A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is
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Question

A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

G1 Physics · Accepted Answer

Initial energy at rest on Earth's surface is Eᵢ = -GMm/R = -mgR. A circular orbit at height R has radius 2R and total energy E𝒇 = -GMm/(4R) = -mgR/4. Rₑquired energy = E𝒇-Eᵢ = 3mgR/4. Correct answer: D.