Question

A constant potential energy of a satellite is given as \[ PE = r \cdot KE \] where PE = potential energy and KE = kinetic energy. The value of \( r \) will be

• A. \( -1 \)
• B. \( -2 \)
• C. \( -\frac{1}{2} \)
• D. \( -\frac{3}{2} \)

Hint:

In gravitational orbits, \( PE = -2 \cdot KE \). Always remember the sign conventions.

Answer 1

The Correct Option is B

For a satellite in a stable circular orbit: - Kinetic Energy: \[ KE = \frac{GMm}{2r} \] - Potential Energy: \[ PE = - \frac{GMm}{r} \] Dividing: \[ \frac{PE}{KE} = \frac{- \frac{GMm}{r}}{ \frac{GMm}{2r}} = -2 \] So, \[ PE = -2 \cdot KE \Rightarrow r = -2 \]