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?A. `(5Gm M)/(6R)`B. `(2Gm M)/(3R)`C. `(Gm M)/(2R)`D. `(Gm M)/(3R)`

What is the minimum energy required to launch a satellite of mass m fr

1.	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?A. `(5Gm M)/(6R)`B. `(2Gm M)/(3R)`C. `(Gm M)/(2R)`D. `(Gm M)/(3R)`
Answer» Correct Answer - A Let `K` be the `KE` given to the satellite on the surface if earth to take it to the desired location. Following the law of conservation of total energy, we have `-(G mM)/(R ) + K = - (G mM)/((2R +R)) + (1)/(2)m((GM)/(3R))` `= - (GM m)/(3R) + (GM m)/(6R) = - (GM m)/(6R)` or `K = (GM m)/(R ) - (GM m)/(6R) = (5GM m)/(6R)`

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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?A. `(5Gm M)/(6R)`B. `(2Gm M)/(3R)`C. `(Gm M)/(2R)`D. `(Gm M)/(3R)`

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