An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the sur

Question

An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.540 s to fall 1.90 m. If the radius of the planet is 8.60×107 m, what is the mass of the planet?

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Nguyệt Ánh 5 years 2021-07-22T01:25:25+00:00 1 Answers 10 views 0

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  1. Farah
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    2021-07-22T01:27:09+00:00
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    Answer:

    The mass of the planet is M_{planet} = 144.5 × 10^{25} kg

    Explanation:

    We know that g for the planet is given by

    g = G \frac{M_{planet} }{r^{2} }

    M_{planet} = \frac{gr^{2} }{G} ——— (1)

    Acceleration is given by

    a = \frac{2(y_2-y_1)}{t^{2} }

    a = \frac{2(1.90)}{0.54^{2} }

    a = g = 13.03 \frac{m}{s^{2} }

    Radius of the planet R = 8.6 × 10^{7} meter

    Now put the value of g  & R in equation (1)

    M_{planet} = \frac{(13.03)(8.6)^{2}(10^{14} ) }{6.67 (10^{-11} )}

    M_{planet} = 144.5 × 10^{25} kg

    Therefore the mass of the planet is M_{planet} = 144.5 × 10^{25} kg

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