What does the formula mean?
In F = GMm/r², M and m are the two masses, r is the distance between their centers, and G is the gravitational constant. Double a mass and the force doubles; double the distance and the force drops to one-quarter—the inverse-square law. Newton's breakthrough was realizing the force pulling an apple down is the same one holding the Moon in orbit. Henry Cavendish first measured G in 1798 with a torsion balance.
What does it explain?
Combined with Newton's laws of motion, it lets you derive Kepler's laws of elliptical orbits. Tides, satellite orbits, and even the 1846 discovery of Neptune came from gravitational calculations. For very strong gravity or the tiny anomaly in Mercury's orbit, general relativity gives the more accurate answer.
FAQ
- Is the apple story true?
- Newton himself recalled late in life that a falling apple in his garden sparked the idea.
- Do two people attract each other?
- Yes, but two 60 kg people 1 m apart feel only about 2.4×10⁻⁷ N.
Sources reviewed: 2026-10-25
References
- Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica, Book III.
- Cavendish, H. (1798). Experiments to determine the density of the Earth. Philosophical Transactions, 88, 469–526.