Problem 9-56 Vector Gravitational Field - Part 7B

A spaceprobe is at the position shown in the figure. Use components to determine the gravitational acceleration (magnitude and direction) of the probe due to the effects of the earth and moon. The masses of the earth and moon are \(6.0 \times10^{24}\; kg\) and \(7.4 \times 10^{22} \; kg\), respectively.

Accumulated Solution

\(g = GM/r^2 \\ g_x = -g_e - g_e \sin18\; \text{or}\; -g_e - g_e \cos 72 \\ g_y = 0- g_m \cos18\; \text{or}\; 0- g_m \sin 72 \\ g_e = -2.28\times 10^{-3} N/kg \\ g_m = -2.20 \times 10^{-4} N/kg \\ g = 2.4 \times 10^{-3}\; N/kg \\ \theta = \tan^{-1}g_y /g_x\)

\(\theta = \tan^{-1}g_y /g_x = \tan^{-1}(2.20\times 10^{-4} /2.28 \times 10^{-3}  ) = 5.1^\circ\)

You should note this problem carefully and compare the concepts and methods with those of the electric field in a later Unit.

You have completed this problem.