Question

What is the ratio of the gravitational pull of the sun on the moon to that of the earth on the moon?

Answer 1

2 answers · Physics

Best Answer
Gravitational force is given by F = {G*m1*m2} / r^2 where m1 and m2 are the masses of the two objects, r is the distance between their centers of gravity, and G is the universal gravitational constant. To do this problem, you need to work the force equation twice, once for sun-moon and the other for earth-moon, then divide the one by the other. Or, there's another way to do it (which I think is easier) by dividing the two equations by each other and canceling out like terms before you ever get started plugging in numbers. I'm going to do it that way:

F_s-m ` {G*m_s*m_m} / r_s^2
--------- = ------------------------------
F_e-m ` {G*m_e*m_m} / r_e^2

Where F_s-m and F_e-m is force of sun-moon and force of earth-moon; m_s, m_e, and m_m are masses of sun, earth, and moon; and r_s and r_e are distance from the moon to sun and earth. F_s-m / F_e-m is, of course, the ratio you're trying to find, the answer. G and m_m are like terms we can cancel out:

m_s / r_s^2
-----------------
m_e / r_e^2

Which is the same thing as:

m_s * r_e^2
-----------------
m_e * r_s^2

Which is easy to plug numbers into:

2.0x10^30 * (3.9x10^5)^2
------------------------------------
6.0x10^24 * (1.5x10^8)^2

Which is:

3.042x10^41
------------------
1.35x10^41

Since the exponents are the same we can just drop them, and the answer is:

3.042 / 1.35 = 2.25

So the force of gravity due to the sun on the moon is 2.25 times stronger than the force of gravity due to earth on the moon.

Answer 2

The ratio of gravitational pull of the moon to that of the Earth is - (a) 6:1