If M and m represent the mass of Earth and mass of a satellite respectively; then the orbital speed v of satellite in a circular orbit of radius r around Earth will be:
Correct answer: A. v2 = GM/r
- A. v2 = GM/r
- B. v2= √GM/r
- C. v2= √r/GM
- D. v2= √2GM/r
- E. v2= √2r/GM
Explanation
In a circular orbit, the gravitational force on the satellite provides the necessary centripetal force to keep the satellite moving in a circle. The gravitational force between Earth and the satellite is given by: F = G(Mm)/r2 where G is the universal gravitational constant. Since the gravitational force provides the centripetal force, we have: F = mv2/r Equating the above two equations, we get: G(Mm)/r2 = mv2/r Simplifying this equation, we get: v2 = GM/r Therefore, the speed of a satellite in a circular orbit of radius r around Earth is given by v2 = GM/r.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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