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10 September, 07:24

Suppose that you travel to a planet that has 4 times the Earth's mass and 4 times the Earth's radius. Calculate how much more or less you would weigh on this planet compared to your weight on Earth.

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  1. 10 September, 10:37
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    Mass on the planet would be 4 times the mass on Earth.

    Explanation:

    Given -

    Let the mass of Earth = Me

    Let the radius of Earth = Re

    Mass of the planet, Mp = 4Me

    Radius of the planet, Rp = 4Re

    Weight on other planet, W = ?

    Weight on planets is determined by the gravitational force

    Gravitational force, F = GMm/r²

    where, G = gravitational constant

    M = Mass of the planet

    m = our mass

    r = radius of the planet

    Gravitational force on Earth:

    F = G X Me X ma / Re² (ma = mass on earth)

    Gravitational force on planet:

    F = G X 4Me X mₓ / (4Re) ² (mx = mass on other planet)

    Dividing both the equations, we get

    mx = 4ma

    Therefore, mass on the planet would be 4 times the mass on Earth.
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