What minimum energy is needed to launch a satellite of mass m from Earth’s surface to a circular orbit at altitude 2R, where Earth’s mass is M and radius R?
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What minimum energy is needed to launch a satellite of mass m from Earth’s surface to a circular orbit at altitude 2R, where Earth’s mass is M and radius R?

G1 Physics · Accepted Answer

Step 1: Initially at rest on Earth’s surface, Eᵢ=−GMm/R. The final circular orbital radius is r=3R, with total energy Eᶠ=−GMm/(2r)=−GMm/(6R). Step 2: Required energy ΔE=Eᶠ−Eᵢ=GMm/R−GMm/(6R)=5GMm/(6R). Final answer: D — 5GMm/(6R).