physics 1

A satellite is in a circular orbit about the earth (ME = 5.98 x 1024 kg). The period of the satellite is 1.77 x 104 s. What is the speed at which the satellite travels?

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  1. F = G Mm/R^2 = m v^2/R

    v^2 R = G M = 6.67*10^-11 * 5.98*10^24
    v^2 R = 39.9 * 10^13

    v T = circumference = 2 pi R
    so
    R = v T/(2 pi)
    R = v [1.77*10^4/(2 pi)]
    R = 2.82*10^3 v
    so
    v^3 (2.82*10^3) = 39.9 * 10^13
    v^3 = 14.1 * 10^10 = 141 * 10^9
    v = 5.2 * 10^3
    v = 5,200 m/s

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  2. v =1.01 m/s

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  3. a lot

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