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| = 160 km/s and the orbital period of each is 14.3 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 1030 kg.)

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-07-11T21:44:55+02:00

The mass M of the star is mathematically given as

M=24.269kg

Question Parameters

Orbital period P= 14.3*24*60*60 s

P= 1235520s

Speed V=160000

Generally, the equation for the Radius is mathematically given as

R =[tex]\frac{ V*t}{ 2*pi}[/tex]

Therefore

R =[tex]\frac{ ( 160000 )*(1235520 s)}{ 2*3.142}[/tex]

R=[tex]3.14581795*10^{10}[/tex]

Where

M*v^2/R = GM^2/(2R)^2

Therefore

M=[tex]=4(v^2)R/G\\\\ =4(240^2)R/G\\\\ = \frac{4*(160000)^2)*3.14581795*10^{10}}{6.67*10^{-11}}[/tex]

M=4.82956159*10^{31}kg

Considering, that the mass of our Sun is 1.99*10^{30} kg.

The mass M of the star is

M[tex]=\frac{4.82956159*10^{31}}{1.99*10^{30}}[/tex]

M=24.269

In conclusion, the mass M of the star is

M=24.269