An X-ray binary consists of 2 stars with masses m1 (the accreting compact object) and m2 (the donor). The orbits are circular with radii r1 and r2 centered on the center of mass.
(a) Find the orbital period T of the binary following the guidelines given in lectures. Express your answer in terms of (m1+m2), (r1+r2) and G (enter m_1 for m1, m_2 for m2, r_1 for r1, r_2 for r2, pi for pi and G for G).
(b) In the case of Cyg X-1 (as discussed in lectures), the orbital period is 5.6 days. The donor star is a “supergiant" with a mass 30 times that of the sun. Doppler shift measurements indicate that the donor star has an orbital speed v2 of about 148 km/sec. Calculate r2 (in meters).
r2=
(c) Calculate r1 (in meters).
hint: Your calculations will be greatly simplified if instead of r1 you set up your equations in terms of r1/r2, and using some relation between the distances and the masses. Once you express your equation in terms of r1/r2, you will find a third order equation in r1/r2. Only one solution is real; the other two are imaginary. There are various ways to find an approximation for r1/r2. You can find the solution by trial and error using your calculator, or you can plot the function.
r1=
(d) Now calculate the mass m1 of the accreting compact object (express that as ratio to the mass of the sun).
m1/MSun=