Consider the system of the Sun, Earth, and Moon, at a moment in time when they h

Question

Consider the system of the Sun, Earth, and Moon, at a moment in time when they happen to be exactly in a line, as shown here. (This drawing is NOT to scale. Assume that all distances "d" are measured between the centers of all bodies, and that all distances "d" are much greater than the physical radii of all bodies. )Calculate the magnitude and direction of the NET (total) gravitational force acting on the Moon, at the moment shown in the diagram above. (Thought question: Try to predict: which body exerts a greater gravitational pull on the Moon: the Earth or the Sun? Does your calculated answer surprise you?) Show your work completely.

Explanation / Answer

a) F sun on earth = G Msun Mearth/d^2

= 6.67E-11*1.99E30*5.97E24/1.5E11^2= 3.52E22 N

so F earth on sun = 3.52E22 N since newtons third law

b)

Fmoon = F sun - F earth

Fearth = 6.67E-11*5.97E24*7.35E22/3.84E8^2= 1.98E20 N

F sun = 6.67E-11*7.35E22*1.99E30/(1.5E11-3.84E8)^2= 4.36E20 N

so Sun is stronger force

F total = 4.36E20 - 1.98E20 = 2.38E20 N

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