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Gravitational potential (often symbolized by Φ) is a mathematical field (function on spatial dimensions) that indicates the strength of gravity's effect on each point in space. It is the amount of energy required per-unit-mass to move a massive object to an infinite distance ("infinite distance" approximated using the distance to some point that is far from any mass), i.e., the field maps to the gravitational potential energy per unit mass at each point in space; the gravitational potential energy of an actual object located at some point is the object's mass times that location's gravitational potential. The dip in gravitational potential that surrounds something massive is termed a gravitational potential well (gravitational well, or gravity well, or in context, a potential well).
The gradient of the gravitational potential (i.e., the direction and magnitude of its most rapid change over distance) is directly related to the acceleration imposed on something at that point, which is the force per unit mass. As such, the gravitational potential is a scaler field that captures the specifics of a gravitational field, but without directly specifying vectors and direction.
The gravitational potential description of the effects of gravity is useful for dynamics and kinematics, such as orbital mechanics.