A satellite has a mass of 6463 kg and is in a circular orbit 4.82 × 105 m above the surface of a planet. The period of the orbit is 2.0 hour

Question

A satellite has a mass of 6463 kg and is in a circular orbit 4.82 × 105 m above the surface of a planet. The period of the orbit is 2.0 hours. The radius of the planet is 4.29 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

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RI SƠ 1 week 2021-07-21T18:53:21+00:00 1 Answers 3 views 0

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    2021-07-21T18:55:11+00:00

    Answer:

    The weight of the planet is 29083.5 N .

    Explanation:

    mass of satellite, m = 6463 kg

    height of orbit, h = 4.82 x 10^5 m

    period, T = 2 h

    radius of planet, R = 4.29 x 10^6 m

    Let the acceleration due to gravity at the planet is g.

    T = 2\pi\sqrt\frac{(R+h)^3}{gR^2}\\\\2\times 3600 =  2\times3.14\sqrt\frac{(4.29+0.482)^3\times10^{18}}{g\times 4.29\times 4.29\times 10^{12} }\\\\24.2 g =108.67\\\\g = 4.5 m/s^2

    The weight of the satellite at the surface of the planet is

    W = m g = 6463 x 4.5 = 29083.5 N

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