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5 March, 11:51

As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 25.1 km.

You hold a hammer and a falcon feather at a height of 1.40 m, release them, and observe that they fall together to the surface in 29.4 s.

Determine the mass of the planet.

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  1. 5 March, 12:18
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    The mass of the planet is M = 7.75 * 10^14 kg

    Explanation:

    From the Newton's law of gravitation;

    F = GMm/r^2

    Where

    F = gravitational force

    G = gravitational constant

    M = mass of planet

    m = mass of other object

    r = radius

    And note that;

    F = mg = GMm/r^2

    g = GM/r^2

    Making M the subject of formula,

    M = gr^2/G ... 1

    g = acceleration due to gravity in the planet.

    From h = 0.5gt^2

    g = 2h/t^2

    given; h = 1.40 m

    t = 29.4s

    g = (2*1.4/29.4^2) m/s

    Circumference of the planet is = 2πr = 25.1km = 25100m

    r = (25100/2π) m

    G = 6.67 10-11m3kg-1s-2

    Substituting the values to equation 1

    M = (2*1.4/29.4^2) * ((25100/2π) ^2) / (6.67 * 10^-11)

    M = 7.75 * 10^14 kg
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