# Gravity

What goes up, must come down. That's one way of looking at the weird phenomenon we call gravity, but it's far from the whole story. Some things—space probes and satellites spinning over our heads—never come down. And the idea of gravity as a simple up-down force happening purely on Earth is very wrong too.

Gravity is like invisible elastic stretched through the whole universe, holding the stars and planets together and pulling them toward one another. Much more significantly, it's a fundamental force between every bit of matter in the universe and every other bit: just like Earth and the Sun, you have your own gravity, and so do I. From Aristotle to Kepler and from Newton to Einstein, understanding gravity has challenged some of the best scientific minds in history. Thanks to their efforts in getting a grip on this tricky topic, we can do all kinds of neat things, from figuring out where we are with GPS satellites to making sure bullets hit the spot. But that still leaves an important question: just what is this thing we call gravity and how does it work? Let's take a closer look!

Photo: Gravity in all its beauty! Gravity's pull varies from place to place, both on Earth and elsewhere. This is a map showing how the strength of gravity varies across the Mare Orientale on the moon. Image courtesy of NASA/JPL-Caltech.

## What is gravity?

Gravity is a pulling force (always a force of attraction) between every object in the universe (every bit of matter, everything that has some mass) and every other object. It's a bit like an invisible magnetic pull, but there's no magnetism involved. Some people like to call this force gravitation and reserve the word gravity for the special kind of gravitation ("what goes up must come down") that we experience here on Earth. To my mind, that's unnecessary and wrong, and I'll explain why when we talk about Isaac Newton in a moment. In this article, I'm going to use the word gravity for everything (both gravity and gravitation).

If you've heard physicists talk about the four fundamental forces (or four fundamental interactions) that control everything that happens around us, you'll know that gravity is one of them—along with the electromagnetic force and the two nuclear forces that work on very small scales inside atoms (known as the strong and weak forces). Gravity is very different from these other forces, however. Most of us can remember playing with magnets in school and one of the first things you learn by doing that is that two magnets can attract or repel. Gravity can certainly attract, but it never repels. While magnetism can be an incredibly strong force over very short distances, gravity is generally a much weaker force, though it works over infinitely long distances. The gravity exerted by your body, right now, is pulling the Sun toward you—just a tiny bit—across a distance of something like 150 million kilometers!

Artwork: Gravity keeps the planets in orbit around the Sun, even at immense, astronomical distances. Spacecraft, like Mariner 10 shown here, sometimes use what's called a "gravity assist" to help them achieve a new orbit or a different velocity. Artwork courtesy of NASA

## Gravity on Earth

Cars, trucks, airplanes, mosquitos, your body and everything around you—it's all stuck to Earth by the force of gravity. If we've just said gravity is a weak force, how is that possible? How can such a weak force pull something like a huge Jumbo jet down toward the ground?

Gravity might be weak, but Earth has a lot of it because our planet is so big and we're relatively close to it (compared to our distance from the Sun, anyway). Often it helps to think of Earth's gravity originating at a single point at the center of the planet's core. The amount of gravity you feel at any place on Earth depends how far you are from this point, so it's slightly more at sea level and slightly less when you're up a mountain. Now Earth isn't a perfect sphere: technically, it's what's called an oblate spheroid—it's flattened at the poles and bulges at the equator. That means gravity also lessens with latitude (it's slightly less at the equator than at the poles). Finally, because Earth is spinning around, and people at the poles are moving less quickly (relative to space) than those at the equator, that also slightly reduces the effects of gravity. Add all these things together and you get a variation in gravity between the equator and the poles of much less than 1 percent, so for most everyday purposes, we can say that gravity at sea level is the same right across Earth. [1]

Artwork: The force of gravity is slightly lower at the equator than at the poles. Please note that this figure is not drawn to scale and Earth's bulge is hugely exaggerated!

Why might it matter that gravity varies on Earth? First, and perhaps least importantly, it affects how much you weigh. If gravity is more at sea level, you weigh more there! The quickest way to lose weight is to climb an especially high mountain—not because all the effort makes you lose any body mass, but because the force of gravity is weaker the further you go from the center of the Earth. Second, gravity pulls everything toward Earth (the invisible, gassy atmosphere around us as well as everything else), and that's why we have air pressure (on land) and water pressure (in the oceans). These things vary with altitude (above Earth's surface) and depth (below sea level).

If gravity is a force tugging us toward a point in the center of the planet, why don't we keep on being pulled in? Why doesn't gravity tug you through the floor of your house and the rocks below to suffer a really rather unpleasant death in the heart of Earth's fiery core, deep beneath your feet? If you're sitting still in a chair right now, it means all the forces on your body are balanced. So the downward pull of gravity must be balanced exactly by another, upward-pushing force. As gravity tries to pull you down, the atoms in the chair push back upward—you can't squash atoms that easily—and counteract with what is essentially an electromagnetic force. When someone stands on the floor and goes nowhere, the ground is effectively pushing back up again and saying "I will not be squashed." We call the upward-pushing force from the ground that balances downward-pulling gravity the normal force.

## Gravity in space

Photo: Astronauts train for space in a "vomit comet": It simulates weightlessness by making deep dives toward Earth. Photo courtesy of NASA on The Commons.

Scientists used to think Earth sat at the center of the Universe: theories of astronomy were geocentric, which means Earth-centered. Until the 16th century, most people thought the Sun rotated around Earth, rather than (as we now know) the other way around. There was tremendous religious opposition to the idea that Earth spun around the Sun, which is called the helicentric (Sun-centered theory). That idea was first put forward by the ancient Greek thinker Aristarchus (c.310–250 BCE), revived by Polish astronomer Nicolaus Copernicus (1473–1543), and championed by Galileo Galilei (1564–1642). When it comes to gravity, we now accept that Earth isn't at the center of things: it isn't special and it's no different from anywhere else. That's one reason why it makes no sense to talk about gravity (Earth's "special" gravitation) and gravitation (other kinds of gravitation, in other situations or elsewhere). But you'll still see both of those two words used widely. (Isaac Newton formulated a law of "gravitation," as we'll discover in a moment.)

Photo: Galileo Galilei, an Italian astronomer, investigated how gravity accelerates things on Earth and championed the idea that Earth orbits the Sun. Picture from Carol M. Highsmith's America Project in the Carol M. Highsmith Archive, courtesy of US Library of Congress

Just like Earth, every planet (or moon) has a different amount of gravity; bigger planets (or moons) have more gravity than smaller ones. So our own Moon has gravity, but it's about one sixth as much as Earth's (because the Moon has less mass and it's much smaller). That's why astronauts weigh one sixth as much on the Moon and why they can jump about four times higher in the air when they're there. Jupiter has gravity too and because it's bigger and more massive than Earth, you'd weigh almost three times more there and struggle to jump very far at all.

Gravity also explains why the universe looks and behaves the way it does. If you've ever wondered why planets are nice round shapes (roughly spherical) and not square boxes, gravity is the answer. When the planets were busily forming from fizzing atoms and swirling atomic dust billions of years ago, gravity was the force that tugged them together. If lots of matter is pulled toward a central point from many different directions, a sphere is what you end up with—just like you end up with a snow ball if you pat snow together hard from all sides. Invisible "strings" of gravity also explain why the planets dance around one another in the strange cosmic patterns we call orbits. Although we often think of orbits as circular, they're actually ellipses, which are stretched-out, oval relatives of circles (a circle is a special kind of ellipse).

... one of the theories proposed was that the planets went around because behind them were invisible angels, beating their wings and driving the planets forward. You will see that this theory is now modified!

Richard Feynman, Six Easy Pieces

## How does gravity work?

Early scientific ideas about gravity were based on watching how things naturally fell toward the ground. Aristotle, the ancient Greek philosopher, who lived about 2350 years ago, famously believed that heavier things fall faster than light ones, so if you drop a stone and a feather at the same time, the stone wins the race and hits the ground first.

Meanwhile, the whole question of how planets moved in space was considered an entirely different matter. In Aristotle's mind, Sun, moon, planets, and stars all marched in circular orbits round Earth. Astronomers such as Ptolemy (Claudius Ptolemaeus, 100–170 CE) built on this model, but didn't really connect motion in space with what was happening back on Earth. Like Aristotle, Ptolemy was confident that the Sun and planets spun in circles round Earth. Even though his ideas were wrong, his book of astronomy, The Almagest, was accepted as scientific truth for over 1400 years (until Nicolaus Copernicus came along) because no-one else had any better ideas. "Almagest" actually means "The Greatest": Ptolemy's really was the greatest scientific explanation of the world people had at that time.

Artwork: Before people understood gravity, they had to devise ingenious explanations for why the planets moved. In this 14th-century illuminated manuscript, angels make the planets rotate by cranking giant handles! For more about the development of these ideas, see the fascinating Wikipedia article Dynamics of the celestial spheres. Illustration attributed to the atelier of the Catalan Master of St Mark, Spain, 14th century, courtesy of the British Library and Wikimedia Commons.

Aristotle was correct in one sense (a stone beats a feather in a race to the ground), but we now know that everything falls at exactly the same rate and the feather only loses because air resistance (drag) pushes up against it, slowing it down. The person who figured this out, toward the end of the 16th century, was Italian astronomer Galileo Galilei (1564–1642). According to some historians, Galileo experimented with metal balls on a tilted ramp, quickly concluding that the force of gravity accelerates every object—feathers just like stones—at exactly the same rate, which we now call the acceleration due to gravity (or g). Other science historians claim Galileo figured out his ideas by dropping balls from the Leaning Tower of Pisa, while a third theory is that all these were "thought experiments" that he carried out in his own mind. Either way, we now know that all masses are accelerated in the same way; for most practical purposes, g is a constant value everywhere on Earth (although, as we saw up above, it does vary slightly due to altitude, latitude, and so on).

Photo: Isaac Newton—the man behind our modern understanding of gravity. Picture courtesy of US Library of Congress.

While Galileo was musing over gravity on Earth, other astronomers had been coming up with more detailed accounts of how planets moved in space. Nicolaus Copernicus (1473–1543) and Galileo advanced the idea that Earth moved around the Sun. The German Johannes Kepler (1571–1630) believed this too—and realized exactly how it might work. He took a treasure trove of very accurate and detailed observations compiled by another astronomer, Tycho Brahe (1546–1601), and used it to figure out three deceptively simple mathematical laws that seemed to sum everything up. Kepler realized that the planets move in ellipses around the Sun, not circles as had long been supposed. He found that they "sweep out equal areas in equal times," which essentially means they move faster when they're nearer the Sun and slower when they're further out—but in a very predictable way. Finally, he showed how the size of a planet's orbit was related to the time it took for the planet to make a complete circuit around the Sun. It's pretty obvious that if a planet has a bigger orbit, it will take longer to go around it, but Kepler figured out the precise relationship between the two things. (Specifically, he showed that the time a planet takes to orbit, squared, is proportional to its distance from the Sun, cubed.)

But the real stroke of genius in understanding gravity came from English scientist Isaac Newton (1642–1727). He realized that the force of gravity that makes things fall to Earth is exactly the same as the force of gravitation that keeps the planets spinning around in space, which is why I prefer to use the same word for both phenomena. According to the popular myth, Newton figured this out when he saw an apple falling in his garden. Whether that really happened, no-one knows—but it was an incredibly impressive insight that changed science forever. Building on Kepler's work, Newton calculated that a falling apple experienced the same gravity as the Moon would experience being pulled toward Earth. That led him to his groundbreaking law of universal gravitation, published in 1687.

Artwork: Three men who revolutionized astronomy: Copernicus (left), Galileo (right), and Kepler (far right) developed our modern view of the universe with the Sun at its center. Illustration by W. Marshall from a book cover c.1640, about a decade after Kepler's death. Artwork courtesy of US Library of Congress.

## The law of universal gravitation

Suppose we have a couple of handy planets and we play around measuring the gravity between them. Let's say the red planet is four times more massive than the blue one and and they're a certain distance apart.

1. Let's say the initial force of gravity between them is F.
2. We replace the blue planet with another red one. Now we'll find the force of gravity between them is 4F.
3. Suppose we make both planets blue. The force of gravity will now be ¼F.
4. If we move the two blue planets so they're twice as close, the gravity force will quadruple to F.

This is what we'd find by experimenting and it might seem mysterious to begin with, but we can explain it quite simply. That's what Isaac Newton did with his law of universal gravitation.

Newton's gravity law is a simple math formula that explains almost everything we need to know about gravity in almost every situation we're ever likely to come across. It says that the force of gravity, F, between two masses, M and m, a distance r apart, is:

F = G × M × m ÷ r2.

What does this actually mean?

1. We can calculate how big the force is between two objects by plugging their masses into the formula. The bigger the masses (M and m) involved, the bigger the force (F) between them: more mass means more gravity. So when we quadruple one of our masses (swap a blue ball for a red one, we quadruple the force of gravity between them.
2. The closer the masses are together (r), the bigger the force (F). But note that F increases as the square of the distance decreases; in other words, F is inversely proportional to r × r. So if you move twice as far from something, you experience a quarter as much gravitational attraction. That's why, when we halved the distance between the two blue balls, we quadrupled the gravity. If you're not sure why that should be, imagine gravity is like a flashlight shining outward, spreading out from a single point at the centre of Earth. If we could make Earth twice the radius but with the same mass, the same amount of gravity (or light) would have to spread across four times more surface area, which would dilute it by a quarter. Double the distance and you quarter the gravity.
3. Newton's law applies to any and every pair of masses anywhere in the universe. So it applies equally to an apple falling toward (being attracted by) Earth and to the Moon spinning round Earth in an orbit. That's why it's called the universal law: it applies to everything. Rather wonderfully, Newton's universal law is completely in agreement with Kepler's laws of planetary motion and Galileo's observations about acceleration due to gravity.
4. Newton said that the force was mutual. So Earth pulls down on a falling apple, but a falling apple pulls up on Earth.

It is hard to exaggerate the importance of the effect on the history of science produced by this great success of the theory of gravitation.

Richard Feynman, Six Easy Pieces

What about the mysterious G in this equation? What's that all about? G is called the universal gravitational constant: a constant is simply a magical, fixed number that makes sure equations like this always work. There are many constants in physics equations and they conceal within themselves very deep truths about the world, though what those truths are, no-one really knows. What does the gravitational constant actually mean? Why is it that exact value? No-one knows!

The first person to come up with a figure for G (indirectly, because he actually measured something else) was the eccentric British physicist Henry Cavendish (1731–1810). Cavendish is also known for discovering hydrogen and gives his name to the famous Cavendish Laboratory at Cambridge University in England (where I studied physics too). The value his experiment led to (6.75 × 10−11 Nm2/kg2) was almost exactly the same as the value we use today (6.67 × 10−11 Nm2/kg2).

## Einstein meets gravity

The Universal Law of Gravitation was an astounding success, but there was one strange thing it couldn't explain: a slight oddity in the motion of the planet Mercury, known as its perihelion precession. When theories don't explain everything, we know they can't be quite right. And indeed, at the beginning of the 20th century, the brilliant German-born physicist Albert Einstein (1879–1955) realized that the "classical", Newtonian picture of gravity wasn't quite right either.

Photo: Albert Einstein's General Relativity is currently our most comprehensive theory of gravity. Photo courtesy of US Library of Congress.

Einstein had already revolutionized physics with a remarkable new theory called relativity. Newton had shown that there was nothing special about Earth's gravity; it was the same as gravity anywhere. But it didn't really explain what caused gravity or how it passed from one side of the universe to the other through all the things that sat in between. In September 1905, Einstein's original idea, known as the Special Theory of Relativity, set out a new way of looking at three-dimensional space and time, blending them together to make four-dimensional space-time (or the space-time continuum). Einstein also had new ways of looking at light, which traveled at a constant speed and set an effective speed limit for the universe. Putting these ideas together suddenly made the sober science of physics look like a painting by Salvador Dali. If you traveled close to the speed of light, someone watching your progress as you passed by would see you shrink and your time slow down!

All very strange, but where did gravity fit in? In 1915, Einstein extended his ideas to make what he called a new, General Theory of Relativity. One key aspect of this theory is called the principle of equivalence, and it says that the force produced by gravity is exactly the same as the force produced by acceleration. In other words, gravity and acceleration are exactly the same thing. That means, for example, that if you wake up to find yourself inside a space rocket and you feel a force very much like weight, you have no way of knowing whether it's caused by gravity (because the rocket is sitting on the launchpad on Earth) or acceleration (because it's hurtling through space at ever-increasing speed, producing a force identical to what you'd normally think of as gravity).

According to Einstein's new model of gravity, big masses (like planets) bend the very fabric of space time, like a heavy ball sitting on a huge rubber mat. That makes other masses, moving nearby, curve in toward them—giving a pulling force or attraction that looks identical to the thing we've always called gravity. In other words, gravity is the curvature of spacetime around mass (or energy, which is the same as mass). This was a weird and revolutionary idea and few people understood it or believed it, to begin with, but it could explain the odd motion of mercury—and much more. In 1919, scientists observing a solar eclipse found the Sun bent light around it exactly as Einstein's theory predicted. (Extending this idea a little bit, we can see that if light was bent in just the right way, it would give optical effects just like a lens. This concept, known as a gravitational lens, was confirmed experimentally in 1979 and 1988.)

Artwork: According to Albert Einstein's General Theory of Relativity, gravity is the curvature of space time around mass or energy. Imagine if the Sun were a heavy metal ball sitting on a rubber mat. If you rolled a marble in a straight line nearby, it would curve inward because the mat is distorted slightly by the heavy ball. This is roughly how a big mass like the Sun curves space-time around it, pulling things like Earth toward it with the force we call gravity.

## How does gravity travel?

Einstein's General Theory completely explains Newton's Universal Law of Gravitation, so you could say that it makes it unnecessary. However, Newton's law is much simpler and works in most everyday situations, so it's still widely used in physics. (The same goes for Newton's "classical" laws of motion and Einstein's Special Theory of Relativity. Newton's laws are perfectly adequate for most everyday situations, so we still those all the time.) And just as Newton's law turned out not to be a complete explanation of gravity, so there are things that Einstein's law doesn't explain. In other words, Einstein's theory isn't complete either.

Photo: Detectors used to help find gravitational waves. Photo courtesy of NASA/JPL-Caltech.

The current way of explaining forces—how they act "invisibly" on things at a distance removed—is to think about particles being exchanged, but this turns out not to be compatible with Einstein's theories. Exactly how gravity works is still not understood. We don't know why it's so weak (compared to other forces) or how it "travels" from one side of the universe to the other. One idea is that it involves the exchange of hypothetical particles known as gravitons, but no-one has ever seen one of those. Despite its incompleteness, we know that much of Einstein's theory is correct, because the predictions it makes have been borne out by experimental observations, like those described up above. Another key prediction from Einstein's theory is that, when large masses are disturbed (for example, when stars explode or black holes swallow one another), they send out rippling waves (gravitational waves) through space-time at the speed of light. That was fully confirmed in September 2015 by scientists at LIGO (Laser Interferometer Gravitational-wave Observatory in the United States—and the discovery earned three scientists the Nobel Prize in Physics in 2017. Einstein's General Theory also tells us that the color of light can be shifted toward red by the pull of gravity—another prediction confirmed in reality.

From Aristotle to Einstein, we've made great progress, but when will we have a complete theory of gravity? Perhaps tomorrow, perhaps never. Science is a never-ending quest to understand—and that's what makes it so fascinating. Long may its mysteries continue to inspire us!

Artwork: Gravity constantly throws up exciting new discoveries. How about this "black hole tango," in which a supermassive black hole is forming through the merging of smaller black holes drawn together by gravity. Artwork courtesy of NASA.

## A brief history of gravity

• 350 BCE: Babylonians could predict the movements of planets and the comings and goings of eclipses.
• 340 BCE: Aristotle (384–322 BCE) publishes On the Heavens, which describes how the sun and planets move in circular orbits around a central Earth. Aristotle's idea of gravity on Earth is based on the idea that heavy things seem to fall faster.
• 300 BCE: Aristarchus (c.310–250 BCE) suggests things might work the other way. Perhaps the Earth really spins around the Sun? This is the first attempt at a heliocentric (Sun-centered) theory.
• 150 CE: Ptolemy (100–170 CE) publishes the Almagest, a detailed geocentric (Earth-centered) theory of the universe. It remains the most influential book of astronomy for the next 1400 years.
• 1543: Rejecting Ptolemy's ideas, Nicolaus Copernicus (1473–1543) decides to revive the heliocentric theory, in a major challenge to the church.
• 1589: Galileo Galilei (1564–1642) demolishes more of Aristotle's ideas. His new theory is that gravity makes objects fall at the same rate, however light or heavy they are. Like Copernicus, he supports a heliocentric model that brings him into conflict with the church.
• 1500s: Tycho Brahe (1546–1601) makes detailed observations of planetary movements and tries to unite Ptolemy's ideas with those of Copernicus. In his model, the Sun and moon spin around Earth (geocentric), but everything else spins around the Sun (heliocentric).
• 1609: Johannes Kepler (1571–1630) uses Brahe's observations to work out three mathematical laws describing how planets move in ellipses.
• 1687: Building on Kepler's work, Isaac Newton (1642–1727) sums up gravity in the universal law of gravitation.
• 1798: Henry Cavendish (1731–1810) comes up with an accurate figure for the gravitational constant, G, in an experiment to measure the weight (density) of the world.
• 1915: Albert Einstein (1879–1955) publishes his General Theory of Relativity, which extends his earlier Special Theory to include gravity.
• 1919: Frank Watson Dyson and Arthur Eddington confirm the General Theory by observing distorted light rays during a solar eclipse.
• 2015: Gravitational waves are detected directly for the first time.
• 2017: The discovery of gravitational waves earns a Nobel Prize in Physics for Rainer Weiss, Kip Thorne, and Barry Barish.

## References

1.    In Geophysics: A Very Short Introduction, p.72, William Lowrie quotes a common estimate of 0.5 percent.

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## Find out more

### On this website

• Bullets: An understanding of gravity is essential if you want to know how to fire a bullet accurately.
• Energy: Energy powers forces like gravity.
• Motion: How Isaac Newton revolutionized our understanding of force and motion.
• Science: A full list of our science articles.
• Science of sport: In many ways, sport is a battle against gravity.

### Books

These are good for ages 9–12:

• A Crash Course in Forces and Motion by Emily Sohn. Capstone, 2019. A graphic/comic introduction to forces.
• Can you Feel the Force? by Richard Hammond. New York/London: Dorling Kindersley, 2007/2015. A simple, fun introduction to physics for ages 8–10.
• Fatal Forces by Nick Arnold. Scholastic, 2014. A more wordy introduction from the Horrible Science series. For ages 10–12, 128 pages.
• Gravity: Scientific Pathways by Chris Woodford. Rosen, 2013. My own little introduction to the history of gravity, from ancient science to Einstein and modern gravity. For ages 9–12, 64 pages.

• Six Easy Pieces by Richard Feynman. Basic Books/Penguin, 2011. Chapter 5, The Theory of Gravitation, is a short overview that covers much the same ground as this article, but with a bit more detail about Kepler and planetary motion.
• Newtonian Mechanics by A.P. French. W. W. Norton, 1971. A classic introduction for undergraduates and bright high-school students.
• Physics: Algebra/Trig by Eugene Hecht. Thomson-Brooks/Cole, 2003.

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