Energy of a Satellite in Orbit – Rankers Physics
Topic: Gravitation
Subtopic: Planet and Satellite

Energy of a Satellite in Orbit

The energy required to put a satellite of mass \(m\) from earth surface into a orbit of radius \(2R\) is \(E_1\). The energy further needed to change the orbit of this satellite from its present orbit to radius \(4R\) is \(E_2\). The ratio \(\frac{E_1}{E_2}\) is (where \(R\) is radius of earth:
\(4 : 1\)
\(1 : 4\)
\(6 : 1\)
\(1 : 6\)

Solution:

The energy required to put a satellite in orbit from earth's surface is \(E_1 = -\frac{GMm}{2(2R)} - \left(-\frac{GMm}{R}\right) = \frac{3GMm}{4R}\). The energy to change orbit from \(2R\) to \(4R\) is \(E_2 = -\frac{GMm}{2(4R)} - \left(-\frac{GMm}{2(2R)}\right) = \frac{GMm}{8R}\). Thus, \(\frac{E_1}{E_2} = 6\), which gives the ratio \(6 : 1\).

Leave a Reply

Your email address will not be published. Required fields are marked *