A visual binary system has a parallax of 0".072, a greatest apparent diameter of its orbit of 1.8" and a perio

Question

A visual binary system has a parallax of 0".072, a greatest apparent diameter of its orbit of 1.8" and a period of 50 years.if the orbit is circular show that the mass of the binary is 25/32 times the sun's mass.

Answer 1

I already answered this for you at least once before...

You need to have the version of Kepler's 3rd law that includes the masses of the orbiting objects.

i.e P^2 = ka^3; where k = 4pi^2/g(m1+m2)

You have the period P.

You can calculate a with trigonometry:

Distance = 1/parallax (in parsecs)

And then you can use separation of the the stars d = D sin theta.

d = a

Now you can solve the Kepler's 3rd law equation for combined masses of the stars.