The critical speed of a satellite of mass 500 kg is 20 m/s. What is the critical speed of a satellite of mass 1000 kg moving in the same orbit ?

Options

A. 0 m/s
B. 20 km/hour
C. 72 m/s
D. 72 km/hour

Explanation

To find the critical speed of a satellite of mass 1000 kg moving in the same orbit as a satellite of mass 500 kg with a critical speed of 20 m/s, we can follow these steps:

### Step 1: Understand the Concept of Critical Speed
The critical speed (or orbital speed) of a satellite is determined by the gravitational force acting on it and does not depend on the mass of the satellite. The formula for the orbital speed \( v \) of a satellite in a circular orbit is given by:

\[ v = \sqrt{\frac{GM}{R}} \]

where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth (or the central body),
- \( R \) is the radius of the orbit.

### Step 2: Analyze Given Information
We are given that the critical speed of a satellite with a mass of 500 kg is 20 m/s. Since the critical speed does not depend on the mass of the satellite, we can conclude that the critical speed for any satellite in the same orbit will remain constant regardless of its mass.

### Step 3: Apply the Concept to the New Satellite
Since the new satellite has a mass of 1000 kg but is moving in the same orbit, we can directly state that its critical speed will also be the same as that of the 500 kg satellite.

### Step 4: Conclusion
Thus, the critical speed of the satellite of mass 1000 kg moving in the same orbit is:

\[ \text{Critical Speed} = 20 \, \text{m/s} \]

### Summary
The critical speed of a satellite does not depend on its mass but rather on the gravitational parameters of the central body and the radius of the orbit. Therefore, both satellites (500 kg and 1000 kg) have the same critical speed of 20 m/s.

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