Earth-Moon System: Confused with Momentum?

[saravananrame]

I have some confusion understanding some concepts of Earth moon system . Why conservation of momentum requires both the Earth and the Moon to revolve around the centre of mass ? What happens if they do not revolve around the centre of mass ? Plz clarify and guide me .

 

[dean barry]

Heres a thing, the Earth and moon have equal momentum (same as all two body systems)
Ive attached a two-body data sheet to chew on.

 

[A.T.]

If they revolved around a different point, then their net center of mass would revolve too, so their net linear momentum would change it's direction continuously. That they revolve at all is a matter angular momentum conservation.

 

[saravananrame]

Thanks for ur answers . But a small query " so their net linear momentum would change it's direction continuously." . What's wrong if this happens ?

 

[A.T.]

Thanks for ur answers . But a small query " so their net linear momentum would change it's direction continuously." . What's wrong if this happens ?

It wouldn't be conserved.

 

[saravananrame]

Thanks a lot for answering my queries . Thanks for all those wonderful answers !

 

[phinds]

Here's a fairly simple way to think about it, that might help. There are a lot of words here, but the concepts are very simple.

Think of, say, a 10 lb cannon ball and a 5 lb cannon ball with a rigid bar in between them. Now if you hold the whole thing horizontally and put the bar on your finger and move your finger along under the bar, you'll find the center of mass pretty easily. Now you can keep your finger under the bar at that point and spin the cannon balls around horizontally and your finger won't move. I think this is pretty easy to see from common human experience, and you can certainly try the experiment with objects laying aound the house.

NOW ... move your finger to a point noticeably off of the place where you found the center of mass. You have an immediate problem that the heaver ball will tilt downwards and the lighter one upwards. SO ... replace your finger with a vertical cylinder mechanism that you can use the force the balls back to horizontal but still be able to spin (put bearings in the cylinder, or whatever). If you move the cylinder back to where you finger was at the center of mass, then again the balls spin freely and the cylinder has no inclination to move horizontally. Again move the cylinder away from the center of mass. Now you have to apply a force to keep the balls horizontal, but OK, do that. Now spin the balls. What you will find is that to keep everything steady with thing spinning, you not only have to apply a force to keep the balls from tilting, but you also have to apply a continually changing (in direction) force to keep the cylinder from moving horizontally. That is you are forcing an unbalanced system to look stable.

Notice that with nothing but your finger under the center of mass, you start the balls spinning and no further force is necessary (we're ignoring here the upwards force to counteract gravity) to keep them spinning (ignoring air and other friction).

The operational phrase here is FORCE. If the system is unbalanced, it requires a force to make it look stable, otherwise it will exhibit its fundamental instability, and not rotating about the center of mass is unbalanced.