To solve this question, we need to understand the relationship between kinetic energy, potential energy, and total energy for an artificial satellite moving in a circular orbit around the Earth.
When a satellite revolves around Earth in a circular orbit:
- The total energy \( E_0 \) of the satellite is given by the sum of its kinetic energy \( K \) and potential energy \( U \).
- The formula for total energy of a satellite in orbit is: \(E_0 = K + U\).
- The potential energy \( U \) of a satellite at a distance \( r \) from the center of the Earth (where \( r \) is the radius of the orbit) is given by \(U = -\frac{GMm}{r}\), where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( m \) is the mass of the satellite.
- The kinetic energy \( K \) of the satellite is given by the formula \(K = \frac{1}{2} \frac{GMm}{r}\).
- The relationship between kinetic and potential energy is: \(K = -\frac{1}{2}U\). Thus, \(U = -2K\).
Substituting these into the total energy equation: \(E_0 = K + U = K - 2K = -K\).
This implies that \(K = -E_0\) (since kinetic energy must be positive, we have \(E_0 = -K\)). Therefore, \(U = 2 \times -E_0 = -2E_0\).
Thus, to find the potential energy \( U \): \(U = 2E_0\).
Therefore, the potential energy of the satellite is 2\(E_0\).