An Apple a Day Keeps the Moon in Orbit

1686: Isaac Newton

It’s not true that an apple bonked Isaac Newton on the head, but falling apples did jostle his thoughts. They inspired Newton to formulate the first universal theory of gravity, which explained the motions of apples, the Moon, planets, comets, and everything else in the universe. A century later, they led to the first concepts of a “dark star.”

Newton owed his insights in part to the plague. He had received a scholarship to Cambridge University in 1664, but within a year of his arrival, plague forced the school to close. Newton returned to his family farm in Woolsthorpe, England, where he spent the next two years contemplating astronomy and mathematics.

One day he watched as apples fell from the trees outside his house. He noted that the apples moved faster as they got closer to the ground, suggesting that they were accelerated by an invisible force: gravity. Apples that fell from higher in the tree moved faster than those that fell from lower branches. Newton wondered if this force might extend even farther — say, all the way to the Moon.

Newton envisioned the Moon “falling” toward Earth just as the apples did, pulled by gravity, which he postulated was a property of all matter.

Newton thought of a cannonball fired from a mountaintop. If more gunpowder were used, the cannonball would travel farther before falling back to the surface. If a gunner could stuff the cannon with enough powder, the cannonball would travel all the way around Earth, with its forward momentum exactly balanced by Earth’s gravitational pull.

Newton calculated the velocity required to accomplish this feat. And because he knew the distance to the Moon, Newton calculated the Moon’s velocity around Earth as well. He found that the Moon’s orbit exactly matched his calculations of the “attraction” of Earth’s gravity if the gravitational attraction fell off at a rate that was inversely proportional to the square of the distance. In other words, if an object is twice is far from a gravitational source, such as Earth, then it “feels” just one-fourth as strong a gravitational pull.

Newton published his discoveries in 1687 in Philosophiæ Naturalis Principia Mathematica, which is Latin for Mathematical Principles of Natural Philosophy. The Principia, as it’s commonly known, is one of the most important works in scientific history. It laid out the mathematics behind Newton’s discoveries, allowing other scientists to apply the laws of gravity to other objects throughout the universe. These laws eventually helped them measure the masses of the other planets in the solar system, and even measure the masses of stars in binary systems.

Although Newton’s laws of gravity would be supplanted by Albert Einstein’s Theory of General Relativity more than two centuries later, his formulae still work perfectly well for most everyday calculations. They break down only in special circumstances — like those encountered in and around black holes.

Even so, two 18th-century scientists, John Michell and Pierre-Simon Laplace, applied Newton’s laws to postulate the existence of “dark stars” — those with such strong surface gravity that not even light could escape from them. Their calculations provided the first evidence that the universe could be populated with countless black holes.

Recursos

Biography: Sir Isaac Newton

Footprints of the Lion: Isaac Newton at Work

Sir Isaac Newton: The Universal Law of Gravitation

A Java applet that illustrates Newton’s calculations of a cannonball fired from a mountaintop

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