Newton's Law of Universal Gravitation

In Newton's theory, gravity is assumed to act instantaneously — any change in one mass immediately affects the force on the other, no matter how far apart they are. This bothered Newton himself, and it is inconsistent with Einstein's special relativity, which forbids information from travelling faster than light. In Einstein's general relativity, gravity propagates at the speed of light as gravitational waves. For nearly all practical purposes — planets, satellites, stars — the difference is negligible, and Newton's instantaneous approximation is excellent. But for very precise measurements and for extreme events like black-hole mergers, the finite speed of gravity is essential and has been confirmed by direct detection of gravitational waves.

Mass is an intrinsic property of an object — a measure of its inertia and of its gravitational "charge." It is measured in kilograms and does not change with location. Weight is the gravitational force on an object in a particular gravitational field: W = mg, where g is the local gravitational acceleration. Weight is measured in newtons and does change with location: an astronaut with a mass of 70 kg weighs about 690 N on Earth, 110 N on the Moon, and 0 N in free-fall orbit, though the mass remains 70 kg in all cases. The universal gravitation formula is what connects these concepts: g = GM/R² for a body of mass M and radius R, and W = mg is the gravitational force on a small mass m at the surface.

No known material can shield gravity. Unlike electric fields, which can be cancelled by opposite charges and blocked by conductors, gravitational fields from different sources simply add as vectors and cannot be cancelled except by placing an equal mass on the opposite side (which creates an unstable equilibrium). The best laboratory searches for gravitational shielding have found no effect down to very high sensitivity. However, gravity can be counteracted by other forces: a rocket launch uses thrust to overcome gravity, a helium balloon rises because the buoyant force of the displaced air exceeds its weight, and a satellite in orbit is in continuous free-fall that produces the sensation of weightlessness. But the gravitational field itself is always present and cannot be turned off.

At the exact center of the Earth, the gravitational force is zero. This is a consequence of the shell theorem: for a spherically symmetric mass distribution, only the mass inside the radius of the observation point contributes to the gravitational field, and all the mass outside the point is symmetrically distributed and cancels itself out. As you descend from the surface toward the center, the effective mass inside your radius decreases, and so does g. In a uniform-density sphere, g would fall linearly from the surface value to zero at the center. For the real Earth, g actually increases slightly just below the surface (because the mantle is denser than the crust) before falling to zero at the center. The pressure at the center, however, is enormous — about 3.6 million atmospheres — because of the weight of all the overlying material.

Kepler's three laws of planetary motion — elliptical orbits, equal areas in equal times, and T² ∝ a³ — were derived empirically from Tycho Brahe's data, before Newton explained them theoretically. Newton showed that all three laws follow from the inverse-square form of the gravitational force combined with his laws of motion. The second law is a consequence of conservation of angular momentum; the first and third laws follow from the specific 1/r² form of the force. In fact, the inverse-square form is the unique force law (among central forces) that produces closed elliptical orbits. If the force fell off differently — say, as 1/r or 1/r³ — the orbits would not close, and Kepler's simple laws would not hold. This is one of the great triumphs of Newtonian mechanics: a single, simple force law explains the entire complexity of planetary motion.

Gravitational waves are ripples in the fabric of spacetime, predicted by Einstein's general theory of relativity in 1916. They are produced by accelerating masses — particularly by violent events such as the merger of two black holes or neutron stars, or the collapse of a massive star. They travel at the speed of light and stretch and squeeze space itself as they pass. The effect is extraordinarily tiny: the first detection by LIGO in 2015 measured a change in length of about 10⁻¹⁸ m over a 4 km baseline — less than the diameter of a proton. Gravitational waves are not the same as gravitational force; they are a separate phenomenon that carries energy and information away from accelerating masses. Their detection (Nobel Prize 2017) opened a new window on the universe, allowing astronomers to observe black holes directly and to study the most extreme events in the cosmos.