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A starship of mass m is traveling between a pair of binary stars that are a distance R apart. the mass of star 2 is exactly twice the mass of star 1. How far from star 1 will the gravitational force on the starship be equal to zero? Express the answer in terms of R.
When I try, I get 2/3R but the answer should be R/2.41
GmM/R^2(x) - Gm2M/R^2(R-x) = 0
GmM/R^2(x) - Gm2M/R^2(R) + Gm2M/R^2(x) = 0
GmM/R^2(x) + Gm2M/R^2(x) = Gm2M/R^2(R)
x = Gm2M/R^2(R)/[3GmM/R^2]
x = 2/3R
When I try, I get 2/3R but the answer should be R/2.41
GmM/R^2(x) - Gm2M/R^2(R-x) = 0
GmM/R^2(x) - Gm2M/R^2(R) + Gm2M/R^2(x) = 0
GmM/R^2(x) + Gm2M/R^2(x) = Gm2M/R^2(R)
x = Gm2M/R^2(R)/[3GmM/R^2]
x = 2/3R