Gravitationfeld

Gravitationfeld, or gravitational field, is a physical field that describes the gravitational interaction in a region of space. At every point it assigns a vector g that represents the acceleration a small test mass would experience there if no other forces acted on it. In Newtonian gravity the field is produced by masses and follows the inverse-square law: the field due to a point mass M at distance r is g = - GM / r^2 r_hat, directed toward the mass. The gravitational force on a test mass m is F = m g. The field can be expressed as the negative gradient of the gravitational potential φ, with φ(r) = - GM / r and g = -∇φ.

Superposition applies: for multiple masses, the total field is the vector sum of the individual fields. In static situations the field is curl-free (∇×g = 0) and satisfies Gauss’s law for gravity, ∇·g = -4πGρ, where ρ is mass density. Near Earth’s surface the field magnitude is about 9.81 m/s^2, though it varies with altitude, latitude and local geophysical structure. The gravitational potential energy of a mass m is U = m φ.

In general relativity gravity is not a force but the curvature of spacetime described by the metric tensor g_{μν}. Free-falling objects move along geodesics, and Newtonian gravity emerges as an approximate description in weak-field limits. Gravitational fields underpin a wide range of phenomena, from planetary orbits and satellite navigation to geodesy and the study of gravitational waves.