A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

Options

A. (a)In the same circular orbit of radius R
B. (b)In an elliptical orbit
C. (c)Such that it escapes to infinity
D. (d)In a circular orbit of a different radius

Explanation

To solve the problem, we need to analyze the situation step by step, focusing on the conservation of momentum and the implications of the collision on the motion of the combined body.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions:**
- We have a satellite of mass \( M \) in a circular orbit of radius \( R \) around the Earth.
- A meteorite of the same mass \( M \) is falling towards the Earth and collides with the satellite.
- Both bodies have the same speed just before the collision.

2. **Conservation of Momentum:**
- Since the collision is completely inelastic, the two bodies will stick together after the collision.
- The total momentum before the collision must equal the total momentum after the collision.
- Let \( v \) be the speed of both the satellite and the meteorite just before the collision.

3. **Calculating the Initial Momentum:**
- The momentum of the satellite before the collision is \( Mv \) (in the direction of its velocity).
- The momentum of the meteorite before the collision is also \( Mv \) (in the direction of its velocity, which is downward towards the Earth).
- Therefore, the total initial momentum \( p_{initial} \) is:
\[ p_{initial} = Mv + Mv = 2Mv \]

4. **Calculating the Final Momentum:**
- After the collision, the combined mass is \( 2M \).
- Let \( V_f \) be the speed of the combined mass after the collision.
- The total final momentum \( p_{final} \) is:
\[ p_{final} = (2M)V_f \]

5. **Setting Initial Momentum Equal to Final Momentum:**
- By conservation of momentum:
\[ 2Mv = (2M)V_f \]
- Dividing both sides by \( 2M \) (assuming \( M \neq 0 \)):
\[ v = V_f \]
- This means the speed of the combined body after the collision is the same as the speed of the satellite (and meteorite) just before the collision.

6. **Analyzing the Motion Post-Collision:**
- The combined body now has a mass of \( 2M \) and is moving with speed \( v \).
- Since the speed remains the same, but the mass has increased, we need to consider the gravitational forces acting on the new body.
- The gravitational force acting on the combined mass will change the dynamics of the orbit.

7. **Determining the New Orbit:**
- The combined body will not be able to maintain a circular orbit due to the change in mass and the dynamics of the gravitational force acting on it.
- The new trajectory will be elliptical because the speed is less than the required speed for a stable circular orbit at that radius \( R \).

### Conclusion:
Thus, the subsequent motion of the combined body after the collision will be in an elliptical orbit.

### Answer:
The correct option is **B: The combined body will move in an elliptical orbit.**