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標題:

college physics

發問:

Find the kinetic energy of a 1700 kg satellite in a circular orbit about the Earth, given that the radius of the orbit is 1.30×104 miles. and How much energy is required to move this satellite to a circular orbit with a radius of 2.70×104 miles?

最佳解答:

Changing to metres, the radius = 1.3 x 104 x 1609 = 2.092 x 107 m Taking mass of earth = 6 x 1024 kg, we have: GMm/r2 = mv2/r mv2/2 = GMm/(2r) = (6.67 x 10-11 x 6 x 1024 x 1700)/(2 x 2.092 x 107) = 1.626 x 1010 J With K.E. = GMm/(2r) and G.P.E. = - GMm/r, we have: Total energy = - GMm/(2r) So when radius of orbit increases from 2.092 x 107 m to 2.7 x 104 x 1609 = 4.344 x 107 m, increase in energy is: (6.67 x 10-11 x 6 x 1024 x 1700)/(2 x 2.092 x 107) - (6.67 x 10-11 x 6 x 1024 x 1700)/(2 x 4.344 x 107) = 8.433 x 109 J

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