Gravitational Potential
V(r) = −GM/r — well shape with smooth transition at the surface.
Key Notes
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.
Formulas
Potential due to point mass
Defined so V → 0 at r → ∞.
Field from potential
Field points toward decreasing potential.
Work done by gravity
Positive when moving 'down' in potential.
Inside uniform sphere
More negative than surface; minimum at center.
Superposition
Scalar sum over all sources.
Important Points
Gravitational potential is always NEGATIVE (taking V(∞) = 0). It is most negative near masses.
Force points 'downhill' — toward more negative potential.
Potential is a SCALAR — easier to compute than the vector field.
Equipotential surfaces are perpendicular to field lines. No work done moving along them.
Surface of Earth is approximately an equipotential — slight deviations exist (geoid).
Combining gravity with rotation gives an EFFECTIVE potential whose equipotentials are oblate spheroids.
Gravitational Potential notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.