Learning Objective: Explore how gravitational potential energy varies with centre-to-centre radius, calculate ΔU between two radial positions, and distinguish Wg from quasistatic Wext.

Parameters

GPE vs Distance: U = -GMm/r

Your browser does not support the graph canvas. The exact relation is U equals negative GMm divided by r and approaches zero from below.

The green curve is the exact radial potential energy. The dashed orange line, when enabled, is the tangent approximation U(RE) + mgE(r − RE) near Earth’s surface.

U = -GMm/r (exact)
U(RE) + m gEh (local tangent)
Point r₁
Point r₂

Two-Point Comparison

Point 1: r₁ (km from centre)

U₁ = -62.5 GJ

Point 2: r₂ (km from centre)

U₂ = -9.44 GJ
ΔU = U₂ - U₁ = +53.1 GJ
Work by gravity: Wg = −53.1 GJ
For a quasistatic move: Wext = +53.1 GJ
Local constant-field estimate: —; percentage error: —
Key Concept: With U = 0 at infinity, U = -GMm/r is negative at every finite radius and approaches zero from below. Near Earth's surface, the change can be approximated by ΔU ≈ m gEh, or the absolute graph by the tangent U(RE) + m gEh. For an outward quasistatic move, ΔU and Wext are positive while Wg is negative.