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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?

1. GMm/2R
2. 2GMm/3R
3. 5GMm/6R
4. 2GMm/3R

Correct answer: 5GMm/6R

Solution

The correct option is derived from calculating the gravitational potential energy and the kinetic energy required for the satellite to maintain a stable orbit at the specified altitude. At an altitude of 2R, the total energy needed accounts for both the gravitational pull from the planet and the energy needed to achieve the orbital velocity, leading to the result of 5GMm/6R.

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