# Homework Help: Explaination for earth-moon centre of rotation

1. Nov 14, 2009

### Boogeyman

1. The problem statement, all variables and given/known data
Explain why both the Earth and Moon must rotate around their common centres of mass, rather than the moon about the centre of the mass of the earth.

2. Relevant equations
sum of clockwise moments=sum of anti-clockwise moments

3. The attempt at a solution
I want to use Principle of Moments to explain this but the earth and moon must be in rotational equilibrium for this to happen right? I do not understand if one of the conditions for rotational equilibrium (total torque=0) is true. If so, how?

2. Nov 14, 2009

### mgb_phys

What does Newton's law of gravity say ?

hint - how many m's are in the equation

3. Nov 15, 2009

### Boogeyman

Newton's law of gravity states Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses:

F = Gmemm/separation squared

Ok so this says that the separation cannot be equal to zero. There are 2 masses. Ok so if we divide by me, then we find gravitational field strength.

So we see gme=Gmm/r2

And this says the separation cannot be equal to zero?

4. Nov 15, 2009

### mgb_phys

No it says that the earth attracts the moon but the moon also attracts the Earth - there is nothign special about the Earth in this equation

5. Nov 15, 2009

### Boogeyman

Ok, but how do we use this to answer the question?

6. Nov 15, 2009

### mgb_phys

The question says explain - that's the explanation
You could also calculate the point where the force from Earth and Moon on a test particle are equal - that's the centre of rotation

7. Nov 16, 2009

### Boogeyman

Oh ok. It just seemed too simple. Anyways thanks.

8. Nov 16, 2009

### Boogeyman

Wait. I forget to mention that it was found that this centre of rotation was in between the the earth and moon. I think they are asking us to explain why this is so, as opposed to the moon rotating around the earth.