Question

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Resources Give Up? Efendi Consider a 455 kg satellite in a circular orbit at a distance of 3.06 x 10 km above the Earth's surface. What is the minimum amount of work W the satellite's thrusters must do to raise the satellite to a geosynchronous orbit? Geosynchronous orbits occur at approximately 3.60 x 10 km above the Earth's surface. The radius of the Earth and the mass of the Earth are Re 6.37 x 10 km and Me = 597 x 10 kg, respectively. The gravitational constant G = 6.67 x 10-' m /kg s? Assume the change in mass of the satellite is negligible. W 4.276 x102

Answer 1

workdone needed to make satellite reach the Geosynchronous orbit

W = kE at that orbit + gravitational k

potential energy

W = 0.5 m vo^2 - GMm / ( R+h).... (i)

as we know orbital velocity

vo^2 = GM / (R + h)

putting in (i)

W = 0.5 m GM / (R +h) - GM m /( R +h)

W = - 0.5 GMm/(R+h)

W = - 0.5*6.67* 10^-11* 5.97* 10^24* 455/ ( 6.37* 10^6 + 3.06* 10^7)

W = - 2.45* 10^9 J

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