Explaination for earth-moon centre of rotation

[Boogeyman]

Homework Statement

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.

Homework Equations

sum of clockwise moments=sum of anti-clockwise moments

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?

 

[mgb_phys]

What does Newton's law of gravity say ?

hint - how many m's are in the equation

 

[Boogeyman]

What does Newton's law of gravity say ?

hint - how many m's are in the equation

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 = Gm_em_m/separation squared

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

So we see g_me=Gm_m/r²

And this says the separation cannot be equal to zero?

 

[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

 

[Boogeyman]

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

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

 

[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

 

[Boogeyman]

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

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

 

[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.