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11 July, 15:11

Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 5580 km. Satellite B is to orbit at an altitude of 21000 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit

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  1. 11 July, 17:17
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    =0.43

    Explanation:

    Given

    mv^2/R=GMm/R^2

    Make V the subject

    V^2 = (GM/R)

    For satellite A

    Va^2 = (GM/R) = (GM / (5580+6370) * 10^3)

    Vb^2 = (GM / (21000+6370) * 10^3)

    Va^2 = (GM/11950*10^3)

    Vb^2 = (GM/27370*10^3)

    But kinetic Energy Ek of orbiting object is MV^2/2=GMm/2R

    Hence EkA = GMm/2*11950*10^3)

    EkB = GMm (2*27370*10^3)

    EkB/EkA = 2*11950*10^3/2*27370*10^3

    =0.43
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