Two satellites are in the parking orbits around the earth. Mass of one is 5 times that of the other. The ratio of their periods of revolution is

Options

A. 1
B. `sqrt(10)`
C. 10
D. 100

Answer

To solve the problem of finding the ratio of the periods of revolution of two satellites with different masses, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Problem**: We have two satellites in a parking orbit around the Earth. The mass of one satellite (let's call it \( m_1 \)) is 5 times that of the other satellite (let's call it \( m_2 \)). We need to find the ratio of their periods of revolution.

2. **Identify the Relevant Formula**: The period of revolution \( T \) of a satellite in orbit is given by the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where \( r \) is the distance from the center of the Earth to the satellite, \( G \) is the gravitational constant, and \( M \) is the mass of the Earth. Importantly, this formula shows that the period \( T \) does not depend on the mass of the satellite.

3. **Set Up the Ratios**: Let \( T_1 \) be the period of the first satellite (mass \( m_1 \)) and \( T_2 \) be the period of the second satellite (mass \( m_2 \)). Since the mass of the first satellite is 5 times that of the second satellite, we have:
\[ m_1 = 5m_2 \]
However, since the period does not depend on the mass of the satellites, we can say:
\[ T_1 = T_2 \]

4. **Calculate the Ratio**: Therefore, the ratio of their periods of revolution is:
\[ \frac{T_1}{T_2} = 1 \]

5. **Conclusion**: The ratio of the periods of revolution of the two satellites is \( 1:1 \).

### Final Answer
The ratio of their periods of revolution is \( 1:1 \).

---