A satellite is moving in a circular orbit round the earth with a diameter of orbit 2R. At a certain point a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially. The resulting orbit of the satellite would be

Options

A. same as before
B. circular orbit with diameter greater than 2R
C. elliptical orbit with minimum distance from the earth equal to R
D. elliptical orbit with maximum distance from the earth equal to R.

Explanation

To solve the problem, we need to analyze the situation of a satellite moving in a circular orbit around the Earth and how its orbit changes when its velocity is increased tangentially.

### Step-by-Step Solution:

1. **Understanding the Initial Orbit:**
- The satellite is initially in a circular orbit with a diameter of \(2R\). Therefore, the radius \(r\) of the orbit is:
\[ r = \frac{2R}{2} = R \]

2. **Calculating Initial Velocity:**
- The velocity \(V\) of a satellite in a circular orbit is given by the formula:
\[ V = \sqrt{\frac{GM}{r}} \]
- Substituting \(r = R\):
\[ V = \sqrt{\frac{GM}{R}} \]

3. **Effect of Firing the Rocket:**
- When the rocket is fired, it increases the satellite's tangential velocity. Let’s denote the new velocity as \(V'\), where:
\[ V' > V \]
- This means that the new velocity is greater than the orbital velocity required for a circular orbit.

4. **Determining the New Orbit:**
- When the satellite's velocity exceeds the circular orbital velocity, it will no longer follow a circular path. Instead, it will enter an elliptical orbit.
- The point at which the rocket is fired becomes the perigee (the closest point to Earth) of the new elliptical orbit.

5. **Finding the Minimum Distance to Earth:**
- In an elliptical orbit, the minimum distance from the Earth (perigee) will be equal to the radius of the original circular orbit, which is \(R\).
- Therefore, the resulting orbit of the satellite will be elliptical with the minimum distance from the Earth equal to \(R\).

### Conclusion:
The resulting orbit of the satellite after the rocket is fired will be an elliptical orbit with a minimum distance from the Earth equal to \(R\).

### Final Answer:
The resulting orbit of the satellite would be **an elliptical orbit with minimum distance from the Earth equal to \(R\)**.

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