L15: Gravitational Potential Explorer

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

Controls

Central Mass M (×10²⁴ kg) 5.97

Gravitational Potential V = -GM/r

V = -GM/r

Slope = -g (field strength)

Work Calculator: W = mΔV

Test Mass m (kg) 100

Point A: r_A (km) 6371

Point B: r_B (km) 15000

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)
• Gravitational field strength g = -dV/dr = GM/r² (points toward mass)
• Work to move mass m between points: W = mΔV = m(V_B - V_A)
• Field lines are always perpendicular to equipotential surfaces