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 question regarding the effect of decreasing the radius of an orbiting satellite on its kinetic energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between orbital radius and velocity**:
The orbital velocity \( V \) of a satellite is given by the formula:
\[ V = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the central body (e.g., Earth), and \( r \) is the radius of the orbit.

2. **Analyze the effect of decreasing the radius**:
If the radius \( r \) is decreased, the value of \( V \) will increase because \( V \) is inversely proportional to the square root of \( r \).

3. **Relate velocity to kinetic energy**:
The kinetic energy \( KE \) of the satellite can be expressed as:
\[ KE = \frac{1}{2} mv^2 \]
Substituting the expression for \( V \) into the kinetic energy formula, we get:
\[ KE = \frac{1}{2} m \left(\sqrt{\frac{GM}{r}}\right)^2 = \frac{GMm}{2r} \]

4. **Determine the effect on kinetic energy when radius decreases**:
From the equation \( KE = \frac{GMm}{2r} \), we can see that as \( r \) decreases, \( KE \) increases because \( KE \) is inversely proportional to \( r \).

5. **Conclusion**:
Therefore, if the radius of an orbiting satellite is decreased, its kinetic energy increases.

### Final Answer:
If the radius of an orbiting satellite is decreased, then its kinetic energy increases.