Another question involving the masses of two stars in a binary syste

[knowlewj01]

Homework Statement

The Spectral lines in a double-lined spectroscopic binary exhibit sinusodal motion with ampliutudes of 15 and 35 km/s in a period of 80hrs. assuming that we view the system close to edge on, calculate the individual masses in solar masses. What would you look for observationally to prove that the system was close to edge on? If the system is not edge on, are the masses lower or higher than the true value and why?

Homework Equations

The Attempt at a Solution

I have an idea on how to answer the second bits but i have no idea how to get the masses of the stars. Anyone know how?

Thanks.

 

[Jhero]

I would first start by using the given information to determine the orbital parameters of the binary system. This includes the period, amplitude, and angle of inclination (assuming we are viewing the system close to edge on). With these parameters, I can then use the Kepler's third law and the mass function equation to calculate the individual masses of the stars.

The mass function equation is as follows:

f(m) = (m1sin^3(i))/(m1+m2)^2 = (K1^3P)/(2piG)

Where m1 and m2 are the individual masses of the stars, i is the angle of inclination, K1 is the amplitude of the first star, P is the period, and G is the gravitational constant.

To prove that the system is close to edge on, I would look for observational evidence such as the presence of eclipses or a secondary Doppler shift in the spectral lines. Eclipses occur when the stars pass in front of each other from our line of sight, causing a decrease in the total light output of the system. A secondary Doppler shift occurs when the spectrum of the secondary star is superimposed on the spectrum of the primary star, resulting in multiple sets of spectral lines.

If the system is not edge on, the masses calculated using the above equation will be lower than the true values. This is because the angle of inclination will be less than 90 degrees, resulting in a lower mass function.