Torque due to earth's gravity on moon

[frostking]

Homework Statement

What is the magnitude of the torque caused by the force of gravity on the moon by the earth? Assume both are spheres of uniform density, the axis of rotation passes through the center of the Earth perpendicular to the plane of the moon's orbit. Earth's mass 5.98 x 10^24 kg, 7.36 x 10^22 kg for moon radius of moon's circular orbit is 3.84 x 10^8

Homework Equations

Torque = r x Fof gravity Fof gravity = GMm/r^2

The Attempt at a Solution

I know I am wrong now but I multiplied the distance between Earth and moon by forge of gravity of earth. I know from the answer key that the Earth's gravity does not exert any torque on the moon. However, I do not understand why. The Earth's center of mass is perpendicular to moon is the key I am sure. Is it because the force of Earth's g on moon is along the same axis of moon's and therefore no torque occurs along the axis of the pivot point? Because I definitely know that the Earth's gravity exerts torque on things on our planet like if a wrench breaks loose a nut from a screw gravity torque is what is acting Right?! Thanks very much for your time and effort. Frostking

 

[Delphi51]

Torque is "twisting force". You need torque to turn a bolt.
But the Earth's gravity pulls equally on both sides of the moon, so it does not twist it.

At least that is the obvious answer. There may in fact be some small twisting force involved because the moon rotates so the same part of it always faces the Earth. That must have been somehow caused by the Earth's gravity over millions of years.