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2 November, 06:54

A planet with a mass of 3.0 x 1023kg orbits 6.0 x 1010m from a star with a period of 3.4 x 1011seconds. Determine the mass of the star.

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  1. 2 November, 07:06
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    M = 1.38 10⁵⁹ kg

    Explanation:

    For this problem we will use the law of universal gravitation

    F = G m₁ m₂ / r²

    Where G is the gravitation constant you are value 6.67 10⁻¹¹ N m2 / kg2, m are the masses and r the distance

    In this case the mass of the planet is m = 3.0 10²³ kg and the mass of the start is M

    Let's write Newton's second law

    F = m a

    The acceleration is centripetal

    a = v² / r

    The speed module is constant, so we can use the kinematic relationship

    v = d / t

    The distance remembered is the length of the circular orbit and the time in this case is called the period

    d = 2π r

    a = 2π r / T

    Let's replace Newton's second law

    G m M / r² = m (4π² r² / T²) / r

    G M = 4 π² r³ / T²

    M = 4 π² r³ / T² G

    Let's calculate

    M = 4 π² (3.0 10²³) ³ / (3.4 10¹¹) ² 6.67 10⁻¹¹

    M = 13.82 10⁵⁸ kg

    M = 1.38 10⁵⁹ kg
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