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 l = 230 km/s and the orbital period of each is 14.1 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 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 ×CM

Explanation / Answer

V = 2.30E5 m/s
T = 1.22E6 s
= 2/T = 5.15E-6 rad/s
R = v/ = 2.30E5 m/5.15E-6 rad/s = 4.47E10 m

Stars centripetal force is provided by mutual grav. attraction..
Mv²/R = G*M²/(2R)²

M = v²*4*R/G
M = (2.30E5 m/s)²*4*(4.47E10 m)/6.67E-11
M = 1.42E32 kg

In solar mass = 1.42E32/1.99E30 .. .. = 71.4 Solar mass

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