Binding EnergyHardQuestion 30715
Question
The minimum energy needed to move a satellite of mass m from Earth's surface (radius R) to infinity is:
- AmgR
- BmgR/2Correct
- C2mgR
- DmgR/4
Correct answer
mgR/2
Explanation
E_binding = −(Total mechanical energy at surface) = −(KE + PE). At rest on surface: KE = 0, PE = −GMm/R = −mgR. Binding energy = mgR. To escape to infinity (U = 0): need mgR of energy. But for a satellite in orbit at surface radius: E_total = −GMm/2R = −mgR/2. Binding energy for orbiting satellite = mgR/2.