physics

How long would our year be if our Sun were two fifths its present mass and the radius of the Earth’s orbit were six times its present value?

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asked by erin
  1. period^2= constant*r^3/M

    T^2/1year=6^3/1* 1/(2/5)

    T^2= 36*6*5/2

    period= 6sqrt15 * 1year

    check my thinking.
    http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6

  2. The gravity force would be less by a factor of (2/5)*(1/6)^2 = 1/90

    The centripetal force would have to decrease my the same factor. That means
    V^2/R becomes 1/90 of the former value.
    Call V1 and R1 the original values and V2 and R2 the new values
    V2^2/R2 = (1/90)V1^2/R1
    V2^2 = (1/90)(R2/R1)*V1 = 1/15
    V2 = 0.258 V1
    The period of an orbit is proportional to R/V. It will increase by a factor
    6/0.258 = 23.3

    That is the new orbital period in years.

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    posted by drwls
  3. dwls thank you very much

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    posted by erin

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