Celestial Windings

Chapter 13 from Universe Down To Earth, © 1994 Neil deGrasse Tyson. Columbia University Press

I know that I am mortal by nature, and ephemeral; but when I trace, at my pleasure, the windings to and fro of the heavenly bodies I no longer touch earth with my feet: I stand in the presence of Zeus, himself, and take my fill of ambrosia.

Claudius Ptolemy

Universe Down to Earth by Neil deGrasse Tyson

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.

Earth

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 1/2 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 1/2 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 1/2 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 1/2 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 1/2 degrees south and 23 1/2 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 1/2 degrees latitude, (which, by the way, is the 90 degree latitude of the pole minus the 23 1/2 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 1/2 degree north latitude is unimaginatively called the Arctic Circle while the 66 1/2 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 A.D. 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.

Moon

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 mis-conception 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 1/2 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 1/2 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.

Eclipses

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 1/2 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 1/2 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.

Planets

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!

Love,
Mom & Dad

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 chord 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-clockwise is the direction that baseball players, track runners, horses, and race cars move around their respective tracks.