Question

How much time will the satellite take to complete one revolution around the Earth? (Radius of Earth = 6400 km.)

Hint:

A geostationary satellite orbits at an altitude of 35780 km and takes 24 hours to complete one revolution, which matches Earth's rotation period.

Answer 1

Step 1: Understanding the given data

• Height of the satellite's orbit: \( h = 35780 \) km
• Radius of Earth: \( R = 6400 \) km
• Tangential velocity: \( v = 3.08 \) km/s

Step 2: Finding the orbital radius
The satellite moves in a circular orbit around Earth. The total orbital radius \( r \) is: \[ r = R + h \] \[ r = 6400 + 35780 = 42180 \text{ km} \]
Step 3: Finding the circumference of the orbit
The satellite travels along a circular path. The circumference (\( C \)) of the orbit is given by: \[ C = 2\pi r \] \[ C = 2 \times 3.1416 \times 42180 \] \[ C \approx 264983.3 \text{ km} \]
Step 4: Calculating the time period
The time period \( T \) is the total distance traveled divided by the velocity: \[ T = \frac{\text{Circumference}}{\text{Velocity}} \] \[ T = \frac{264983.3}{3.08} \] \[ T \approx 86000 \text{ seconds} \] Converting to hours: \[ T = \frac{86000}{3600} \approx 23.89 \text{ hours} \] Thus, the time taken by the satellite to complete one revolution is approximately 24 hours.