The question is a simple one. The answer is not as simple as the question, and the search for it led to the defining moment of science: the moment that precipitated the scientific revolution and the Age of Enlightenment; the moment when natural philosophy was placed on its course to become modern science, with mathematics as its language.
The reason why the planets stay in orbit is contained within Isaac Newton’s theory of gravity, as detailed in his groundbreaking book Philosophiae Naturalis Principia Mathematica, usually referred to as the Principia. In Newton’s time, the late 17th century, the question was posed as “Why does the Moon stay in orbit and not come crashing down on us?” but the solution is exactly the same; it is just a question of scale. The Moon orbits the Earth while the planets, including the Earth, orbit the Sun. The answer rests on a mathematical understanding of gravity.
The central concept of the Principia is “universal gravitation.” This states that everything with mass generates gravity: the Earth, the Moon, the Sun, all the planets and the moons, all the stars—everything. The amount of gravity generated by a celestial object is proportional to the mass it contains and the resulting gravity affects anything else with mass that is nearby; in other words, everything pulls everything else. Newton’s Theory of Universal Gravitation broke the mold of human thinking. It was partly based upon the pioneering work of Johannes Kepler, who had mathematically described planetary motion several decades earlier.
The first of Kepler’s three laws of planetary motion states that each planet moves in an elliptical orbit, with the Sun at one focus. (An ellipse has two focal points and the further apart these foci are, the more elongated the ellipse.) Previously, planets had been assumed to move in circles, but Kepler deduced from analyzing the detailed observation data of the Danish astronomer Tycho Brahe that all the planets follow their individual elliptical orbits.
The second law he deduced is that, as a celestial object follows its orbit, it sweeps out equal areas of the ellipse in equal times. To visualize this, imagine a long extensible tether between a planet and the Sun. As the planet moves a small distance through its orbit, so the tether pivots at the Sun, sweeping out a triangular area. When the planet is far away from the Sun, the tether is longer and the planet does not have to move far to sweep out a large area. Conversely, when the planet is close to the Sun, the tether is much shorter and the planet has to move much faster to sweep out the equivalent area in the same time. Hence, what the law is saying is that when a planet is far from the Sun it travels slowly and when it is closer to the Sun it travels faster. This was an important clue because it implied that whatever force was moving the planet weakened with distance.
“If there is anything that can bind the heavenly mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living, then it is verily the enjoyment of the mathematical sciences and astronomy.”
JOHANNES KEPLER 17TH CENTURY ASTRONOMER
KEPLER’S SECOND LAW: THIS LAW OF PLANETARY MOTION STATES THAT EQUAL AREAS ARE SWEPT OUT IN EQUAL TIMES DURING THE COURSE OF AN ELLIPTICAL ORBIT
The third law follows on from the second, expressing as an equation the link between the size of the planet’s orbit and the time it takes to complete that orbit. In essence, it quantifies a planet’s average speed dependent on its distance from the Sun.
What Kepler could not explain was why the planets moved in this way. The Greek philosopher Aristotle had stated that everything finds its place in the Universe because of a balance of two forces: “gravity” and “levity.” Thus the Moon was balanced in the sky because not only was gravity pulling it down but levity was also pushing it up. The problem with this interpretation was that the Moon is not balanced in the sky, it is moving in orbit around the Earth.
Newton showed that the Moon does indeed stay in orbit because of the interplay of two forces, but not ones that are in opposition to one another; instead, they must act at right angles. In fact English experimenter Robert Hooke was probably the first person to realize this, but he could not draw together the mathematics to prove it. This took the mathematical ingenuity of Newton. It is popularly thought that Newton took his inspiration from watching an apple fall but this story is apocryphal, or certainly not verifiable, as Newton never wrote about such an incident himself—but what he did write about were cannon balls.
Newton asked his readers to visualize a cannon atop an incredibly tall tower, pointing horizontally and firing its projectile. If we ignore the effects of air resistance, the cannon ball will zoom off parallel to the ground. However, the gravity of the Earth will immediately begin to pull it downward, eventually dragging it all the way to the ground. The greater the explosive charge, the faster the projectile will be ejected and the further it will travel before gravity pulls it down. Now imagine the cannon loaded with sufficient explosive to eject the cannon ball so fast that, by the time it has started to fall, the curvature of the Earth has resulted in the ground beneath dropping away and so the cannon ball finds itself still at the same altitude above the Earth. Remember that we are neglecting air resistance, so the projectile is still traveling at the same speed as when it left the cannon, and the whole situation starts again. Every time the cannonball drops a little, so the curvature of the Earth compensates, allowing the projectile to continue around the Earth—forever. In effect, it has been placed into orbit.
CANNONBALLS AND ORBITS: THE DIFFERENT AMOUNT OF EXPLOSIVE CHARGE DETERMINES WHICH PATH THE CANNON BALL TAKES
This theoretical analogy gives us the solution to the question of what stops the Moon crashing into the Earth. The Moon is falling toward us, but also traveling along so fast that it “overshoots” the Earth and continues in a circular path. Newton formulated the mathematics to show that orbital motion is produced when gravity works in conjunction with the tangential movement of a celestial object. In the case of the planets, they were naturally born with this tangential motion because they condensed out of a spinning cloud of dust and gas (see How Did the Earth Form?).
Newtonian gravity changed the way astronomers thought about the night sky. Most had been content to chart the positions of the stars as an aid to navigation; indeed, this was considered the principal use of astronomy. After Newton’s work however, they could understand the motion of the celestial objects and, more importantly, predict their future movements. The dates of future eclipses, the return of comets, the conjunctions of the planets—all were prescribed by Newton’s theory. It also showed that there are four possible orbital shapes: circles, ellipses, parabolas and hyperbolas. These can be understood in terms of the cannon on the tower. First is the circular orbit, produced when just enough explosive is used to stop the cannon ball falling to Earth. Next is the elliptical orbit, produced by increasing the amount of explosives so that the cannon ball increases its altitude above the Earth before falling back and starting the circuit again. The more explosive used, the more elongated the orbit becomes until, eventually, it opens up and the projectile escapes altogether from the Earth’s gravitational attraction. When just enough explosive is used to break the cannon ball free, it follows a curve called a parabola; as even more explosive is used, the curve opens up wider, becoming a hyperbolic shape. In both cases, the projectile never returns to Earth. The velocity at which a projectile must be fired to place it on a parabolic orbit is known as the “escape velocity.” For Earth, this is 11 kilometers per second (7 miles per second). It varies from celestial object to object, depending upon how much mass the object contains. For Mars it is 5 kilometers per second (3 miles per second), for Jupiter it is 60 kilometers per second (37 miles per second). The value for the Moon is just 2.4 kilometers per second (1.5 miles per second), which explains why the Apollo astronauts did not need another giant rocket to come home.
ORBITAL SHAPES: ORBITS COME IN FOUR BASIC TYPES
When a celestial object follows a closed orbit in space, where there is no air resistance, it circulates time and time again, and ellipses and circles are the observed orbital shapes for the planets, moons and asteroids in the Solar System. Some comets, such as Halley’s famous one that we see every 76 years, also follow closed orbits. Stars follow closed orbits around the center of their galaxy and even the mighty galaxies follow closed orbits around the centers of galaxy clusters.
By contrast, an open orbit is a one-time deal. A celestial object on an open orbit makes a fleeting visit and then disappears off into deep space never to be seen again. Many comets follow open orbits, and unmanned space probes have been directed into open orbits to view the surface of one planet before coasting onwards to the next.
As important as the understanding of orbits proved to be, Newton’s theory applied to a breathtaking range of other phenomena, not all of them celestial. His work gave the natural philosophers of the day a way of estimating the mass of the planets and the Sun, and a means of explaining why the Earth and other planets bulged at the equator. It gave those more minded of engineering problems a method of calculating the movement of falling objects on Earth, and, not least in the 17th century, of predicting the trajectory of projectiles fired from cannons. All motion, it seemed, could be understood in Newtonian terms. The Universe behaved as a clockwork mechanism, unremittingly following the laws that he had deduced.
“If I have seen further than others, it is by standing upon the shoulders of giants.”
ISAAC NEWTON 17TH CENTURY MATHEMATICIAN
Unsurprisingly, Newton’s work was heralded as “the system of the world”; a phrase for what we would now refer to as “the theory of everything.” Over the course of the next few centuries, scientists came to realize how much else there was still to understand in the physical world: electricity and magnetism, nuclear forces, and relativity and quantum effects. But at the time, Newton’s work was a triumph, and one of its victories was providing the explanation of the tides. The tidal changes were an all-important phenomenon for a sea-faring nation at that time, but their cause was a mystery until Newton proved in the Principia that they were due to the gravitational attraction of the Moon and the Sun on the oceans.
TIDES: THE SIZE OF THE TIDE DEPENDS ON THE POSITION OF THE MOON AND THE SUN; THE HIGHEST TIDES, KNOWN AS “SPRING TIDES” ARE WHEN THE SUN AND MOON ARE IN ALIGNMENT
Consider the Moon’s gravity pulling on the Earth: the Moon’s tug is stronger on the side of our planet facing the Moon than on the opposite side, because gravity weakens with distance. This pulls the Earth into an elongated shape, which we experience as tides because the water is much freer to move than the rocks. The rocks beneath our feet do move too, albeit by less than a meter per day. The Sun’s gravity also has a tidal effect and it is the interplay between the solar and lunar gravitational forces that gives the different height of the tides at different times of year. When the Sun, Earth and Moon all fall into approximately a straight line, we get a large tide, called a spring tide; when the configuration is perpendicular, we get the low, neap tides.
In the same way, the Earth’s gravity simultaneously deforms the Moon and, because Earth is larger and more massive, the lunar tide is correspondingly larger, amounting to an elongation of the Moon by many meters. These changes to the spherical shape of the Earth and the Moon have an inertial effect, making it harder for each to spin. This constantly saps their rotational energy, and in the case of the Earth it causes the length of the day to slowly but perceptibly increase. This is one of the reasons why an extra second must be occasionally added to the midnight chimes at New Year. Called a “leap second,” it prevents the day-lengthening from accumulating and causing the time of day to fall out of step with the Sun’s position. The slowing of the rotation of the Moon is more profound; over the billions of years since its formation, the Moon’s rotation has slowed so much that it is now locked into rotating just once every orbit. This is why the Moon constantly presents the same face to Earth.
Astronomers see tidal forces at play wherever two large objects are in orbit around one another. Because of its large size, Jupiter creates enormous tidal forces on its collection of moons. The one that suffers the most is the innermost moon, Io. This world is just a little bigger than our Moon at 3640 kilometers (2261 miles) across, and is the most volcanically active place in the Solar System. Io’s volcanoes are constantly erupting, spewing sulfurous lava onto the moon’s surface. The energy to drive this extraordinary activity comes from the tidal force that Io feels from Jupiter. This periodically squeezes Io, producing heat that melts the interior, driving the eruptions. Further out from Io is the moon Europa; because of the larger distance, the tidal force is less extreme and there is no spectacular volcanism. There is, however, strong evidence that below Europa’s icy crust is a global ocean of water, which is kept liquid by the squeezing of the tidal force. This ocean may be anything from 10 to 100 kilometers (6 to 60 miles) deep—if so, there is more water on Europa than there is on Earth.
On a much larger scale, tidal forces are responsible for stretching whole galaxies. If two galaxies approach each other on a collision course, the strength of gravity acting on the near side of each galaxy is stronger than that acting on the far side. So the near sides accelerate faster than the far sides, elongating the galaxies as they plunge into one another. In the extreme, when matter falls into a black hole, it is elongated so much that it is literally pulled apart in an event known, somewhat tongue-in-cheek, as “spaghettification” (see What is a Black Hole?).
Astronomers continue to exploit Newton’s gravitational theory for further discoveries about the Universe. Over the last two decades, it has allowed them to find more than 400 planets orbiting other stars; they have only actually seen a few of these planets, but their presence is certain because the stars are “wobbling.” We are used to the idea of a planet orbiting a star but that is only half the story; just as the star pulls the planet into an orbit, so the planet pulls back on the star. But because the star is so much more massive, the planet cannot cause the star to move through a large orbit; instead, it makes the star wobble. Take for example, our largest planet Jupiter. The Sun pulls it around its 750-million-kilometer (466-million-mile) orbit in twelve Earth years. In the same time, all Jupiter can manage is to force the Sun to pirouette about a point approximately 50,000 kilometers (31,000 miles) above the fiery surface. Such a pirouette is the periodic wobble that astronomers look for when searching other stars for planets. The size of the star’s movement and the time it takes to complete one wobble allows astronomers to compute the mass and orbital radius of the unseen planet. The surprise is that instead of finding slow pirouettes like the Sun’s that take years, most of the wobbling stars found so far have shown that their planets are large like Jupiter but complete their orbits in a matter of days. This indicates that the planets orbit very close to their parent stars (see Are There Other Intelligent Beings?). As technology improves and data is collected over longer timescales, astronomers expect to find planetary systems more nearly resembling our own.
WOBBLING STARS: AN ORBITING PLANET’S GRAVITY WILL PULL ON ITS PARENT STAR, CAUSING THE STAR TO PIROUETTE
For all its success, there was a paradox at the heart of Newton’s work. Newton knew it was there and even used it later in his life to defend himself when he was accused of being an atheist. The paradox lay in the concept of “universal” gravitation: the idea that everything in the Universe generated gravity, including the stars. If the stars were all pulling on one another, Newton could not understand why there was not general collapse. Observation suggested that the stars were in the same positions that they had been since the earliest ancient records, forming the same constellations that the Babylonians and the Greeks had seen, so naturally the assumption was that the Universe was static. Yet, paradoxically, the otherwise successful Theory of Universal Gravitation implied that it should be collapsing inwards.
Newton’s religious beliefs were being questioned because his theory seemed to dispense with the need for God to move the heavenly objects about. To get around both the scientific conundrum and the religious criticism, Newton stated that it must be the hand of God preventing the Universe from collapsing. The real answer, not determined until centuries later, is that the stars are in orbit around the center of the Milky Way, so they are supported by their own orbital motion in the same way as the planets in the Solar System.
Nowhere in the Principia did Newton explain the nature of gravity; his success was to describe it mathematically. Subsequent natural philosophers and scientists grappled with the fundamental origin of gravity, though none came close to any discovery and the world had to wait until the second decade of the 20th century to receive a mind-bending answer from Albert Einstein with his General Theory of Relativity.