An earth satellite is moving around the earth in circular orbit. IN such case what is conserved

Options

A. velocity
B. linear momentum
C. angular momentum
D. none of the above

Answer

To determine what is conserved when an Earth satellite is moving in a circular orbit around the Earth, we can analyze the forces and motion involved. Here’s a step-by-step solution:

### Step 1: Understand the Forces Acting on the Satellite
The satellite is in a circular orbit due to the gravitational force exerted by the Earth. This gravitational force provides the necessary centripetal force to keep the satellite in its circular path.

### Step 2: Identify the Key Concepts
In a stable circular orbit, several physical quantities can be considered:
- **Gravitational Force:** The force that pulls the satellite towards the Earth.
- **Centripetal Force:** The force required to keep the satellite moving in a circular path.
- **Orbital Velocity:** The speed at which the satellite must travel to maintain its orbit.

### Step 3: Conservation of Angular Momentum
For an object in circular motion, angular momentum is conserved if no external torques are acting on it. The angular momentum \( L \) of the satellite can be expressed as:
\[ L = m \cdot v \cdot r \]
where:
- \( m \) is the mass of the satellite,
- \( v \) is the orbital speed,
- \( r \) is the radius of the orbit.

Since the satellite is moving in a circular path and there are no external torques acting on it, the angular momentum remains constant.

### Step 4: Conservation of Mechanical Energy
In a satellite's orbit, the total mechanical energy (kinetic energy + potential energy) is also conserved. The gravitational potential energy decreases as the satellite moves closer to the Earth, while the kinetic energy increases, but the total remains constant.

### Step 5: Conclusion
In conclusion, when an Earth satellite is moving around the Earth in a circular orbit, the following quantities are conserved:
1. **Angular Momentum**
2. **Mechanical Energy**

### Final Answer
The quantities that are conserved when an Earth satellite is moving in a circular orbit are **angular momentum** and **mechanical energy**.

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