The Penny Wheeel Diagram Confusion

[MajorComplex]

Okay, so I'm a total noob at physics but I'm interested in it, so please bare with me... It's discribed that space is like a flat sheet of cloth and that masses that rest on this cloth curve the space around it inwards. Like this...

http://www.zarm.uni-bremen.de/2forschung/gravi/research/EP/images/gravity_middle.jpg

What confuses me though is what this diagram suggests... So the little dot on the right hand side is caught in the curvature created by the sun. Imagine for a second that that little dot is a tiny mass and is being pulled into the sun. This doesn't actually discribe what happens right? If this where so, wouldn't the smaller mass be attracted to the southern pole and not the center of mass? Also, even if that dot was just a planet caught in orbit, it would still fall inwards wouldn't it?

I understand the dinamics of space and that there is no upside down, so it applies to what ever vector you're facing the sun. But this diagram always confuses me...

 

[pervect]

You might try http://www.eftaylor.com/pub/chapter2.pdf for a slightly better analogy.

The point of the penny example is basically supposed to illustrate that objects, moving along geodesic paths (the equivalent of straight lines on curved surfaces) will not maintain a constant distance. This is why "parallel lines" can meet on a curved surface.

Why does this matter? It turns out that objects move on geodesic paths in space-time according to general relativity. (Or very nearly so, at any rate - I oversimplify slightly in the intersts of clarity).

The diagram makes a crucial simplification, in that it only shows curved space. It's really curved space-time that's the issue. If you've seen space-time diagrams from special relativity, the point is that while we actually draw them on flat sheets of paper, in the presence of gravity they should really be drawn on "curved" surfaces.

This is still a little bit over-simplified, but it's a lot better than what you call the "penny-wheel" diagram.

We've got some past threads on the topic too.

BTW, the ants on the apple illustration is somewhat famous, but I think that a simpler example in the same vein (two ants, crawling in a sphere, starting at the south pole, and rejoining at the north) is better.

In this simpler example, time runs up and down, on a line from the north pole to the south pole. Space is perpendicular to time.

You can see the two ants start out together, move further away, then rejoin. The ants think that they are simply following straight lines, but one can also interpret their motion as some sort of "attraction" that draws them together.