mars, I.
HELENA: I especially think, under Mars.
PAROLLES: Why under Mars?
HELENA: The wars hath so kept you under that you must needs be born under Mars.
PAROLLES: When he was predominant.
HELENA: When he was retrograde, I think rather.
PAROLLES: Why think you so?
HELENA: You go so much backward when you fight.
Unlike amusement park rides and Shakespeare’s Parolles, planets require months of careful tracking to watch them enter and emerge from retrograde motion against the background stars. The observation is a task best accomplished by astronomers and insomniacs.
Of all the cosmic objects that one might observe with a backyard telescope, the planet Saturn, with its banded surface, its orbiting moons, and its awesome ring—parted in its middle by Cassini’s division, would fall high on the list for its ability to excite passers-by. In my youth, I did not have a backyard, only the roof of my urban apartment building. And there were no passers-by, except for the occasional grumpy police officer who would mistake my telescope for an M-79 grenade launcher. My telescope’s motor, which allows the telescope to track stars across the sky as Earth rotates, requires electricity. I would often lower a 100-foot extension cord from the roof through my bedroom window, which police would reliably mistake for a rappelling rope. I had a total of five such encounters. In three of the five cases, I was promptly saved by the planet Saturn, with a dialogue such as:
OFFICER (shooting-hand poised near gun, other hand holding flash light): What the hell is that thing, and what are you doing on the roof?
ME (maneuvering Saturn quickly into field of view): Good evening officer. Ever see the planet Saturn through a telescope before?
OFFICER (shooting-hand now scratching head): No, just in pictures.
ME: Turn off your flashlight and have a look.
OFFICER (looking through telescope): Wow! Saturn really does have rings! Maybe I’ll buy one of these for my kids!
The police officers may have learned that in life and in the universe, it is always best to keep looking up. But if somebody really does set up a roof-top grenade launcher, I hope it will still attract their attention.
- 1 Or, at least that is how astronomers look at it. To most other people, it is the stars that migrate systematically in the opposite direction behind the Sun.
- 2 Note that you cannot freeze your standing shadow in its place while you mark the ground. If your shadow behaves as it ought to then it will follow you as you bend, so you may wish to solicit help from a friend. This shadow problem is a variant on the mirror problem, where your reflection does exactly what you do. The consequence: you can only kiss your reflection on the lips.
- 3 The Jewish Sabbath lasts from sunset Friday to sunset Saturday.
- 4 During your life, if all the clocks you have seen had digital faces, then
counter-clockwiseis the direction that baseball players, track runners, horses, and race cars move around their respective tracks.
From the Publisher
This witty, often amusing exploration of the physical universe explains fundamental concepts in a language that is clear even to those with little or no science background. Tyson transforms everyday experiences into venues of cosmic enlightenment as he probes the philosophy, methods, and discoveries of science, including stellar evolution, the conservation of energy, the electromagnetic spectrum, gravity, and thermodynamics.
Beginning with the history of counting, Tyson takes us up and down the number line from picometers to light years as he demonstrates the universality of mathematics. We then learn about the scientific method and its importance not only to cutting-edge researchers but also to laypeople like television advertisers, who use it in commercials to prove the worth of products that lift stains, eradicate “ring-around-the-collar,” and absorb “excess stomach acid.”
Tyson deftly demystifies astronomical terms and concepts such as the Big Bang, black holes, redshifts, syzygy, and Kirkwood Gaps; traces the life of the stars from birth to death; presents the Periodic Table of Elements, highlighting noteworthy elements such as titanium, iron, and hydrogen; gives an unorthodox yet entertaining tour of famous constellations; and tackles modern-day astrology.
Universe Down to Earth makes vivid analogies between scientific laws and household items such as oven-baked pies, tossed tomatoes, and lightbulbs, as well as amusement park rides, Hollywood films, and junk food. Consequently, each idea presented etches delightful impressions on the reader’s mind. Bringing demonstrations of the principles of nature into the living room, Tyson writes in a lucid, easygoing style that finally makes scientific literacy possible for enthusiasts and those with math and science phobias alike.
Tyson wrote Universe Down to Earth out of his experience in teaching astronomy to real people who have little scientific background. This makes it different from the many books written without such experience. Tyson writes in a simple style with a lightness of touch, which can come only to one who is absolute master of his subject.
Universe Down to Earth is a most original book, designed to explain modern astronomy to the uninitiated. Its very clear descriptions are supplemented by many analogies with everyday experience, which are unusually informative as well as highly entertaining. The book stands out as a remarkable example of effective and enjoyable communication in a fascinating field of science.
A sprightly, easy-to-read introduction to some key ideas of physics and astronomy, marked by well-chosen anecdotes and lucid explanations. An ideal present for anyone interested in science.