Gravitational Potential

Gravitational potential V at a point is the work done per unit mass in bringing a test mass from infinity to that point (against gravity).

For a point mass M: V(r) = −GM/r. Always negative (potential is zero at infinity, decreases as you approach).

Potential is a SCALAR. Add potentials directly (not vector addition) for multiple sources.

Gravitational field g = −∇V — points 'downhill' on the potential.

Potential difference does work on a moving mass: W = −m·(V_B − V_A). Moving DOWN potential gives KE.

On Earth's surface: V_surface = −GM/R ≈ −6.25 × 10⁷ J/kg.

For a uniform sphere outside: V(r) = −GM/r (like a point mass). Inside: V(r) = −GM(3R² − r²)/(2R³).

Equipotential surfaces are perpendicular to gravitational field lines — flat ground locally, spheres around a point mass.