# Question on binary stars & binary stars

#### mikky_t

Hi.
What a great forum, so many interesting things

I am facing a problem with the working out for my last question in my practice paper, for my mid-year examinations.

i dont know how to write the notation here, so i have just attatched a screenshot, i hope u dont mind.

i just have to derive it. The hint says, use Kepler's third Law and that it is a description of the orbits of binary stars around their common centre of mass.

Thank You.

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#### mikky_t

Wooooops!

Sorry about the name of the thread, I dont know where the extra, "& binary stars" came from.

Also, where is the picture? I uploaded it.

I just read Tom's post at the start so i will write up what I have. Its all on a piece of a paper:

mA = mass of star A
mB = mass of star B

Keplers third law,
r^3/T^2 = GM/4(pi^2)

Would it be sufficient to say that since in a binary system, they would robit according to Keplers third Law,

mA + mB = r^3/T^2......(1)

The text states formula (1) only, without any explanations.

Even from here if I try to prove that,

mA + mB = 4(pi^2)(r^3)/G(T^2)

It doesnt work out.

As you can probably see, i am a bit confused. Sorry about the messy-ness.

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