1. The problem statement, all variables and given/known data I attached the problem. 2. Relevant equations F=G*m1*m2 / r^2 3. The attempt at a solution Fs=mutual attraction force between particle and sun Fe=mutual attraction force between particle and earth mass of sun(ms)=330,000*mass of earth(me) mp(mass of particle) x=distance between centers of earth and sun=149.6*10^9m Fs=G*mp*ms / d^2 = G*mp*me / (x-d)^2 I cancel out G and mp and cross multiply to get ms*(x-d)^2 = me*d^2 330000*me*(x-d)^2=me*d^2 330000 (x^2-2dx+d^2) = d^2 330000(149.6*10^6)^2 - 2*(149.6*10^6)*d+329999*d^2=0 I then applied the quadratic formula and got d=0, 2.992*10^11 m. Do those look right? Also the last part wants me to "justify the 2 solutions physically." I'm having some trouble on how to do that. Can someone give me a hint?