The Earth is about 81 times more massive than the moon. During the gravitational interation of the Earth and the Moon, the magnitude of the gravitational force acting on the Earth _______ the gravitational force acting on the Moon.

A) is greater than
B) is less than
C) is the same as
D) not enough information

To determine the magnitude of the gravitational force acting on the Earth compared to the gravitational force acting on the Moon, we need to use Newton's law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let's denote the mass of the Earth as E and the mass of the Moon as M. Given that the Earth is about 81 times more massive than the Moon, we can write the relationship as:

E = 81M

Now, let's compare the gravitational forces acting on each object. The equation for gravitational force is:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the objects,
and r is the distance between the centers of the objects.

Since both the Earth and the Moon are involved in the gravitational interaction, we can compare the gravitational forces using the following ratio:

F_Earth / F_Moon = (G * (E * M) / r^2) / (G * (M * M) / r^2)

The gravitational constant, G, and the distance between the centers, r, cancel out, leaving us with:

F_Earth / F_Moon = E / M

Substituting the given relationship E = 81M, we get:

F_Earth / F_Moon = 81M / M = 81

Therefore, the magnitude of the gravitational force acting on the Earth is greater than the gravitational force acting on the Moon.

So, the answer is:

A) is greater than