Masses of binary system (quick q)

[Jhero]

I have this problem:

Given is period of an eclipsing binary star system is 34 days, rest wavelength is 6563 angstroms while max doppler shift of 2.34 angstroms

I used the doppler equation to figure out the orbital speed of the star; now the question says to use the simplistic model of being in a circular orbit about the other star , calculate the sum of the masses of the stars in solar units.

I know I have to use the modified kepler 3rd law to find the combined mass but how do i get 'a' or semi major axis? Do I just multiply the orbital speed by the period in seconds to get this?

thanks

 

[blumfeld0]

Hi. can't you use the fact that
Velocity = Circumference/ Period = 2 Pi r / Period

 

[sir-pinski]

Hi there,

Great job using the Doppler equation to find the orbital speed of the star. To calculate the sum of the masses of the stars in solar units, you will indeed need to use the modified Kepler 3rd law. To find the semi-major axis, you can use the equation a = (GM T^2/4π^2)^(1/3), where G is the gravitational constant, M is the combined mass of the stars, and T is the orbital period in seconds.

So, to find the combined mass, you will first need to convert the orbital period from days to seconds. Then, plug in the values for a and T into the equation and solve for M. This will give you the combined mass of the stars in terms of solar units.

I hope this helps! Let me know if you have any other questions. Good luck!