wt is d min energy required to launch satellite of mass m from the surface of planet of mass M and radius R in a circular orbit at an altitude of 2R
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Answer: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 ? ... altitude 2R=GMm6R. The gravitational potential energy at altitude 2R=−GMm3R.
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HunterPettigrew1982:
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As we know, Gravitational potential energy = - GM /r
and orbital velocity, v0 = vGM/R+h
Ef = ½ mv20 – GMm/3R = ½ m GM/3R – GMm/3R
= GMm/3R (1/2-1) = - GMm/6R
Ei = - GM/R + K
Ei = Ef
Therefore minimum required energy, K = 5GMm/6R
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