Energy Required for Satellite Orbit Transfer – Rankers Physics
Topic: Gravitation
Subtopic: Planet and Satellite

Energy Required for Satellite Orbit Transfer

A satellite of mass \(m\) is in a circular orbit of radius \(2R\) about the earth. How much energy is required to transfer it to a circular orbit of radius \(4R\) :  (\(R =\) Radius of earth)
\(\frac{mgR}{8}\)
\(\frac{mgR}{4}\)
\(\frac{mgR}{2}\)
None of these

Solution:

The total energy of a satellite is \(E = -\frac{GMm}{2r}\). The required energy is \(\Delta E = E_f - E_i = -\frac{GMm}{8R} - \left(-\frac{GMm}{4R}\right) = \frac{GMm}{8R}\). Since \(g = \frac{GM}{R^2}\), we get \(\Delta E = \frac{mgR}{8}\).

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