The height of communication statellite from the surface of the earth is approximately

Options

A. `36 xx 10^(3) km`
B. `36 km`
C. `36 xx 10^(4) km`
D. `36 xx 10^(2) km`

Answer

To determine the height of a communication satellite from the surface of the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Geostationary Satellites**:
- Geostationary satellites are used for communication purposes. They orbit the Earth at a height where they can remain stationary relative to a point on the Earth's surface.

2. **Height Calculation**:
- The height \( h \) of a geostationary satellite can be derived from the formula:
\[ h = \frac{T^2 \cdot g \cdot R^2}{4 \pi^2} - R \]
where:
- \( T \) is the time period of the satellite (24 hours),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( R \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \, \text{m} \)).

3. **Convert Time Period to Seconds**:
- Since \( T \) is given in hours, convert it to seconds:
\[ T = 24 \, \text{hours} = 24 \times 60 \times 60 = 86400 \, \text{seconds} \]

4. **Substituting Values**:
- Substitute \( T \), \( g \), and \( R \) into the formula:
\[ h = \frac{(86400)^2 \cdot 9.8 \cdot (6.4 \times 10^6)^2}{4 \pi^2} - 6.4 \times 10^6 \]

5. **Calculating the Height**:
- After performing the calculations, we find:
\[ h \approx 3.6 \times 10^7 \, \text{meters} \]

6. **Convert to Kilometers**:
- To convert meters to kilometers, divide by 1000:
\[ h \approx 3.6 \times 10^7 \, \text{m} = 36 \times 10^3 \, \text{km} \]

7. **Final Answer**:
- The height of the communication satellite from the surface of the Earth is approximately \( 36 \times 10^3 \, \text{km} \).

### Final Answer:
The height of the communication satellite from the surface of the Earth is approximately \( 36 \times 10^3 \, \text{km} \).

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