## astrophysics question

A forum designed mainly for high school physics students in New South Wales, Australia.
r.jenkins
Posts: 11
Joined: Sat May 01, 2010 10:43 pm

### astrophysics question

Hi, just in addition to the previous question...

Q: The ratio of radii of orbits of two stars in a binary is about 3:5. Use this to estimate the massess of each star.

A: Since the ratio of diameters of orbits is 3:5, then ratio of their masses is 5/8 and 3/8. These masses are therefore 5.25x10^30kg and 3.15x10^30kg

Can you explain,

Thanks
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: astrophysics question

In a binary star system, the two stars orbit around their centre of mass.

By Newton's third law, the magnitudes of the forces on them are equal.
F1 = F2. so
m1a1 = m2a2
Where the centripetal acceleration is r omega^2 = r (2 pi/T)^2
But the period T of their rotation is also the same, so we write
m1 r1 (2 pi/T)^2 = m2 r2 (2 pi/T)^2. So
m1 r1 = m2 r2
and so, as you say,
m1/m2 = r2/r1

To do more than that, one needs more information and presumably that was given in the question. On the other question (more convenient if you keep them on the same thread) you ask what happens if there are three or more stars. This situation is famous for having no analytical solution.

See
http://www.animations.physics.unsw.edu. ... avity.html

Joe