The PE of a satellite is -U . Its KE is

Options

A. U
B. 2U
C. `-U`
D. `U//2`

Answer

To find the kinetic energy (KE) of a satellite given its potential energy (PE) as -U, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Potential Energy**:
The potential energy (PE) of a satellite in orbit around a planet is given by the formula:
\[ PE = -\frac{G M m}{r} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the planet, \( m \) is the mass of the satellite, and \( r \) is the distance from the center of the planet to the satellite.

2. **Given Information**:
According to the problem, the potential energy of the satellite is given as:
\[ PE = -U \]
This implies:
\[ -\frac{G M m}{r} = -U \quad \Rightarrow \quad \frac{G M m}{r} = U \]

3. **Finding Kinetic Energy**:
The kinetic energy (KE) of the satellite can be expressed in terms of its orbital velocity (\( v_0 \)):
\[ KE = \frac{1}{2} m v_0^2 \]
The orbital velocity \( v_0 \) can be derived from the gravitational force acting on the satellite, which provides the necessary centripetal force for circular motion:
\[ \frac{G M m}{r^2} = \frac{m v_0^2}{r} \]
From this equation, we can solve for \( v_0^2 \):
\[ v_0^2 = \frac{G M}{r} \]

4. **Substituting into Kinetic Energy**:
Now, substituting \( v_0^2 \) into the kinetic energy formula:
\[ KE = \frac{1}{2} m \left(\frac{G M}{r}\right) \]

5. **Relating Kinetic Energy to Potential Energy**:
We already established that:
\[ U = \frac{G M m}{r} \]
Therefore, we can express the kinetic energy in terms of \( U \):
\[ KE = \frac{1}{2} U \]

6. **Final Answer**:
Thus, the kinetic energy of the satellite is:
\[ KE = \frac{U}{2} \]

### Conclusion:
The kinetic energy of the satellite is \( \frac{U}{2} \).