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

AI Thread Summary
The discussion revolves around calculating the distance and masses of a binary star system using given parameters, including the apparent magnitude and spectral type of the primary star. Participants explore equations related to mass and luminosity, noting the importance of the spectral type in estimating the primary star's mass. There is uncertainty about whether the spectral type should be used in the solution, as it was not covered in lectures or textbooks. One participant suggests that the inclusion of spectral type implies it should be utilized, while another argues that extraneous information is often included in problem sets. The conversation highlights the challenges of applying theoretical knowledge to practical problems in astrophysics.
rockyleg
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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.
 
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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.
 
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!
 
rockyleg said:
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.
 
haruspex said:
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?
 
rockyleg said:
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.:frown:
 
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