Newtonian Gravitation: Structures & Vocabulary

Newton's law of universal gravitation describes the attractive force between masses as proportional to the product of their masses and inversely proportional to the square of their separation. Combined with Newton's laws of motion, it explains planetary orbits, falling bodies, tides, binary stars, and much of spacecraft dynamics.

Gravity continually accelerates orbiting bodies toward one another. An orbit occurs when sideways velocity and inward gravitational acceleration combine so that a body continuously falls around, rather than directly into, its primary. The inverse-square dependence causes gravitational influence to weaken rapidly with distance but never abruptly vanish.

Planetary motions, lunar motion, laboratory torsion-balance measurements, satellite trajectories, tides, and binary-star orbits agree with Newtonian predictions in regimes where relativistic corrections are negligible. Measured orbital periods and sizes allow masses of planets and stars to be inferred.

The gravitational constant G sets the coupling strength, while gravitational field and potential describe force or energy per unit test mass. Spherical symmetry allows the exterior gravity of a body to behave as though its mass were concentrated at the center. Center-of-mass motion keeps the two-body problem symmetric.