Learning Objective: Explore how gravitational potential energy varies with distance and calculate the work needed to move between orbits.

Parameters

GPE vs Distance: U = -GMm/r

U = -GMm/r (exact)
U ≈ -mgh (approx)
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 needed to move mass from r₁ to r₂ against gravity
Positive ΔU = energy must be supplied (work done on the system)
Key Concept: The gravitational potential energy U = -GMm/r is always negative for bound systems, approaching zero as r → ∞. The mgh approximation (U ≈ mgh) is only valid near the surface where g is approximately constant — it appears as a tangent line to the exact curve at r = R. Moving to a larger orbit requires positive work (energy input) because ΔU > 0 (U becomes less negative).