Final answer:
The net force exerted on the Moon during the third quarter phase is approximately 4.79 x 10^20 N, at an angle of 65.38° from the line connecting the Moon and the Earth, towards the line connecting the Moon and the Sun.
Step-by-step explanation:
When the Earth, Moon, and Sun form a right triangle with the Moon at the right angle, the gravitational forces exerted by the Earth and Sun on the Moon are at right angles to each other. To find the net force on the Moon, we use the Pythagorean theorem since the forces are perpendicular. Given that the force by Earth on the Moon (FEM) is 1.98 × 1020 N and the force by the Sun on the Moon (FSM) is 4.36 × 1020 N, the net force (Fnet) can be calculated as follows:
∑F = √(FEM2 + FSM2)
= √((1.98 × 1020 N)2 + (4.36 × 1020 N)2)
= √((3.9204 × 1040 N2) + (19.0096 × 1040 N2))
= √(22.93 × 1040 N2)
= 4.79 × 1020 N
The direction of this net force is at an angle θ from the FEM, which can be found using the tangent function:
tan θ = FSM/FEM
θ = tan-1(FSM/FEM)
= tan-1(4.36 × 1020 N / 1.98 × 1020 N)
= tan-1(2.2020)
≈ 65.38°
Therefore, the net force on the Moon during the third quarter phase is approximately 4.79 × 1020 N, at an angle of 65.38° from the line connecting the Moon and the Earth, towards the line connecting the Moon and the Sun.