Show how to solve mass using kepler's 3rd law?

Question

given distance of a binary star is 10pc & largest & smallest angular separation is 7 and 1.orbital period is100 years

Answer 1

The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

Use this I think your question is not too clear. If it is then I dont know the answer to this question

I will check back what people have to say.

Answer 2

P^2 = ka^3

where P is the period and a is the semi-major axis of the orbit.

But the constant of proportionality depends on the mass of the thing being orbited.

For the sun: k = 4 pi^2 /GM_sun

but it also works for any bodies orbiting each other.

them k - 4 pi^2 / G (M1 + M2)

where the masses M1 and M2 are the masses of the orbiting bodies.

This would apply to your binary stars.

If you need to extract the individual masses, you need to work out where the center of mass is (sort of)...

basically you should be able to show that M1R1 = M2R2

and R1 +R2 = a (where R1 and R2 are the distances of the stars from the center of mass.