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tcarr2014 tcarr2014
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12 years ago
The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 9 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 6.0×104 m/s.
What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass.

I used a=(pv) / (2pi) and then Newton's version of Kepler's third law rearranged to find the combined mass... then converted it to solar masses and finally divided it in half to get the mass of each stars. I ended up with 3.3 * 10^3 but it's wrong... can anyone help?
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petey2008petey2008
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12 years ago
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12 years ago
Here's what I have so far:

p = mv where p = momentum
m = mass
v = velocity = 6,0 x 10^4
9 months = 0.75 years

Kepler's third law P^2 = a^3 -- 0.75 years ^2 = 0.82548182 AU^3 = separation of centers of mass of the two stars

F = GMm/a^2
(a^2)F/6.77 x10^-11 = 1.021219243 x 10^10 F newtons/2 = 5.108097715 x 10^9 x F

I have no idea if that's right, but the magnitude (x 10^9) seems more correct than 10^3. I hope it helps you some.
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3 years ago
fanks
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