Physics

Problem

Two planets, A and B, form a binary system in otherwise empty space. Planet A has mass

6.0\times10^{24}\,\text{kg}

. The center-to-center separation of the planets is

3.8\times10^{8}\,\text{m}

. 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\times10^{8}\,\text{m}

from the center of Planet A. Use

G=6.67\times10^{-11}\,\text{N}\!\cdot\!\text{m}^2/\text{kg}^2

. (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

1200\,\text{kg}

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.

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