Suppose that a binary-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each

5.55*10^29kg

Explanation:

To start, let us say, F(c) = F(g)

F(c) = m.4.π².r(1/2)/T²

F(g) = Gm1m2/r²

since, F(c) = F(g), then

m.4.π².r(1/2) / T² = Gm1m2/r², so that

4π²r(1/2)/T² = Gm2/r²

Since we're after m2, we make it the subject of formula. So that

m2 = 4π²r(1/2).r²/T²G

m = 4π²(1.8*10^11)(3.6*10^11²)/(1.5768*10^8²)(6.67*10^-11)

m = 4π² * (1.8*10^11)(1.296*10^23) / 2.487*10^16

m = 4π² * 2.333*10^34 / 1.658*10^6

m = 9.212*10^35/1.658*10^6

m = 5.56*10^25kg

because if the tool that you are using is not balanced it there would be false mass.