13.4 Gravitational potential

Gravitational potential at a point is the work done per unit mass by an external agent bringing a small mass from infinity to that point, with zero potential at infinity.

For an attractive field around a point mass, potential is negative because the field releases energy as the mass moves inward.

Moving a test mass farther from a planet raises its gravitational potential toward zero.

Potential is energy per unit mass, not force; equal potential does not imply equal field strength everywhere.

For a point mass, gravitational potential Φ is work done per unit mass from infinity and equals Φ=−GM/r.

The negative sign reflects attraction: moving a mass inward releases energy, while moving it outward requires work. Use centre distance r.

At twice the distance from a planet’s centre, potential is half as negative and closer to zero.

Potential is not the same as field strength g; Φ can be negative while g is a positive magnitude directed inward.

A potential difference ∆Φ is energy transferred per unit mass; a mass m changes gravitational potential energy by ∆E_P=m∆Φ.

Use the sign to determine whether the field or an external agent supplies energy, and choose a reference consistently.

Moving outward from a planet raises Φ toward zero, so an external agent does positive work against gravity.

Equal potential difference does not imply equal force over a path; field strength is the spatial rate of potential change.