If radius of an orbitating satellite is decreased , then its kinetic energy

Options

A. And potential energy decrease
B. And potential energy increase
C. Decrease and potential energy increases
D. Increases and potential energy decreases

Answer

To solve the problem of how the kinetic energy of an orbiting satellite changes when its radius is decreased, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between kinetic energy and radius**:
The kinetic energy (KE) of a satellite in orbit is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is the mass of the satellite and \(v\) is its orbital velocity.

2. **Relate orbital velocity to gravitational force**:
The gravitational force provides the necessary centripetal force for the satellite's circular motion. Therefore, we can equate the gravitational force to the centripetal force:
\[ \frac{GMm}{r^2} = \frac{mv^2}{r} \]
where \(G\) is the gravitational constant, \(M\) is the mass of the Earth, and \(r\) is the radius of the orbit.

3. **Solve for orbital velocity**:
Rearranging the equation gives us:
\[ v^2 = \frac{GM}{r} \]
Thus, we can express the kinetic energy in terms of \(r\):
\[ KE = \frac{1}{2} m \left(\frac{GM}{r}\right) = \frac{GMm}{2r} \]

4. **Analyze the effect of decreasing radius**:
If the radius \(r\) is decreased, the kinetic energy becomes:
\[ KE \propto \frac{1}{r} \]
This means that as \(r\) decreases, \(KE\) increases.

5. **Consider potential energy**:
The gravitational potential energy (PE) of the satellite is given by:
\[ PE = -\frac{GMm}{r} \]
As the radius \(r\) decreases, the absolute value of potential energy increases (becomes less negative), indicating that potential energy is increasing.

6. **Conclusion**:
From the analysis:
- Kinetic energy increases as the radius decreases.
- Potential energy increases (less negative) as the radius decreases.

Thus, the correct answer is that the kinetic energy increases and the potential energy decreases.

### Final Answer:
**Kinetic energy increases and potential energy decreases.**