The Force Exerted on the Moon (Figure 1)shows the Earth, Moon, and Sun (not to scale) in their relative positions at the time when the Moon is in its third-quarter phase.

Question

Though few people realize it, the force exerted on the Moon by the Sun is actually greater than the force exerted on the Moon by the Earth. In fact, the force exerted on the Moon by the Sun has a magnitude of FSM=4.34×1020N, whereas the force exerted by the Earth has a magnitude of only FEM=1.98×1020N. These forces are indicated to scale in the figure.

a- Find the direction of the net force acting on the Moon

b- Find the magnitude of the net force acting on the Moon

Answer 1

You need to look at the geometry of the situation. In the third phase of the moon the sun and the earth will be exerting forces at right angles. As a result you can get the magnitude of the total force by taking the pythagorean sum of the forces F = sqrt(F_S² + F_E²). The direction will be a little trickier as you have to establish the angle you are talking about. If the sun is a 0 degrees and the earth at 90 degrees, then the angle from the direction of the sun will be arctan(F_E./F_S) . If the sun is to the left at -180, just subtract 180 from the last solution.

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