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A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. The time-period of a spy satellite orbiting a few hundred kilometers above the earth's surface will approximately be (Radius of earth = 6400 km).
  • a)
    1/2h
  • b)
    1 h
  • c)
    2 h
  • d)
    4 h
Correct answer is option 'C'. Can you explain this answer?
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Geostationary Satellite and Spy Satellite

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. The time-period of a spy satellite orbiting a few hundred kilometers above the earths surface will approximately be (Radius of earth = 6400 km).

Formula Used

For a circular orbit, the time period is given by the formula:

T = 2πr/v

where T is the time period, r is the radius of the orbit, and v is the velocity of the satellite.

Calculation

- Radius of the spy satellite orbit = radius of the earth + a few hundred kilometers = 6400 + 500 = 6900 km
- Velocity of the spy satellite = √(GM/R), where G is the universal gravitational constant, M is the mass of the earth, and R is the distance between the center of the earth and the spy satellite.
- Velocity of the spy satellite = √(6.67 × 10^-11 × 5.97 × 10^24 / 6.9 × 10^6) = 7.9 km/s (approx.)
- Time period of the spy satellite = 2πr/v = 2π × 6900 / 7.9 = 110 minutes (approx.)

Conclusion

Therefore, the time period of the spy satellite orbiting a few hundred kilometers above the earth's surface will approximately be 2 hours (option C).
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