Plaskett\'s binary system consists of two stars that revolve in a circular orbit

Question

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v^rightarrow| = 150 km/s and the orbital period of each is 11.3 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99times l0^30 kg.) _______ If you know the orbital period and the speed of an object undergoing constant circular motion, how do you calculate the radius of the circle? solar masses

Explanation / Answer

T=2pi*r/v

and

m*v^2/r = G*M*m/r^2

==> v^2 = G*M/r

r=G*M/v^2 ---(1)

==>

and

T=2pi*r/V --(2)

from (1) and (2),

V*T/2pi=G*M/V^2

T/2pi=G*M/V^3

11.3*(24*60*60)/(2pi) = 6.674*10^-11*M/(150000)^3

====> M=7.86*10^30 kg

mass of the star, M=7.86*10^30 kg

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