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

Question

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 7590 km. Satellite B is to orbit at an altitude of 15800 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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Gerda 4 years 2021-07-27T18:21:55+00:00 1 Answers 5 views 0

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    2021-07-27T18:22:56+00:00

    Answer:

    0.63

    Explanation:

    We are given that

    Radius of earth,R_E=6370 km

    Radius of orbit A,R_A=7590+6370=13960 km

    Radius of orbit B,R_B=6370+15800=22170 km

    We have to find the ratio of the potential energy of satellite B to that of satellite A in orbit.

    Potential energy of orbit A=U_A=-\frac{GM}{R_A}=-\frac{GM}{13960}

    Potential energy of orbit  B=U_B=-\frac{GM}{R_B}=-\frac{GM}{22170}

    \frac{U_B}{U_A}=\frac{13960}{22170}=0.63

    Hence,the ratio of the potential energy of satellite B to that of satellite A in orbit=0.63

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