Hohmann Transfer EnergyHardQuestion 30749
Question
A spacecraft moves from circular orbit r₁ to r₂ (r₂ > r₁) via Hohmann transfer. Total energy change is:
- A−GMm(1/r₁ − 1/r₂)/2
- BGMm(1/r₁ − 1/r₂)/2Correct
- C−GMm/2r₁
- DGMm/r₂
Correct answer
GMm(1/r₁ − 1/r₂)/2
Explanation
E₁ = −GMm/2r₁. E₂ = −GMm/2r₂. ΔE = E₂−E₁ = −GMm/(2r₂) + GMm/(2r₁) = GMm(1/r₁−1/r₂)/2 > 0 (energy input needed for higher orbit).