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 a

Question

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 6370 km. Satellite B is to orbit at an altitude of 19 110 km. The radius of Earth RE is 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? (b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? (c) Which satellite has the greater total energy if each has a mass of 14.6 kg? (d) By how much?

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Maris 2 months 2021-07-29T05:16:06+00:00 1 Answers 7 views 0

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    2021-07-29T05:17:44+00:00

    Answer:

    Explanation:

    Orbital radius of satellite A , Ra = 6370 + 6370 = 12740 km

    Orbital radius of satellite B , Rb = 6370 + 19110 = 25480 km

    Orbital potential energy of a satellite = – GMm / r where G is gravitational constant , M is mass of the earth and m is mass of the satellite

    Orbital potential energy of a satellite A = – GMm / Ra

    Orbital potential energy of a satellite B = – GMm / Rb

    PE of satellite B /PE of satellite A

    =  Ra / Rb

    = 12740 / 25480

    = 1 / 2

    b ) Kinetic energy of a satellite is half the potential energy with positive value , so ratio of their kinetic energy will also be same

    KE of satellite B /KE of satellite A

    = 1 / 2

    c ) Total energy will be as follows

    Total energy = – PE + KE

    – P E + PE/2

    = – PE /2

    Total energy of satellite B / Total energy of A

    = 1 / 2

    Satellite B will have greater total energy because its negative value is less.

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