D.1.11 (HL)—Gravitational equipotentials

Define an equipotential

An equipotential surface is a surface on which every point has the same gravitational potential $V_g$. Moving a mass along one equipotential gives $\Delta V_g=0$, so no work is done by the field and no external work is required for quasistatic motion along the surface.

Read the geometry

Around an isolated spherical mass, equipotential surfaces are concentric spheres; in a two-dimensional diagram they appear as concentric circles. For multiple masses, the shape is distorted by the scalar sum of the individual potentials. The numerical spacing of drawn surfaces is a choice, so use labelled potential values rather than assuming equal physical spacing means equal potential difference.

Compare movements

The external work needed to move a mass slowly between surfaces is $W_{\text{on}}=m\Delta V_g$. The greatest work for a fixed mass occurs for the largest potential difference, not automatically for the longest geometric path. Equipotentials help identify where the potential changes and where the field is strong.

Common trap

Do not claim that every move between nearby-looking surfaces requires equal work. Read the potential labels and the starting and ending surfaces; motion along one surface has zero potential difference.