When the Moon is directly between the Earth and the Sun,what is the ratio of the force on the Moon due to the Earth to the force on the Moon due to the Sun? The masses of Sun,Earth,and Moon are 1.99 * 10³⁰ kg,5.97 * 10²⁴ kg,and 7.36 * 10²² kg,respectively.The Earth-Moon distance is 3.84 *10⁸ m,while the Earth-Sun distance is 1.51 * 10¹¹ m.

Question

Quizplus · Accepted Answer

The force is given by the formula F = G(m1m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. When the Moon is directly between the Earth and the Sun, the forces due to the Earth and the Sun add up, so we have:
Ftotal = Fearth + Fsun = G(mearth mmoon)/dEM^2 + G(msun mmoon)/dSM^2
where dEM is the Earth-Moon distance and dSM is the Sun-Moon distance. Since dSM > dEM, the force due to the Sun is smaller than the force due to the Earth. We want to find the ratio Fearth/Fsun, which is just (mearth/msun)(dSM/dEM)^2:
Fearth/Fsun = (mearth/msun)(dSM/dEM)^2 = (5.97*10^24 kg)/(1.99*10^30 kg)(1.51*10^11 m/3.84*10^8 m)^2 ≈ 0.46

When the Moon Is Directly Between the Earth and the Sun,what