Physics 1 word problem. PLEASE HELP!! :))

Question

1. Planet X has a mass of 7.91023 kg and Moon Y has a mass of 3.51018kg. The average distance between the two bodies is approximately 750,000 km. If you were in a rocket flying in a straight line from Planet X to Moon Y, how far away from Planet X would you need to be before the force of gravity from Moon Y was greater than the force of gravity from Planet X?

Please show your work and explain each you did step

Helpful equations: Fg=G* (M1*M2/r^2) ; Fg=mg ; g=G* (M/r^2)

Answer 1

use the equation given as g= G^*M/r² and let g_x = G^*M_x/r² and g_y = G^*M_y/ (750000 -r)² gravity due to y will begin to prevail when the gravitational force due x and y are equal and increase going to y. So let g_x -g_y =0. So g_x = g_y or 7.91023/ r² = 3.51018/ ( 750000 -r)² and solving for r gives ( 750000- r)² = 3.51018 r²/ 7.91023 which gives (750000 -r)² = .4438r² and 750000-r = .666r so that 1.666r = 750000 and r= 450000km so that when the object reaches this distance from planet x it falls under the influence of planet y.