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The Tidal Force

By Neil deGrasse Tyson

Natural History Magazine

Published under the title “Tides and Time.”

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 the 1.5 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 1500 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 1500of 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 1,000 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 reshaped and ripped apart in such an encounter. As confirmed by computer simulations, telltale 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 nicknamed 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.