Why is the sun's gravitational pull on the moon greater than the Earth's?

[btrkun]

Homework Statement

Is the sun's gravitational pull on the moon greater or less than the Earth's pull on the moon? Well, the sun doesn't steal our moon away, so the Earth must be pulling harder, right? Well, if you do that calculations you will find that it is not true! The sun pulls more than the earth, so why don't we lose the moon?

Homework Equations

The Attempt at a Solution

The sun's gravitational pull is greater than Earth's. Essentially, the moon and Earth orbit the sun, together, as one entity at about the same speed. Knowing that the distance between the center of Earth and the moon is less than the distance between the center of the sun and Earth helps us to understand that the gravitational force of Earth has a greater affect on the moon than the sun does, even though the sun's gravitational pull is about twice as that of earth's. However, despite not 'losing' the moon, the moon is drifting further and further away from Earth at approximately 2 cm/yr.


Good?

 

[Irid]

Not good, especially the drifting away of the Moon doesn't have anything to do with the Sun.

Actually, the Earth orbiting the Sun is an inertial system of reference. It means that in this system there's a centrifugal force, so please include it while calculating the Sun's force on the Moon.

 

[tiny-tim]

Hi btrkun!

The sun pulls more than the earth, so why don't we lose the moon?
… the gravitational force of Earth has a greater affect on the moon than the sun does, even though the sun's gravitational pull is about twice as that of earth's.

erm … aren't you contradicting yourself?

I think you're missing the point, which is that "it's all relative".

As Newton, with his apple, might have put it, both the moon and the Earth are falling toward the sun at roughly the same rate.

So the apparent attachment of the moon to the Earth is just an illusion.

We don't lose the moon because we're falling with it.

 

[Defennder]

Actually it's more like we're falling towards the Sun in a circle so we won't be toast, although I can't remember if our orbit is circular or elliptical. And the moon doesn't just orbit around the Earth; the Earth orbits around the moon as well, as in a barycentre.