Gravity in Two Dimensions Two point masses, m, and m2, lie in the xy-plane, with m, held in place at the origin and m2 free to move a distance r away at a point P having coordinates X and y (Fig. 7.27). The gravitational potential energy of these masses in found to be U(r) = - Gm1m2/r, where G is the gravitational constant.
(a) Show that the components of the force on m2 due to m1 are (Hint: First write r in terms of X and y.) (b) Show that the magnitude of the force on m2 is F = Gm1m1r2. (c) Does m, attract or repel m2? How do you know?

nz P(, y) mi (x2 + y2)