posted by Allison on .
The two stars in a certain binary star system move in circular orbits. The first star, Alpha, has an orbital speed of 36 km/s. The second star, Beta, has an orbital speed of 12 km/s. The orbital period is 137 d.
a) What is the mass of the star alpha?
b) What is the mass of the star beta?
c) One of the best candidates for a black hole is found in the binary system called A0620-0090. The two objects in the binary system are an orange star, V616 Monocerotis, and a compact object believed to be a black hole. The orbital period of A0620-0090 is 7.75 hours, the mass of V616 Monocerotis is estimated to be 0.67 times the mass of the sun, and the mass of the black hole is estimated to be 3.8 times the mass of the sun. Assuming that the orbits are circular, find the radius of the orbit of the orange star.
d) Find the radius of the orbit of the black hole.
e)Find the orbital speed of the orange star.
f)Find the orbital speed of the black hole.
These are Kepler's third law problems. Please show your work for further assistance.
Or harvest your answers somewhere else
I know I have to find angular speed in order to find the radius of orbit.
With the radius of orbit and velocity I can find centripetal acceleration. I then apply Newton's 2nd Law to solve for the mass.
I am stuck on finding angular speed...
Hey there Aliison,
For this problem, you don't actually need to use kepler's laws, all you have to do is 1) find both the radii of the of the stars to the center of the system (denoted by R_a and R_b using the period equation T=(2*pi*R)/v) then, since they are in stable orbits, you can relate the centripetal force (mV^2/R note that the radius here is either R_a or R_b) with he gravitational force between the two (G(m_a*m_b)/R^2 -- the R here is R_a+R_b) Hope this helps
m_a = 7.80 x 10^29
not sure about m_b
m_b is 2.34*10^30
radius of the orbit of the black hole
R = 3.40×108 m
orbital speed of the orange star
orbital speed of the black hole