Two stars in a binary system orbit around their center of mass the centers of the two stars are 7.17 multiply 10 to the power 11 apart The larger of the two stars has a mass of 3.7 x 10 to the power 30 kg is 2.08 multiply 10 to the power 11 from the system center of mass what is the mass of the smaller star

1.512 × 10^(30) kg

Explanation:

Distance between centre of the 2 stars: x_2 = 7.17 × 10^(11) m

Mass of larger star; m1 = 3.7 x 10^(30) kg

Distance of larger star from the system center of mass; x_cm = 2.08 × 10^(11) m

Let the initial distance be x1 = 0

Thus, to find the mass(m2) of the smaller star, we will use the formula;

m2 = m1(x_cm - x1)/(x_2 - x_cm)

Plugging in the relevant values, we have;

m2 = (3.7 x 10^(30)) × ((2.08 × 10^(11)) - 0)/((7.17 × 10^(11)) - (2.08 × 10^(11)))

m2 = 151.2 × 10^(28) kg = 1.512 × 10^(30) kg

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered