force

I am often asked by students whether their toilet bowl will flush clockwise or counterclockwise in the southern hemisphere, or whether it will flush straight down in Ecuador. This would, of course, be important information if you were ever kidnapped and blindfolded and dropped off in a strange land. If we assume a commode of conventional size, then this toilet bowl test will fail because the answer lies in the manufacturer's design. But if your northern hemisphere toilet bowl were a few hundred miles in diameter then the Coriolis force of the rotating Earth would easily overcome the random water currents, and force the bowl to empty its contents in a counter clockwise swirl. If you have southern hemisphere friends with an equally large toilet, then theirs would indeed empty in the opposite (clockwise) direction.

The circulation within oversized flush toilets is a natural consequence of motion on the surface of an object that rotates. We owe our detailed understanding of the effect to the work of Gaspard Gustave de Coriolis who, in 1831, presented details of the laws of mechanics in a rotating reference frame to the Academie des Sciences in Paris. Earth's surface provides an excellent place to demonstrate why the origin of the Coriolis force is relatively simple. Our planet rotates on its axis approximately once every 24 hours. In that 24 hour period, objects on Earth's equator travel a circle with a circumference of nearly 25,000 miles, which corresponds to a speed of a more than 1,000 miles per hour. By 41 degrees north, the latitude of New York City and the American Museum of Natural History, the circumference traveled is only about 19,000 miles. The west-to-east speed is now approximately 800 miles per hour. As you continue to increase in Earth latitude (north or south of the equator) your west-to-east speed decreases until it hits exactly zero miles per hour at the poles. (For this reason, most satellites are launched as close to the equator as possible, which enables them to get a good running start in their eastward orbits.

Imagine a puffy cloud in the northern hemisphere and a meteorological low pressure system directly to its north. The cloud will tend to move toward the low. But during the journey its greater eastward speed will enable the cloud to overtake the low, which is itself in motion, and end up east of its destination. Another puffy cloud that is north of the low will also tend to move toward the low, but will naturally lag behind and end up west of its destination. To an unsuspecting person on Earth's surface, these curved north-south paths would appear to be the effects of a mysterious force (the Coriolis force) yet no true force was ever at work.

When many puffy clouds approach a low pressure system from all directions you get a merry-go-round of counter-clockwise motion, which is better known as a cyclone. In extreme cases you get a monstrous hurricane with wind speeds upwards of a hundred miles per hour. For the southern hemisphere the same arguments will create a cyclone that spirals clockwise. The military normally knows all about the Coriolis force and thus introduces the appropriate correction to all missile trajectories. But in 1914, from the annals of embarrassing military moments, there was a World War I naval battle between the English and the Germans near the Falklands Islands off Argentina (52 degrees south latitude). The English battle cruisers Invincible and Inflexible engaged the German war ships Gneisenau and Scharnhorst at a range of nearly ten miles. Among other gunnery problems encountered, the English forgot to reverse the direction of their Coriolis correction. Their tables had been calculated for northern hemisphere projectiles, so they missed their targets by even more than if no correction had been applied. They ultimately won the battle against the Germans with about sixty direct hits, but it was not before over a thousand missile shells had fallen in the ocean.

In high school I knew all about the Coriolis force, but I never had the opportunity to test it on something as large as a swimming pool until the summer after my junior year when I worked as a lifeguard. At the mid-summer cleaning, I opened the drain valve to the pool and carefully observed the circulation. The water funneled in the wrong direction—clockwise. The last I had checked, I was life-guarding in Earth's northern hemisphere so I was tempted to declare Coriolis forces to be a hoax. But a fast back of the envelope calculation verified that the difference in Coriolis velocity across the pool was a mere 1/2 inch per minute. This is slow. The water currents from somebody just climbing out of the pool, or even a gentle breeze across the water's surface would easily swamp the effect and I would end up with clockwise one half the time and counterclockwise the other half of the time. A proper experiment to demonstrate the insignificance of the Coriolis forces would require that I empty and refill the pool dozens of times. But each try would dump 15,000 cubic feet of water and diminish my job security. So I didn't.

The air circulation near a high pressure systems, which are inelegantly known as anticyclones, is a reverse picture of our cyclone. On Earth, these high pressure systems are the astronomer's best friend because they are typically devoid of clouds. The surrounding air still circulates, but it does so without the benefit of clouds as tracers of the air flow. The circulation around low and high pressure systems, known as geostrophic winds presents us with the paradox that Coriolis forces tend to move air along lines of constant pressure (isobars) rather than across them.

Now imagine, if you will, a place that is not only fourteen hundred times larger than Earth, but has an equatorial speed that is about twenty-five times as fast, and has a deep, thick, colorful atmosphere. That place is the planet Jupiter, where a day lasts just 9 hours and 56 minutes. It is a cosmic garden of atmospheric dynamics where all rotationally induced cloud and weather patterns are correspondingly enhanced. In the most striking display of the Coriolis force in the entire solar system, Jupiter lays claim to the largest, most energetic, and longest-lived storm ever observed. It is an anticyclone that looks like a great red spot in Jupiter's upper atmosphere. We call it Jupiter's Great Red Spot. Discovered in the mid 1660s by the English physicist Robert Hooke and separately by the Italian astronomer Giovanni Cassini, the feature has persisted for over 300 years. It was not until the twentieth century when the Dutch-born, American astronomer Gerard Kuiper was the first to supply the modern interpretation of the Spot as a raging storm.

The Great Red Spot, by the way, is bigger than Earth, although its size and shape has varied over the years. It lives in Jupiter's southern hemisphere and rotates counterclockwise, which immediately tells us we have a high pressure system. The coloration, from orange-red to a barely visible pale cream, is generally attributed to various concentrations of phosphorus and sulfur compounds. Close-up images from the Voyager flyby missions of the late 1970s revealed a maelstrom of colorful curlicues at the interface of the Great Red Spot and the surrounding atmosphere. There were also strikingly resolved horizontal belts and zones interlaced with countless smaller cyclones and anticyclones that give Jupiter the appearance of an archaeological cross section of a Big Mac hamburger from McDonald's, bun included. Above all else, however, the Voyager data posed renewed theoretical challenges. It resolved Jovian features down to twenty miles in diameter—astonishingly small when one remembers Jupiter's size relative to Earth. Models of cosmic phenomena are often clean and tidy until they are tested outside of the limits in which they were formulated. Higher image resolution is one such example. When this happens, many models are discarded, others are modified, while some are freshly invented, but jumps in resolution have always been followed by a deeper understanding of the universe.

Whatever else a model of Jupiter's atmosphere is designed to explain, it should as a minimum, account for basic properties of the Great Red Spot such as its longevity, and perhaps its distinguished size, and that it is an anticyclone. An ideal model would be able to account for all atmospheric motion on Jupiter. The tools available to the theorist are Newton's laws of motion as adapted to the properties of gases and liquids—otherwise known as fluid mechanics.

Contemporary models do capture the basic features of the Great Red Spot, but very little is known about the structure of Jupiter's under-layers. Jupiter radiates more heat than it receives from the Sun, and there are enormous thermal reservoirs in Jupiter's interior that can drive atmospheric flow patterns. One source is the radioactive decay of trace elements while another is the left-over heat form Jupiter's initial contraction from a proto-planetary cloud to a planet in the early solar system. The sustaining source of energy for the Spot could also (or instead) be tapped from other sources. On Earth, hurricanes are partially driven by the latent heat released to the atmosphere when rain drops condenses out of the air. A similar mechanism may dominate in Jupiter's atmosphere as its gases condense toward its liquid interior. The Spot has also been observed (and successfully modeled) to dine upon smaller turbulent eddies in its vicinity. This cannibalistic behavior is yet another source of energy. Clues to the deeper cloud layers will almost certainly be gained when the spacecraft Galileo passes Jupiter (in December 1995) and parachutes a mini-probe that will measure temperature, density, composition, wind speeds, and lightning events as it descends through the outer atmosphere.

For now, there is no reasonable hope of describing every one of Jupiter's surface features in detail. A more realistic approach is to construct an atmospheric model that provides a statistically equivalent picture of Jupiter's surface features. In other words, a model of a Big Mac can approximate all Big Macs even though it may not look like any one in particular.

One nagging problem with models that always produce a single, sustained anticyclone is the blunt reality that Jupiter's northern hemisphere is devoid of a twin Great Red Spot. Clearly, if models show that big spots are inevitable, then the north ought to have one too. Elsewhere in the solar system, the Coriolis force has given rise to a great dark spot on Neptune. We call it Neptune's Great Dark Spot. Like Jupiter's Great Red Spot, it is an anticyclone of epic proportions in Neptune's southern hemisphere that appears without a twin in the north. This is a problem that may require an as yet unexplored north-south asymmetry in both Jupiter's and Neptune's internal structure. One way to induce such an asymmetry would be to survive a cosmic collision in one of your two hemispheres. The July 1994 encounter between Jupiter and the dozens of crumbled comet parts from Shoemaker-Levy 9 left visible and sustained scars on Jupiter's outer gaseous surface. The long-term effects of this impulse of deposited energy remains to be seen. Will the scars form stable new structures among the cloud-tops? Or will the scars dissipate completely into the atmosphere? For the moment, feel free to consider the new blemishes to be extra ingredients in your hamburger.

Science consists in discovering the frame and operations of Nature, and reducing them, as far as may be, to general rules or laws—establishing these rules by observations and experiments, and thence deducing the causes and effects of things.

Sir Isaac Newton, The Principia 1687

In scientific inquiry, often the answer to one simple question fortuitously explains the answers to many others; they may even answer questions that have yet to be conceived. Powerful ideas unify concepts or phenomena that were previously thought to be unrelated. For example, Sir Isaac Newton identified a falling apple and Earth's orbiting moon as different effects of a single law of universal gravitation represented by a simple equation. (The falling apple did not actually hit Sir Isaac on the head. He saw it fall from afar.)

Newton's famous equation is a recipe to compute the force of gravity between any two objects in the universe. With a basic application of Newton's equation you can show that the force of gravity is greatest where an object is nearest another object and least at the point where it is farthest. As you stand on Earth, for example, Earth's gravity is slightly stronger at your feet than at your head. The differential is small, so don't blame your light-headedness on this phenomenon. Earth pulls on your feet with a force that is only one ten thousandths of one percent stronger than that at your head.

This simple difference in gravity, officially known as the tidal force, is felt by all objects as they are pulled by the gravity of all other objects in the universe. Tidal forces are the direct cause of a diverse array of cosmic phenomena that otherwise seem to have nothing to do with one another. Some of my favorites: the daily rise and fall of Earth's oceanic tides; Earth's gradually slowing rotation rate, which is making the days longer and longer; the Moon's slow spiral away from Earth; the Moon showing only one face toward Earth at all times; Pluto, and its lone moon Charon, showing each other only one face during their mutual orbit; the geological (or is it iological?) activity of Io, one of Jupiter's moons; the breaking apart of comet Shoemaker Levy-9 in its close encounter with Jupiter; the long tails of colliding galaxies in collision; and the spectacularly gory death to which you would succumb if you approached the center of a black hole (as detailed in last month's Universe essay Death by Black Hole).

Tidal forces are strongly dependent on distance. A mild increase in distance between two objects can make a large difference in the strength of the tidal force. For example, if the Moon were just twice its current distance from us, then its tidal force on Earth would decrease by a factor of eight. At its current average distance of 240,000 miles from Earth, the Moon manages to create sizable atmospheric, oceanic, and crustal tides by attracting the part of Earth nearest the Moon more strongly than the part of Earth that is farthest. (The Sun is so far away that in spite of its generally strong gravity, its tidal force on Earth amounts to less than half that of the Moon.) The oceans respond most visibly in being stretched toward the direction of the Moon. Meanwhile, as the solid Earth continues to rotate, the continental shelves are constantly trying to push forward the1.5 quintillion tons of bulging ocean water.

In this force-war, the oceanic bulge is always found slightly ahead of the Moon's location in its monthly orbit. Rotating within the bulge, Earth suffers an enormous source of friction between the sloshing oceanic water and the continental shelves and shores. (Tidal energy is lost to friction at a slightly higher rate than the rate of consumption of electrical energy by all quarter billion residents of the United States.) The consequence? Earth rotates more and more slowly—the days are getting longer at a rate of about 1/500 of a second per day per century. It doesn't sound like much, until you stop and think about it: every century, the duration of every day increases by 1/500 of a second. While not reported in the newspapers next to the table of coastal tides, it ought to be, because at this rate, full seconds add up fast. Since the 1970s, we have been officially adjusting our daily time-reckoning with leap seconds that are added every few years at the end of June or December. Don't tell anybody, but I have actually attended one or two leap second parties, where everybody counts down from 61 beginning at 11:59 p.m.

The best evidence for the slowing down of Earth's rotation comes from detailed records of total solar eclipses that date back many centuries. If Earth's rotation rate were faster in the past, then a total solar eclipse as seen on Earth's surface would miss the expected spot and occur west of where we thought it would, which is precisely what the records show — the earliest recorded eclipses were offset along Earth's surface by nearly a thousand miles.

Meanwhile, Earth's bulged gravity field, positioned slightly ahead of the Moon in its orbit, acts in return as an energy pump. Like the effect of rocking your legs in rhythm with a playground swing, the Moon slowly ascends into larger and larger orbits. You want proof? In 1969, when the Apollo 11 astronauts Neil Armstrong and Buzz Aldrin visited the Moon's Sea of Tranquillity, they left behind (among other things) a series of corner reflectors that are designed to reflect light in exactly the same direction that it arrives. Starting shortly after the Moon landing, and continuing today in places such as the McDonald Observatory Laser Ranging Station in west Texas, high-powered lasers on Earth are beamed to the Moon, and the return signal is carefully timed.

Knowing the speed of light, one can compute the Moon's distance with unprecedented accuracy: with a twenty-five year baseline of measurements we know that the Moon is spiraling away from us at a rate of about two inches per year, just as predicted by tidal theory. Earth's rotation will continue to slow down, and the Moon will continue to spiral away until the Earth day exactly equals the lunar month. At that time, one Earth rotation will last over 1000 hours, which would require 4 million leap seconds per day. No need to panic just yet. You have over a trillion years to think about it.

Earth's tidal force upon the Moon has completed its job long ago: the Moon's rotation has slowed so that its period of rotation exactly equals its period of revolution around Earth. Whenever this happens, an orbiting object will always show the same face to the body it orbits—it becomes tidally locked. In other words, as seen from Earth, the Moon has a permanent near side and far side, and when viewed from the near side of the Moon, Earth never sets. At one time or another during a lunar month, however, all sides of the Moon receive sunlight. So contrary to common parlance, folklore, and the title of Pink Floyd's best-selling 1973 rock album, there is not now, nor was there ever, a dark side of the moon.

When Earth's rotation slows down until it exactly matches the orbital period of the Moon, then Earth will no longer be rotating within its oceanic tidal bulge and the Earth-Moon system will have achieved a double tidal lock. In what sounds like an undiscovered wrestling hold, double tidal locks are energetically favorable (like a ball coming to rest at the bottom of a hill), and are thus common in the universe. The planet Pluto and its lone moon Charon, have achieved it in a 6.4 day cosmic waltz. A related phenomenon will unfold before your eyes when you spin one of the mobiles of the American sculptor Alexander Calder. If any pair of the dangling parts are elongated, then they will eventually align with each other and, in effect, become tidally locked, although energy, not gravity is the active ingredient here.

The Earth-Moon, and Pluto-Charon systems are orbiting pairs in which the satellite is nearby and relatively large when compared with the host. One could accurately describe them as double planets. Such configurations lead to strong tidal forces and are also found among all closely orbiting double star systems, which themselves become doubly tidally locked. After learning about the general strength and prevalence of lunar tides, students often asked me whether the Moon's tidal forces can affect human behavior. Yes, provided you had a very, very big head. For example, if your brain were, say, 7,000 miles in diameter (the size of Earth), then the Moon's tidal forces would indeed give you an oblong-shaped cranium and impart untold consequences on your mental faculties. For normal Homo sapiens, however, the Moon's difference in gravity from one side of the head to the other is immeasurably small. The weight of an understuffed down pillow imparts a squeezing force that is over seven trillion times larger than the Moon's tidal force on your head—a fact not shared with you by those who write about werewolves and other moon-based dysfunctional behavior.

No discussion about tidal forces would be complete without due respect to the planet Jupiter. Packing more mass than all other planets combined, Jupiter has tidally locked all of its inner satellites, including Galileo's famous four: Io, Europa, Ganymede, and Callisto. To be tidally locked should mean that there is no energy being lost to friction, but a careful study of Io shows that the exact shape of its orbit is noticeably affected by the combined gravity of other nearby satellites. In other words, Io's distance from Jupiter varies, which also means it predictably speeds up as it orbits closer to Jupiter and slows down as it orbits farther. Now consider that Io's rotation rate exactly equals the time it takes for one complete trip around Jupiter and you have a satellite that shows only one face to Jupiter—but its face appears to jiggle to and fro as Io's Jupiter-facing tidal bulge continually flexes the satellite.

When the Moon flexes Earth's oceans, they simply slosh back and forth. But when a Jupiter-sized tidal force acts upon a nearby solid body, then the internal stress can become a prodigious source of heat. In one of the more timely and impressive predictions in the history of space probes, Stanton Peale of the University of California and collaborators published a paper in 1979 titled, Melting of Io by Tidal Dissipation. Later that year, images sent by the Voyager 1 space craft revealed extraordinary volcanic activity, complete with mountain calderas and plumes.

Jupiter's tidal forces also wreak havoc on comets that wander too close. The late comet Shoemaker-Levy 9 was minding its own business in orbit around the Sun when during one of its trips it came too close to Jupiter and was captured into a greatly elongated orbit. In 1992 it came so close to the giant planet that tidal forces ripped apart the comet into dozens of pieces. On the next pass, in July 1994, none of the two dozen comet parts cleared the cloud-tops. As if to exact a kamikaze-style revenge, they all blazed into Jupiter's thick and colorful atmosphere at a speed of nearly 40 miles per second, and exploded with the equivalent energy of hundreds of billions of tons of TNT.

On a cosmic scale, the tidal forces between two colliding galaxies can create spectacular photo-opportunities. Whole galaxies are often re-shaped and ripped apart in such an encounter. As confirmed by computer simulations, tell-tale evidence includes long, often distorted tidal tails of stars that are created during the encounter. One such system is a pair of colliding galaxies 50 million light years away, NGC4038 and NGC4039. They are nick-named Antennae but they really look like two procreating mice. Another galactic wreckage looks like the old-fashioned model of the atom (complete with orbiting electrons), superimposed upon a peace symbol. Astronomers affectionately refer to this one as Atoms for Peace.

The next time you find yourself on a shoreline watching the tide come in, remember that the frame and operations of Nature extend to the farthest galaxies, and causes and effects of things are, fortunately, remarkably few in number.