When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters small air resistance to its motion. Then

Options

A. its kinetic energy increases
B. its kinetic energy decreases
C. its angular momentum about the earth decreases
D. its period of revolution around the earth increases

Answer

To solve the problem, let's analyze the effects of a satellite entering the atmospheric region on its kinetic energy, angular momentum, and period of revolution.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A satellite is in a circular orbit around the Earth.
- As it enters the atmospheric region, it experiences air resistance, which affects its motion.

2. **Kinetic Energy Analysis**:
- The kinetic energy (KE) of the satellite in orbit can be expressed as:
\[ KE = \frac{GMm}{2R} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( R \) is the distance from the center of the Earth to the satellite.
- When the satellite enters the atmosphere, it moves to a lower orbit, which means \( R \) decreases.
- Since kinetic energy is inversely proportional to \( R \), as \( R \) decreases, the kinetic energy \( KE \) increases.

3. **Angular Momentum Analysis**:
- The angular momentum \( L \) of the satellite can be expressed as:
\[ L = m \cdot v \cdot R \]
where \( v \) is the orbital velocity.
- The orbital velocity \( v \) can be derived from:
\[ v = \sqrt{\frac{GM}{R}} \]
- Substituting for \( v \) in the angular momentum equation gives:
\[ L = m \cdot \sqrt{\frac{GM}{R}} \cdot R = m \cdot \sqrt{G \cdot M \cdot R} \]
- As the satellite enters the atmosphere, \( R \) decreases, which means \( L \) also decreases.

4. **Period of Revolution Analysis**:
- The period \( T \) of revolution can be expressed as:
\[ T = \frac{2\pi R}{v} = 2\pi R \cdot \frac{1}{\sqrt{\frac{GM}{R}}} = 2\pi \sqrt{\frac{R^3}{GM}} \]
- From this equation, we see that the period \( T \) is proportional to \( \sqrt{R^3} \).
- As \( R \) decreases (the satellite moves closer to Earth), the period \( T \) also decreases.

5. **Conclusion**:
- Based on the analysis:
- Kinetic energy increases (Option A is correct).
- Angular momentum decreases (Option C is correct).
- The period of revolution decreases (Option D is incorrect).

### Final Answers:
- **Kinetic Energy**: Increases
- **Angular Momentum**: Decreases
- **Period of Revolution**: Decreases