Gravity Analogy: Why Does Moon Orbit Earth?

[oneamp]

An intuitive gravity analogy that explains why the moon orbits the Earth is, the Earth's mass' effect on space creates a 'dip' that the moon circles around in a frictionless orbit, kind of like like a marble in a bowl. Am I understanding this right? If so, I am confused about something. If I drop something out of my hand, it hits the earth. The 'bowl' shouldn't be anywhere near my hand... at least it's not in the pictures that I've seen, that try to explain gravity. What up with that?

Thanks

 

[A.T.]

If I drop something out of my hand, it hits the earth. The 'bowl' shouldn't be anywhere near my hand..

Not sure if a get what you mean. But you should read this regarding this analogy:

http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity

As far General Relativity is concerned, that analogy doesn't work for objects that you let fall from rest. You need the time dimension like shown here:

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[mathman]

If the moon stopped in its orbit it would fall to earth.

 

[Ibix]

You're talking about a picture like this, I take it: http://en.wikipedia.org/wiki/File:GPB_circling_earth.jpg.

That kind of picture is astonishingly bad as soon as you start to ask questions. The bowl that is shown is a two-dimensional surface; spacetime is four-dimensional. What they've actually drawn is a 2d slice through spacetime, and a 3d slice through Earth. The result is contradictory, to say the least, although it looks pretty.

If they were being consistent, they'd also draw a 2d slice through the Earth. Then it would appear as a circle embedded in the curved surface, rather than as a sphere on top of it. Then you could imagine yourself as a little stick figure on the edge of the circle, and you would see that your hand is in the bowl.

You still have no clear explanation why the ball falls, but AT's video might help with that.

 

[oneamp]

Thank you

 

[A.T.]

If they were being consistent, they'd also draw a 2d slice through the Earth. Then it would appear as a circle embedded in the curved surface, rather than as a sphere on top of it. Then you could imagine yourself as a little stick figure on the edge of the circle, and you would see that your hand is in the bowl.

Right. In all those analogies that reduce dimensions to 2D everything actually happens within those 2D dimensions. Things shown outside of the 2D sheet are not part of the model, and just there to show the relation to the real world situation. What matters is their projections onto the 2D sheet.