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Law of periods

  1. Dec 3, 2006 #1
    1. The problem statement, all variables and given/known data

    Two planets A and B, where B has twice the mass of A, orbit the Sun in elliptical orbits. The semi-major axis of the elliptical orbit of planet B is two times larger than the semi-major axis of the elliptical orbit of planet A.

    What is the ratio of the orbital period of planet B to that of planet A?

    2. Relevant equations

    [tex]T^2 = (\frac{4 \pi^2}{G M}) r^3[/tex]

    3. The attempt at a solution

    [tex]M_B = 2 M_A[/tex]
    [tex]a_B = 2 a_A[/tex]
    [tex]\frac{T_B}{T_A} = \frac{\sqrt{\frac{4 \pi^2}{G 2 M_A} 8 a_A^3}}{\sqrt{\frac{4 \pi^2}{G M_A} a_A^3}} = \sqrt{\frac{8}{2}} = \sqrt{ 4 } = 2[/tex]
    but that was wrong. ????
  2. jcsd
  3. Dec 3, 2006 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Planetary Mass is not a factor. Kepler's Third law states that [itex]T^2/a^3 [/itex] is the same for all planets. The M in your equation is the mass of the sun.

  4. Dec 3, 2006 #3
    thank you.
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