The mass of one star is 1 solar mass, the mass of the second star is 2 solar masses, and the distance between them is 100 * solar radius.What is the period of this binary star system?Use Kepler's third law.
P^2 = 4 pi^2 d^3/(G(M1+M2))
If we use Years, Astronomical Units and Solar Masses as units this reduces to
P^2 = d^3/(M1+M2)
So we have P = sqrt (100^3 / (1+2)) = 577 years.What is the period of this binary star system?First use this equation to find the stars' barycenter:
R1= A x (M2/(M1+M2)
M1= mass of the more massive stars
M2= mass of the less massive star
A= the distance between the two stars
R1= is the distance of the 1 solar mass star from its barycenter.
R1= 100 x (2/(2+1)
(2/(2+1)= 0.67
0.67 x 100=67=R1
67 solar radii = the distance of the 1 solar mass star from the barycenter.
to find the distance between the barycenter and the 2 solar mass star you do 100-67=33
33 solar radii= The distance of the 2 solar mass star from the barycenter
To find the orbital period for each stars, do each of the distances to the 1.5 power.
67^1.5=548.42
33^1.5=189.57
P of the 1 solar mass star= 548.42 years
P of the 2 solar mass star= 189.57 years
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