gravitational field
The vector field g(r) = −GM/r² r̂ giving the acceleration any test mass would experience at each point in space.
Definition
The gravitational field is a map of acceleration: at every point in space, it tells you the direction and magnitude of the gravitational pull a small test mass would feel. For a point mass M, the field is g = −GM/r² directed radially inward. The concept separates the source of gravity (M) from its effect (the acceleration felt by m), which becomes essential when you have many sources or want to describe gravity as a property of space itself.
The field concept leads naturally to gravitational potential Φ = −GM/r, a scalar whose gradient gives the field: g = −∇Φ. Equipotential surfaces are spheres around an isolated mass. The potential energy of a test mass m is U = mΦ = −GMm/r, negative because you must add energy to pull the mass to infinity. This sign convention — zero at infinity, more negative means more tightly bound — runs through all of orbital mechanics.