Two planets, A and B, form a binary system in otherwise empty space. Planet A has mass 6.0×1024kg. The center-to-center separation of the planets is 3.8×108m. Along the line joining their centers is a point P where a small test mass would experience zero net gravitational field. Point P is located 1.5×108m from the center of Planet A.
Use G=6.67×10−11N⋅m2/kg2.
(a) Derive an equation that relates the masses of Planets A and B to the given distances at point P where the net gravitational field is zero.
(b) Determine the mass of Planet B.
(c) A 1200kg spacecraft is placed exactly at point P and then is given a slight nudge toward Planet A. Describe qualitatively the subsequent motion of the spacecraft and explain your reasoning in terms of the gravitational forces acting on it.