If height of a satellite from the surface of earth is increased , then its

Options

A. Potential energy will increase
B. Kinetic energy will decrease
C. Total energy will increase
D. All of these

Answer

To solve the question regarding the effects of increasing the height of a satellite from the surface of the Earth, we will analyze the potential energy, kinetic energy, and total energy of the satellite step by step.

### Step-by-Step Solution:

1. **Understanding the System**:
- A satellite is orbiting the Earth at a certain height. We denote the mass of the satellite as \( m \) and the mass of the Earth as \( M \). The distance from the center of the Earth to the satellite is \( R \) (which is the radius of the Earth plus the height of the satellite).

2. **Potential Energy**:
- The gravitational potential energy \( U \) of the satellite at a distance \( R \) from the center of the Earth is given by the formula:
\[ U = -\frac{GMm}{R} \]
- If the height of the satellite increases, the value of \( R \) increases. Since \( U \) is negative, increasing \( R \) (the denominator) makes the absolute value of \( U \) smaller, which means that the potential energy is increasing (becoming less negative).

3. **Kinetic Energy**:
- The kinetic energy \( K \) of the satellite in orbit is given by:
\[ K = \frac{GMm}{2R} \]
- As \( R \) increases, the kinetic energy \( K \) decreases because it is inversely proportional to \( R \).

4. **Total Energy**:
- The total energy \( E \) of the satellite is the sum of its kinetic and potential energy:
\[ E = K + U = \frac{GMm}{2R} - \frac{GMm}{R} \]
- Simplifying this gives:
\[ E = -\frac{GMm}{2R} \]
- Since \( E \) is also negative and inversely proportional to \( R \), as \( R \) increases, the magnitude of \( E \) decreases, meaning the total energy is increasing (becoming less negative).

5. **Conclusion**:
- Based on the analysis:
- Potential energy increases (becomes less negative).
- Kinetic energy decreases.
- Total energy increases (becomes less negative).
- Therefore, the correct answer is that all of these changes occur.

### Final Answer:
All of these (Potential energy increases, Kinetic energy decreases, Total energy increases).

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