Question

A satellite is revolving in a circular orbit around the earth with total energy \( E \). Its potential energy in that orbit is

• A. \( \frac{E}{2} \)
• B. \( 2E \)
• C. \( E \)
• D. \( 4E \)

Hint:

The total energy of a satellite in a circular orbit is related to its potential energy by \( E = \frac{U}{2} \), so the potential energy is twice the total energy.

Answer 1

The Correct Option is B

Step 1: Total energy in a circular orbit.
The total energy \( E \) of a satellite in a circular orbit around the Earth is the sum of its kinetic energy \( K \) and potential energy \( U \). For a satellite in orbit, the total energy is given by: \[ E = K + U \] The kinetic energy is \( K = \frac{1}{2} m v^2 \), and the potential energy is \( U = -\frac{GMm}{r} \), where \( m \) is the mass of the satellite, \( v \) is its velocity, \( G \) is the gravitational constant, and \( r \) is the radius of the orbit. Step 2: Relationship between kinetic and potential energy.
The kinetic energy of a satellite in orbit is related to its potential energy by: \[ K = -\frac{U}{2} \] Thus, the total energy is: \[ E = K + U = -\frac{U}{2} + U = \frac{U}{2} \] Therefore, the potential energy \( U \) is: \[ U = 2E \] Step 3: Conclusion.
Thus, the potential energy of the satellite in its orbit is \( 2E \), which corresponds to option (B).