Finding the Masses of a binary star using the distance, angle and orbital period

[PaulWright]

Homework Statement

Two stars are in a circular visual binary system. The orbital
period of the binary is 30 years. The distance to the binary is 20
parsecs. The angular radius of the orbit of each star is 1". What
are the masses of the two stars?

Homework Equations

I am assuming that the two stars are of the same mass.
$$\frac{a^3}{p^2}=2M$$

The Attempt at a Solution

as the angle is 1" this is 0.000290888209 radians

using the small angle approx opp/adj should = 0.000290888209 radians
we have adj, which is 20pc, therefore the opp (the radius of the orbit) should be 5.81776418*10^-3pc, which is 1200AU, which is therefore the distance between the two stars in AU, which is required for the equation.

therefore we get $$\frac{1200^3}{30^2}=M_1+M_2$$ which is 1920000 Solar masses, therefore each mass is 960000 Solar mass.

This seems way too big, and I would like someone to show me where I have gone wrong.

Cheers,
Paul

 

[willem2]

1'' = 1/3600 degrees = 4.848 * 10^(-6) radians.

 

[PaulWright]

1'' = 1/3600 degrees = 4.848 * 10^(-6) radians.

Jees, I never saw that I assumed 1"=1'

Cheers