13.4.3—The concept of gravitational potential leads to the gravitational potential

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.