How to Calculate Mass of Binary Star Systems Using Kepler's Law and Iteration?

[quasarLie]

Homework Statement

I have to calculate the mass of an astrometric binaries with P=10 years, and a1=15mas, parallax w=64mas
the luminosity is neglected

Homework Equations

The Attempt at a Solution

i used this equation:
$$M_1 + M_2 = \frac{(a/w)^3}{p^2}$$
but the problem is taht i don't have M1

 

[phyzguy]

I suspect when the problem asks you to calculate the mass, they mean the total mass of the system, i.e. M1+M2.

 

[quasarLie]

No finally, i think that i have to use q =M2/M1= a1/a2 replace in the equation but then i will get a 3 dgree equation which i have to solve it with iterative methode (i don't know how yet)

 

[phyzguy]

No finally, i think that i have to use q =M2/M1= a1/a2 replace in the equation but then i will get a 3 dgree equation which i have to solve it with iterative methode (i don't know how yet)

How will you know a1 and a2?

 

[quasarLie]

I have a1 i will use Kepler law, it will become
$$\frac{a_1}{p^2}= M_1\frac{q^3}{(1+q)^2} w^3$$
the resolution will give a 3rd degree equation which can be solved using:
$$q_i = (1+q_{i-1})^{2/3} q_0$$
Until it converge but i don't know how to use this part (to solve this equation with iteration)