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Suppose the Sun were twice as massive as it actually is. What would be the orbital period of a planet at a distance of 10AU from the Sun?

  • Astronomy - ,

    For the actual sun's mass, according to Kepler's third law,
    P^2/a^3 = 1 = P^2/1000
    P = 31.6 years

    For a sun that is twice as massive, the centripetal gravity force is twice as large, so V must increase by a factor of sqrt2 to balance it.

    The period will be lower by a factor 1/sqrt2 due to the higher speed

    Period = 31.6/1.414 = 22.4 years

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