gravitationssystem

A gravitational system is a collection of bodies that interact through gravity. In classical mechanics, gravity is described by Newton's law of universal gravitation and Newton's laws of motion. Such systems can be bound, with bodies orbiting each other, or unbound, with flybys and scattering events.

The fundamental force is attractive, proportional to the product of the masses, and inversely proportional to the square distance between them: F = G m1 m2 / r^2 along the line joining the bodies. In vector form, F12 = −G m1 m2 (r12)/|r12|^3. The motion of all bodies follows Newton's second law, giving a set of coupled equations for their positions.

In an N-body system, each body experiences the gravitational pull of all others, leading to a complex dynamics described by m_i d^2 r_i/dt^2 = ∑_{j≠i} G m_i m_j (r_j − r_i) / |r_j − r_i|^3. If only two bodies are involved, the problem reduces to an effective one-body problem with reduced mass μ and a relative coordinate r, yielding keplerian orbits characterized by energy E and angular momentum L. The gravitational potential energy is U = −G m1 m2 / r, and the motion is constrained by conserved quantities such as total energy and total angular momentum.

Common gravitational systems include the solar system, binary star systems, planetary moons, star clusters, and galaxies. Observations of orbits, timings, and dynamics enable estimation of masses, distances, and evolutionary states. Extensions beyond Newtonian theory—general relativity and post-Newtonian corrections—become important in strong-field regimes or tight binaries, where gravitational radiation can drive long-term changes.