The force that causes objects to fall to the ground (gravity) is also the force that keeps the planets moving around the Sun, but this fact was not realized until the end of the 17th century. The ancient Greeks thought that solid bodies fall because they are seeking their natural place (under the lighter elements, water, air, and fire), while the planets are moved by invisible crystalline spheres. Even the German astronomer Johannes Kepler, who proved in 1609 that the planets’ orbits are ellipses around the Sun, thought that they must be moved by motions in the ether.
It was the English scientist and mathematician Isaac Newton who first realized, and proved in his Principia published in 1687, that the planets naturally move in ellipses because of an attractive force between the Sun and each of the planets. He showed that this force depends on the product of the masses of the two bodies divided by the square of the distance between them. He also showed that it was this same force that attracts an apple toward Earth by comparing the force on the apple with the force needed to keep the Moon in orbit about Earth. Since the distances from the center of Earth to the apple and to the Moon were known, he could demonstrate that these forces also depended on the inverse square of the distance—that is, the force decreases as the square of the distance increases. The real genius of Newton showed when he generalized his findings by stating that all bodies attract each other gravitationally, the force between them varying in the same way as it does between the Sun and the planets.
Measuring gravity
The force of gravity is actually extremely weak, and it is only because Earth is so massive that its gravitational effects are obvious. The attractive force between two 44 lb. (20 kg) objects 1 ft. (0.3 m) apart is only the same as the weight of one millionth of an ounce on Earth. The first measurement of gravitational force between two bodies of known mass was made in 1798 by the English natural philosopher and chemist Henry Cavendish.
His apparatus consisted of two lead balls 2 in. (50 mm) in diameter (each weighing 1.7 lbs., 0.8 kg) hung from the ends of a 6 ft. (2 m) long deal beam, which was supported at the center by a long wire, allowing the beam to swing horizontally. Two lead balls 1 ft. (0.3 m) in diameter (each weighing one-sixth of a ton) were placed near the small balls on opposite sides so that the gravitational attraction between each pair of large and small balls caused the beam carrying the latter to swing toward the large balls. The 1 ft. balls were then moved to the other side of the small balls, making the beam swing the other way. The total swing measured at the end of the beam was 0.3 in. (7.6 mm), and from this number, Cavendish calculated the force between the balls. He expressed his results as the gravitational force between two one-kilogram masses one meter apart, a quantity usually called G. Cavendish’s value for G was the best for almost a century and is within 1 percent of the best modern value (6.673 × 10–11 N).
Newton’s gravitational theory also explains the experimental results of the Italian scientist Galileo, who, in 1590, showed that all objects fall equally fast toward the center of Earth, irrespective of their masses (as long as there are no other forces acting on them, we have to add today for accuracy). The ancient Greeks, in particular Aristotle, had maintained that heavy bodies always fall faster than lighter ones, an assumption that is still intuitively felt to be true even today. Galileo disproved the Greeks’ hypothesis, according to legend, by dropping two objects of different mass from the top of the Leaning Tower of Pisa in Italy, whence they hit the ground simultaneously. Newton showed that although the gravitational forces acting on the two masses are different, their accelerations, and hence speed of descent, are independent of their masses and depend only on the mass of Earth. The observation that a feather and a marble fall at different speeds is explained by air resistance.
