During a solar eclipse the Moon is positioned directly between Earth and the Sun

Question

During a solar eclipse the Moon is positioned directly between Earth and the Sun. Find the magnitude of the net gravitational force acting on the Moon then, due to both Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99 × 1030 kg, 5.98 × 1024 kg, and 7.36 × 1022 kg, respectively. The Moon's mean distance from Earth is 3.84 × 108 m, and Earth's mean distance from the Sun is 1.50 × 1011 m. The gravitational constant is G = 6.67 × 10-11 Nm2/kg2.

What is the direction of the force?

towards the sun

ealsewhere

towards the earth

towards the venus

Explanation / Answer

We know gravitational force is given as

F = GMm/r^2

Force due to earth on moon

F(e-m) = 6.67*10^-11*5.98*10^24*7.36*10^22/(3.84*10^8)^2=19.9*10^19 N

Force due to sun on moon

F(s-m) = 6.67*10^-11*7.36*10^22*1.99*10^30/(1.5*10^11-3.84*10^8)^2 = 43.65*10^19 N

Fnet = F(m-e) - F(s-m) = 19.9*10^19 N - 43.65*10^19 N= - 2.375*10^20 N

Fnet = 2.374*10^20 N in direction towards the sun

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