The distance of geostationary satellite from the centre of the earth (radius R) is nearest to

Options

A. (a)18 R
B. (b)10 R
C. (c)7 R
D. (d)5 R

Answer

To find the distance of a geostationary satellite from the center of the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Geostationary Satellites**:
- A geostationary satellite orbits the Earth at a height where it appears to be stationary relative to a point on the Earth's surface. This occurs at a specific altitude above the Earth's equator.

2. **Know the Altitude of Geostationary Satellites**:
- The altitude of a geostationary satellite is approximately 36,000 kilometers above the Earth's surface.

3. **Determine the Radius of the Earth**:
- The average radius of the Earth (R) is approximately 6,400 kilometers.

4. **Calculate the Total Distance from the Center of the Earth**:
- To find the total distance (D) from the center of the Earth to the geostationary satellite, we need to add the radius of the Earth to the altitude of the satellite:
\[ D = \text{Altitude of satellite} + \text{Radius of Earth} \]
\[ D = 36,000 \text{ km} + 6,400 \text{ km} \]
\[ D = 42,400 \text{ km} \]

5. **Express the Distance in Terms of Earth's Radius**:
- We can express this distance in terms of the Earth's radius (R):
\[ D = 42,400 \text{ km} = \frac{42,400}{6,400} R \]
- Simplifying this gives:
\[ D = \frac{424}{64} R \approx 6.625 R \]
- Rounding this to the nearest whole number gives approximately:
\[ D \approx 7 R \]

6. **Conclusion**:
- Therefore, the distance of the geostationary satellite from the center of the Earth is approximately \( 7R \).

### Final Answer:
The distance of the geostationary satellite from the center of the Earth is nearest to \( 7R \).