posted by James .
a certain binary star system consists of two stars of masses m and 3m respectively separated by a distance of 1.5 x 10^12 m, measured between their centres. Theres stars revolve in sync with each other around their common centre of mass like a giant dumbbell. If the smaller star has a mass of 1.0 x 10^30 kg, what is their common period of revolution?
In principle, it is easy.
calculate the distance each star is from the center of mass, that is the radius of rotation for each star.
Hint: the mass m is 3 parts of separation distance, whilst the 3m star is one part away. So divide the distance by 4, and you know the two radius of roataions. You need this in the centripetal force calculation.
for the small star...
G3m^2/distance^2=m w^2 (3/4 distance)
solve for w
but shouldn't the w for the large star be the same? Lets check..
G3m^2/distance^2=3m w^2 (1/4 distance)
hmmm. it is the same angular velocity.
Oh, period. Convert w (knowing w=2PI/period) to period.