A satellite is in a circular orbit about the earth (M_{E} = 5.98 x 10^{24} kg). The period of the satellite is 2.09 x 10^{4} s. What is the speed at which the satellite travels?

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First we find the radius R of the orbit:

R = cubed root of (T^2*G*Me / 4*pi^2) where T is the period

= cubed root of ((2.09x10^4)^2*6.673x10^-11*5.98x10^24 / 4*pi^2)

= 1.64x10^7 m

Then velocity is

v = sqrt(G*Me / R)

= sqrt(6.673x10^-11*5.98x10^24 / 1.64x10^7)

= 4932.75 m/s

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