1. The problem statement, all variables and given/known data A binary star system consists of a star P and a star Q, of mass 4.0 x 10^10 kg and 2.0 x 10^10 kg respectively, separated 6.3 x 10^9 m apart. Star P and Star Q move in circular orbits with their centers at the center of mass which remains at rest. Find the position of the center of mass of the binary star system. 2. Relevant equations g = GM/r^2 (I used this and equated the field strengths from both) But I have some worked solution to this from my teacher, and he used moments to solve this so I am just adding that equation here as well. Moments = F x Perpendicular distance (This is just what my teacher used, but in many similar questions I have done, I never used this moments for such a question) Or is it because this is a binary system that moments have to be used? And in space normally, with no binary system or anything, we must use the g-field? Also, I don't use calculus or vectors, so please don't use that for this question. 3. The attempt at a solution Let x be the distance of the Center of Mass from Star P At that point, Gravitational Field Strength of P = Gravitational Field Strength of Q g (p) = g (q) (G(4 x 10^10))/(x^2) = (G(2 x 10^10))/(6.3 x 10^9 - x)^2 2 = (x^2)/(6.3 x 10^9 - x)^2 2(6.3 x 10^9 - x)^2 = x^2 solving the quadratic equation, I get x = (3.7 x 10^9) m I would appreciate if someone could help me with this. And also, if someone could tell me if this is the way I am supposed to work it out for binary star systems and normal masses in space at a distance, or does it differ for this type of binary star system questions?