Question

Tidal forces are gravitational forces exerted on different parts of a body by a second body. Their effects are particularly visible on the earth's surface in the form of tides. To understand the origin of tidal forces, consider the earth-moon system to consist of two spherical bodies, each with a spherical mass distribution. Let re be the radius of the earth, m be the mass of the moon, and G be the gravitational constant.
Let r denote the distance between the center of the earth and the center of the moon. What is the magnitude of the acceleration the gravitational pull of the moon?

Answer 1

Answer:

$a_e = \frac{Gm}{r^2}$

Explanation:

We assume that:

M to represent the mass of the earth

m to equally represent the  mass of the moon

r should be the distance between the center of the earth to the center of the moon.

Then;

the expression for the gravitational force can be written as:

$F = \frac{GMm}{r^2}$

Where $a_e$ is the acceleration produced by the earth; then:

$F =M *a_e$

Then:

$M*a_e = \frac{GMm}{r^2}$

$a_e = \frac{GMm}{Mr^2}$

$a_e = \frac{Gm}{r^2}$

Therefore, the  magnitude of the acceleration of the earth due to  the gravitational pull of the moon  $a_e = \frac{Gm}{r^2}$

Answer 2

Answer:

The magnitude of the acceleration of earth due to the gravitational pull of earth is a = Gm/r^2

Where r = the center to center distance between the earth and the moon,

m = mass of the moon, and,

G is the gravity constant.

Explanation:

Detailed explanation and calculation is shown in the image below