Learning Objective: Understand gravitational potential V = -GM/r as a scalar field and its relationship to gravitational field strength g = -dV/dr.

Controls

Gravitational Potential V = -GM/r

V = -GM/r
Slope dV/dr = |g|; signed gᵣ = −dV/dr

Work Calculator: W = mΔV

V at r_A
-62.5 MJ/kg
V at r_B
-26.6 MJ/kg
Work W = m(V_B - V_A)
+3.59 GJ
Key Relationships:
• Gravitational potential V = -GM/r (scalar, units J/kg)
• With outward positive: gr = -dV/dr = -GM/r²; magnitude |g| = GM/r²
• Work to move mass m between points: W = mΔV = m(V_B - V_A)
• Field lines are always perpendicular to equipotential surfaces