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25 June, 08:59

An asteroid orbits the Sun at an average distance of a = 4 AU. How long does it take to orbit the Sun? Use Kepler's Third Law (p2 = a3) to calculate the answer.

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  1. 25 June, 09:22
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    7982 seconds

    Explanation:

    Parameters given:

    Distance of asteroid, a = 4 AU = 5.984 * 10^8 m

    Mass of sun, M = 1.9891 * 10^30 kg

    Orbital period, P, is given as:

    P² = (4π²a³) / (GM)

    Where G = 6.6774 * 10^ (-11) m³/kgs²

    P² = [4 * π² * (5. 984 * 10^8) ³] / (6.674 * 10^ (-11) * 1.9891 * 10^30)

    P² = (8.459 * 10^27) / (1.328 * 10^20)

    P² = 6.372 * 10^7

    => P = 7982 seconds
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