Question:

Net force on Artifical satellies - please help...?

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Six artificial satellites complete one circular orbit around a space station in the SAME amount of time. Each satellite has mass m and radius of orbit L. Rank the net forces acting on each satellite from largest to smallest.

A) m = 800kg, L = 5000m

B) m = 300kg, L = 7500m

C) m= 400kg. L = 2500m

D) m = 200kg, L = 5000m

please help me to show the formula for the calculation and the concept behind it... many thanks....

Cheers!

from Singapore......

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  1. assumed time to circulate the orbit = 1

    A) v = (2pi*5000) / 1 =  31,416

    Fg = GMm / (R^2)

    = (6.673E-11*5.98E+24*800) / (6.37E+6)^2

    = 9.83*800 = 7,867

    Fs = (m)(v^2) / (R + L)

    Fs = (800)(31416 ^ 2) / (6.37E+6plus 5000)

    Fs = 123,854

    net = 123854 - 7867 = 115,987 N

    B) v = (2pi7500) / 1= 47,124

    Fg = 9.83 * 300 = 2950

    Fs = 104,457

    net = 104457 - 2950 = 101,507 N

    C) v = (2pi2500) /1 = 15,708

    Fg = 9.83 * 400 = 3934

    Fs = 15,488

    net = 15488 - 3934 = 11,554 N

    D) v = (2pi5000) = 31,416

    Fg = 9.83 * 200 = 1967

    Fs = 30,964

    net = 30964 - 1967 = 28,997 N

    A) largest net thrown out the space first

    B) 2nd

    D) 3rd

    C) last

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