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Finding the mass of a planet is a binary system

  1. Oct 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Plaskett’s binary system consists of two stars that revolve
    in a circular orbit about a center of mass midway between
    them. This statement implies that the masses of the two
    stars are equal. Assume the orbital speed
    of each star is 220 km/s and the orbital period
    of each is 14.4 days. Find the mass M of each star.

    2. Relevant equations


    3. The attempt at a solution
    Kelper's 3rd Law

    Mass of the planet = (4(pi)^2(r)^3)/GT^2

    T = 1244160
    r = 8.72 x 10^10
    G = 6.672 x 10^-11

    Mass = 2.54 x 10^32, but the answer is 1.26 x 10^32 which is exactly half of my answer

    why should I further divide my answer by 2? Is it because there are two planets in the system? But if I use the same equation to calculate the Sun's mass, I just need to substitute all those unknown into the equation without the need to consider the mass of the Earth. So what's wrong?

    Thanks in advance!
     
  2. jcsd
  3. Oct 29, 2015 #2

    haruspex

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    Kepler's third law was originally in the context of planets orbiting the sun. In that context, the sun is so massive compared with the planets that the orbital radius is effectively the distance from the sun's centre. That won't be the case with two equal mass stars, so I'm not sure what the appropriate r is here. Also, how did you obtain r?
     
  4. Oct 29, 2015 #3
    orbital speed of each star = 220 km/s
    orbital period of each = 14.4 days.
    Distance Traveled in one period = (220000)(14.4 x 24 x 60 x 60)m. Then, you can get the radius from 2(pi)r

    I have solved the problem by using centripetal force= gravitational pull. So probably using Kepler's third law is wrong for binary system.

    Thanks anyway
     
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