At a certain instant, the earth, the moon, and a stationary 1250-kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84 X 105 km in length. (a) Find the magnitude and direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle measured from a line connecting the earth and the spacecraft. In a sketch, show the earth, the moon, the spacecraft, and the force vector. (b) What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? Ignore any gravitational effects due to the other planets or the sun.
Problem (a) Step 1: To find the magnitude of the net gravitational force 24 Mass of Earth M = E97 x 10 kg 22 Mass of Moon M = 7.M x 10 kg Mass of Satellite M = 1250 kg S Distance between Earth or Moon and Satellite R = 3.84 x 10 km or 3.84 x 10 m 8 Gravitational constant G = 6.67 x 10 -11N.m kg -2
