The time period of a geostationary satellite is

Options

A. 12 hours
B. 24 hours
C. 36 hours
D. 48 hours

Answer

To determine the time period of a geostationary satellite, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Geostationary Satellites**:
A geostationary satellite is one that orbits the Earth at the same rotational speed as the Earth itself. This means that it appears to be stationary relative to a point on the Earth's surface.

2. **Angular Velocity**:
The angular velocity (\( \omega \)) of the Earth can be calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
where \( T \) is the time period of the Earth's rotation. For Earth, \( T \) is 24 hours.

3. **Time Period of Earth**:
The time period of the Earth’s rotation is:
\[ T_{earth} = 24 \text{ hours} = 24 \times 3600 \text{ seconds} = 86400 \text{ seconds} \]

4. **Equating Angular Velocities**:
For a geostationary satellite, its angular velocity must equal that of the Earth:
\[ \omega_{satellite} = \omega_{earth} \]

5. **Time Period of the Satellite**:
Since the angular velocities are equal, the time period of the geostationary satellite (\( T_{satellite} \)) is equal to the time period of the Earth:
\[ T_{satellite} = T_{earth} = 24 \text{ hours} \]

6. **Conclusion**:
Therefore, the time period of a geostationary satellite is 24 hours.

### Final Answer:
The time period of a geostationary satellite is **24 hours**.

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