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15 January, 15:28

A certain satellite travels in an approximately circular orbit of radius 2.0 * 106 m with a period of 7 h 11 min. Calculate the mass of its planet from this information.

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  1. 15 January, 17:12
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    Answer: Mass of the planet, M = 8.53 x 10^8kg

    Explanation:

    Given Radius = 2.0 x 106m

    Period T = 7h 11m

    Using the third law of kepler's equation which states that the square of the orbital period of any planet is proportional to the cube of the semi-major axis of its orbit.

    This is represented by the equation

    T^2 = (4π^2/GM) R^3

    Where T is the period in seconds

    T = (7h x 60m + 11m) (60 sec)

    = 25860 sec

    G represents the gravitational constant

    = 6.6 x 10^-11 N. m^2/kg^2 and M is the mass of the planet

    Making M the subject of the formula,

    M = (4π^2/G) * R^3/T^2

    M = (4π^2 / 6.6 x10^-11) * (2*106m) ^3 (25860s) ^2

    Therefore Mass of the planet, M = 8.53 x 10^8kg
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