Eclipsing binaries and masses

Question

An eclipsing binary is observed to have a period of 0.10 years and each component has a speed in its orbit of 19AU ( about 90km/sec) Assuming that both stars have the same mass and that their orbits are circular, calculate the separation of the two stars in AU and the mass of each star relative to the mass of the Sun.

Answer 1

Do your own homework.

But I'll help.

First of all, 19 AU is not the speed of anything, it's a distance.  It's not clear from your description what the speed is supposed to be (aside from the statement that the speed is about 90 km/s).  Perhaps the speed is 19 AU per year?  That's about 91 km/s.

You know from the Earth-Sun system that the radius of the orbit is 1 AU, the total mass of the system is 1 solar mass, and the period is 1 year.

The period of the orbit is the distance around divided by the speed.

P = 2*pi*R/v gives R.

Energy equation:

1/2 v^2 = M/R

If M is in solar masses, R is in AU, and v is in AU/year.

Answer 2

I answered this question a few days ago.  Try searching YA; under "binaries" might be a good place to start.