A satellite in a circular orbit of radius r_1 has total energy E_1. It is transferred to a higher circular orbit of radius r_2 = 2*r_1. How much work was done by its propulsion system during this transfer?
Answer and explanation
Correct answer: D. G M m / (4 * r_1)
- Step 1: Initial energy: E_1 = -GMm / (2*r_1).
- Step 2: Final energy: E_2 = -GMm / (2r_2) = -GMm / (4r_1).
- Step 3: Work done: W = Delta E = E_2 - E_1 = -GMm / (4r_1) - (-GMm / (2r_1)) = GMm / (4*r_1).
Answer
G M m / (4 * r_1).
Why not the others: GMm / (2r_1) computes the difference in potential energy alone; negative work implies energy was removed; 3GMm / (4*r_1) adds energies instead of taking their difference.
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