Question

A satellite of mass \(m\) rotates round the earth in a circular orbit of radius \(R\). If the angular momentum of the satellite is \(J\), then its kinetic energy (\(K\)) and the total energy (\(E\)) of the satellite are:

• A. \(K = \frac{J^2}{mR^2}, \, E = \frac{J^2}{2mR^2}\)
• B. \(K = \frac{J^2}{2mR^2}, \, E = -\frac{J^2}{2mR^2}\)
• C. \(K = \frac{J^2}{2mR^2}, \, E = -\frac{J^2}{mR^2}\)
• D. \(K = \frac{J^2}{mR^2}, \, E = -\frac{J^2}{2mR^2}\)

Hint:

For orbital motion, the total energy is negative and is equal to the kinetic energy but with a negative sign. Use the angular momentum formula to find relationships between kinetic and potential energy.