The Universal Law of Gravity

After discovering his three laws of motion, Newton could have easily enjoyed a quiet, early retirement in the English countryside. Fortunately for us, he decided to make yet another groundbreaking contribution to physics. (In fact, he made several more revolutionary contributions to math and physics, which you can read about in other Idiot’s Guides.)

One day, while sitting and thinking in his garden—as all the world’s luminaries are prone to do—Newton observed an apple falling from its tree toward the ground. This led him to wonder why it fell straight downward, and not sideways or at some random angle. He concluded that there must be a force attracting it toward the very center of the Earth.

As one of the world’s great thinkers, he didn’t stop there. Could that same force, he wondered, be the one holding the moon in orbit around Earth? As you certainly know, he named this force “gravity.” But you may not know that he went on to derive a mathematical rule to explain the strength of the gravitational force between two objects. To wit, he showed that the attractive force (F) between two massive objects (of masses m₁ and m₂) separated by a specific distance (r) is given by . The additional term (G) in this equation is just a constant value that is needed to make the relationship true.

According to this rule, the gravitational attraction between two objects increases as they get near and decreases as they move farther apart. What’s more, the force of gravity is stronger between heavy objects and weaker between light objects. So the next time you feel guilty about raiding the fridge for a midnight snack, just remember that you are helping to increase your gravitational attractiveness.

Here, the arrows represent the gravitational forces of each pointing to Earth’s center (not to scale, of course). Incidentally, the gravitational force on the moon is 800,000,000,000,000,000,000 times stronger than that on the apple, due to the moon’s much greater size.

Newton hypothesized that the force pulling on an apple downward to the ground had the same origin as the force keeping the moon in its orbit. Of course, the gravitation force doesn’t just act between apples, the moon, and Earth. It leads to the attraction of all bodies that have any mass whatsoever. Newton’s theory predicts that no matter how massive or how far apart two bodies are, they will still feel a gravitational attraction to one another. In other words, Newton’s theory of gravity is a universal theory of gravity.

By applying his theory of gravity and his laws of motion to the moons and planets in the night sky, Newton was able to explain why the moon orbits Earth and why Earth orbits the sun. In fact, Newton’s laws are all we need to send spacecraft to the distant reaches of the solar system.

QUANTUM QUOTE

I think Isaac Newton is doing most of the driving now.

—Apollo 8 Commander Bill Anders, when asked who was “driving” his capsule back from the moon to Earth.

Now that you know massive bodies attract one another through gravity, you may be wondering why the planets aren’t simply pulled into the sun and engulfed in one last, fiery hurrah. The answer lies in the fact that that the planets are not sitting lazily in space. They are busily racing at great speeds in large orbits about the sun.

At any given moment, a planet is traveling in a straight line along a path that is parallel to the sun’s surface. Newton’s first law tells us that it will continue to travel in the direction of that straight line, unless a force acts on it. The sun’s gravitational attraction does just that, and it pulls the planet downward along a line perpendicular to the sun’s surface. The planet essentially splits the difference between the parallel and perpendicular motions, and as a result it moves in a curved orbit about the sun.

Though the motion of the planets had been observed by astronomers for millennia, it wasn’t until Newton applied his theories that it could be accurately and elegantly described, using only the pair of equations we showed you above. As a tribute to this remarkable contribution, the unit that physicists use today to measure force is named in Newton’s honor.