An artificial satellite moving in a circular orbit around the earth has a total energy `E_(0)`. Its potential energy is

Options

A. 1. `-E_(0)`
B. 2. `E_(0)`
C. 3. `2E_(0)`
D. 4. `-2E_(0)`

Explanation

To find the potential energy of an artificial satellite moving in a circular orbit around the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Total Energy of the Satellite**:
The total energy \( E \) of a satellite in a circular orbit is given by the formula:
\[ E = -\frac{GMm}{2r} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the satellite,
- \( r \) is the distance from the center of the Earth to the satellite.

2. **Setting Total Energy Equal to Given Value**:
According to the problem, the total energy is given as \( E_0 \). Therefore, we can write:
\[ -\frac{GMm}{2r} = E_0 \]

3. **Finding Potential Energy**:
The potential energy \( U \) of the satellite in orbit is given by the formula:
\[ U = -\frac{GMm}{r} \]

4. **Relating Potential Energy to Total Energy**:
From the expression for total energy, we can express potential energy in terms of total energy:
\[ U = 2E \]
Substituting \( E = E_0 \):
\[ U = 2E_0 \]

5. **Final Expression for Potential Energy**:
Thus, the potential energy \( U \) of the satellite is:
\[ U = -2E_0 \]

### Final Answer:
The potential energy of the artificial satellite is:
\[ U = -2E_0 \]