Question

Two stars in a binary system orbit around their center of mass. The centers of the two stars are 7.50 1011 m apart. The larger of the two stars has a mass of 3.80 1030 kg, and its center is 2.90 1011 m from the system's center of mass. What is the mass of the smaller star?

Answer 1

let mass of the smaller star is m kg.

let the two masses are present along x axis.

let the bigger star is at origin.

then the smaller star is at d=7.5*10^11 m

then the center of mass will be situated at d1=(3.8*10^30*0+m*7.5*10^11)/(m+3.8*10^30)

as given that, the center of mass is at a distance of 2.9*10^11 m from the center of the bigger mass i.e. the origin.

then (3.8*10^30*0+m*7.5*10^11)/(m+3.8*10^30)=2.9*10^11

==>m*7.5*10^11=m*2.9*10^11+3.8*2.9*10^41

==>m*4.6*10^11=11.02*10^41

==>m=2.3956*10^30 kg

hence the smaller mass is 2.3956*10^30 kg.