A 201-kg satellite is in circular orbit around the Earth and moving at a speed o

Question

A 201-kg satellite is in circular orbit around the Earth and moving at a speed of 2.97 km/s. How much work must be done to move the satellite into another circular orbit that is twice as high above the surface of the Earth?

Explanation / Answer

At initial position GMm/r^2 = mv^2/r => r = GM/v^2 = 45194.75 Km now increasing height to double = 90 389.5 km Total energy in orbit = -GMm/2r now from 1st position to the 2nd we have TE = GMm/2(1/r2 -1/r1) = GMm/2(1/90 389.5 - 1/45194.75) = -GMm/(2*90 389.5*10^3) = -443.25*10^6 J so energy needed is = 443.25*10^6 J

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