Orbit Shift Energy of Satellite – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

An artificial satellite is moving in a circular orbit of radius \(r\) around a planet. Total energy of satellite is \(E\). Energy required to move this satellite into a new orbit of radius \(2r\), is
\(\frac{E}{4}\)
\(-\frac{E}{4}\)
\(\frac{E}{2}\)
\(-\frac{E}{2}\)

Solution Explained:

To solve this problem, we apply the core principles of Gravitational Potential Energy. Understanding the underlying formula is key to arriving at the correct answer below:

The total energy in orbit is \(E = -\frac{GMm}{2r}\). In the new orbit of radius \(2r\), total energy is \(E' = -\frac{GMm}{4r} = \frac{E}{2}\). The required energy is \(\Delta E = E' - E = \frac{E}{2} - E = -\frac{E}{2}\).

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