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 1.99 times 10^30 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

Here ,

T = 11.3 days

angular speeed , w = 2pi/T = 2pi/(11.3 * 24 * 3600)

w = 6.434 *10^-6 rad/s

radius , r = v/w = 150 *10^3/(6.434 *10^-6)

r = 2.33 *10^10 m

for the mass of the stars

6.663 *10^-11 * M^2/(2 * 2.33 *10^10)^2 = M * (150 *10^3)^2/2.33 *10^10

solving for M

M = 3.15 *10^31 Kg

the mass of each star is 3.15 *10^31 Kg

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