A: When a satellite is orbiting then no energy is required to keep moving n its orbit .
R : The total mechanical energy of a satellite is conserved .

Options

A. If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)
C. If Assertion is true statement but Reason is false , then mark (3)
D. It will move the same speed , tangentially to the spacecraft

Answer

To solve the question regarding the assertion and reason about a satellite in orbit, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that when a satellite is orbiting, no energy is required to keep it moving in its orbit. This means that once the satellite is in motion, it does not need additional energy to maintain that motion.

2. **Analyzing the Forces Acting on the Satellite**:
- A satellite in orbit experiences a gravitational force acting towards the planet. This force provides the necessary centripetal force that keeps the satellite in its circular path.
- The gravitational force (Fg) can be expressed as \( F_g = \frac{GMm}{r^2} \), 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.

3. **Centripetal Force Requirement**:
- For a satellite to remain in a stable orbit, the gravitational force must equal the required centripetal force, which can be expressed as \( F_c = \frac{mv^2}{r} \).
- Therefore, we have \( \frac{GMm}{r^2} = \frac{mv^2}{r} \). This shows that the gravitational force is providing the necessary centripetal force for the satellite's motion.

4. **Work Done on the Satellite**:
- Work done is defined as the force applied in the direction of displacement. In the case of a satellite in orbit, the gravitational force acts towards the center of the planet, while the satellite's displacement is tangential to the orbit.
- Since the gravitational force and the direction of the satellite's motion are perpendicular, the work done by the gravitational force on the satellite is zero (Work = Force × Displacement × cos(θ), where θ = 90°).

5. **Conservation of Mechanical Energy**:
- Since no work is done on the satellite, there is no energy loss, and thus the total mechanical energy of the satellite (kinetic + potential energy) remains constant throughout its orbit.
- This conservation of mechanical energy implies that the satellite does not require any additional energy to maintain its motion.

6. **Understanding the Reason (R)**:
- The reason states that the total mechanical energy of a satellite is conserved. This is indeed true because, as established, no work is done on the satellite, leading to the conservation of its mechanical energy.

7. **Conclusion**:
- Both the assertion and the reason are true. The reason correctly explains the assertion. Therefore, the correct answer is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.

### Final Answer:
Both assertion (A) and reason (R) are true, and R is the correct explanation of A.

---