What is the distance and mass of a binary star system with given parameters?

[rockyleg]

Homework Statement

In an visual binary star system,the apparent magnitude of the primary star is m=9.8 and its spectrral type is G2V.The angular semi-major axis is φ=0''.1 and the period of the system is 24y.Find the distance of the system r and the two masses.The Sun's absolute magnitude is a given.(The luminance-mass relation $L \propto M^{3.5}$ is also known.)

Homework Equations

$$ M_1 +M_2 = \frac {A^3}{P^2}$$
$$ A= \frac{\phi}{\pi}$$

The Attempt at a Solution

$$ M-m=5-5logr $$
$$ M-M_{sun} = 2.5 log (\frac{L_{sun}}{L} = 3.5 x 2.5 log( \frac{M_{sun}}{M_1} ) ) $$
$$ \pi = \frac{1}{r}$$
And I'm stuck.

 

[mfb]

Can you use the spectral type to estimate the luminosity or mass of the primary star?
Otherwise I think you are missing one equation.

Your luminosity/mass relation equation looks odd.

 

[rockyleg]

Thanks for replying!
Well,according to wikipedia,the mass of a standard G2V star is 1.07 solar masses but I don't think this would be an accepted solution by the examiner since spectral types weren't mentioned in the lecture and there is no spectral type to mass index in the textbook.
I might use it anyway,though.
Thanks again!

 

[haruspex]

I don't think this would be an accepted solution by the examiner since spectral types weren't mentioned in the lecture and there is no spectral type to mass index in the textbook

There's no point in having the question specify spectral type unless you are expected to use it somehow.

 

[rockyleg]

There's no point in having the question specify spectral type unless you are expected to use it somehow.

Not really.It is common in this course's problem sets to be given information that isn't part of the solution.I would guess this is common in many places,is it not?

 

[haruspex]

Not really.It is common in this course's problem sets to be given information that isn't part of the solution.I would guess this is common in many places,is it not?

It should be more common than it is.