Time period of a satellite in a circular obbit around a planet is independent of

Options

A. Radius of the orbit
B. Mass of the planet
C. Mass of the statellite
D. Radius of the planet

Answer

To determine the factors on which the time period of a satellite in a circular orbit around a planet is independent, we can analyze the formula for the time period of a satellite.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The time period \( T \) of a satellite in a circular orbit is given by the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where:
- \( T \) = time period of the satellite,
- \( r \) = radius of the orbit (distance from the center of the planet to the satellite),
- \( G \) = universal gravitational constant,
- \( M \) = mass of the planet.

2. **Identifying Dependencies**:
From the formula, we can see that the time period \( T \) depends on:
- The radius \( r \) of the orbit (the distance from the center of the planet to the satellite).
- The mass \( M \) of the planet.

3. **Independence from Other Factors**:
The time period \( T \) does not depend on:
- The mass of the satellite itself.
- The radius of the orbit in terms of the specific mass of the satellite.
- The specific shape of the orbit (as long as it remains circular).

4. **Conclusion**:
Therefore, we conclude that the time period of a satellite in a circular orbit around a planet is independent of:
- The mass of the satellite,
- The mass of the planet (as long as the radius is considered),
- The radius of the orbit in terms of the satellite's mass.

### Final Answer:
The time period of a satellite in a circular orbit around a planet is independent of the mass of the satellite and the mass of the planet.