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 with arrow| = 230 km/s and the orbital period of each is 15.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 1030 kg.)

Answer 1

`1.554* 10^(32)\ \text{kg}`

Step-by-step explanation:

M = Mass of each star

T = Time period = 15.5 days

v = Orbital velocity = 230 km/s

G = Gravitational constant =
`6.674* 10^(-11)\ \text{Nm}^2/\text{kg}^2`

Radius of orbit is given by

`R=(vT)/(2\pi)`

We have the relation

`(Mv^2)/(R)=(GM^2)/((2R)^2)\\\Rightarrow M=(4Rv^2)/(G)\\\Rightarrow M=(4(vT)/(2\pi)v^2)/(G)\\\Rightarrow M=(2v^3T)/(\pi G)\\\Rightarrow M=(2* 230000^3* 15.5* 24* 60* 60)/(\pi* 6.674* 10^(-11))\\\Rightarrow M=1.554* 10^(32)\ \text{kg}`

The mass of each star is
`1.554* 10^(32)\ \text{kg}`