D.1.6 (HL)—Gravitational potential energy

Define the reference

Gravitational potential energy is defined as the work done to assemble the masses of a system from infinite separation. Set the potential energy at infinite separation to zero. Because gravity is attractive, bringing masses together releases energy, so the gravitational potential energy of a bound system is negative.

Interpret the sign

Moving a mass farther from an attracting body increases gravitational potential energy toward zero and requires positive external work if done slowly. Moving it inward makes the potential energy more negative; the gravitational field can do positive work and transfer potential energy into kinetic energy.

Use the field model

Gravitational force is conservative, so the work between two fixed positions depends only on the endpoints, not the path. Near Earth’s surface, where $g$ is approximately constant, changes can be approximated by $\Delta E_p=mg\Delta h$; for large distances use the field-based potential model rather than a constant-g approximation.

Common trap

Do not make gravitational potential energy positive simply because the mass is high above a planet. With zero at infinity, every finite point in the isolated attractive field has negative potential energy.