Problem with Rubber and Metal Ball Analogy

[jdeboi]

I'm struggling to understand how the stretched rubber & metal ball analogy explains the relativistic conception of gravity. It's possible that there is a simple and obvious solution to my confusion. It's also possible that this question has been answered many times. But I'll go ahead and ask anyways.

An object with mass dents spacetime in the same way that a bowling ball dents a trampoline. If I roll tennis balls across the trampoline, their trajectory will be affected by the dip. They might crash into, orbit, or fly off in an alternate direction after passing the heavy ball. Replace tennis balls with, say, planets. Cool. And the bowling ball? How about the sun. Gotcha. So far so good.

My problem is this: it seems to me that the tennis balls on the trampoline accelerate towards the bowling ball/dented space because of gravity, in the same way that any object will roll down a ramp or hill. So, I don't understand how this analogy gets any closer to explaining gravity if it depends upon gravity for the demonstration to work.

Or is this just a 3D model to illustrate how massive objects are "aware" of the presence of other massive objects and a not a model used to explain the process by which objects like planets accelerate towards one another in a 4D universe?

Am I completely missing the point or failing to notice something obvious?

Thanks!

[A.T.]

I'm struggling to understand how the stretched rubber & metal ball analogy explains the relativistic conception of gravity. It's possible that there is a simple and obvious solution to my confusion.
Have a look at this thread:
http://www.physicsforums.com/showthread.php?t=286926
My problem is this: it seems to me that the tennis balls on the trampoline accelerate towards the bowling ball/dented space because of gravity,
Yes, it is a circular explanation using gravity to explain gravity. Forget it, look at the links given here for better analogies:
http://www.physicsforums.com/showpost.php?p=2244927&postcount=21

[dx]

So, I don't understand how this analogy gets any closer to explaining gravity if it depends upon gravity for the demonstration to work.

The analogy is not an explanation of gravity. It is only meant as a non-technical illustration of certain aspects of the general theory of relativity.

[Matterwave]

In general relativity, it is space-time that curves. This means, the "warping" occurs on a region that is four dimensional.

Humans tend to have problems imagining in four dimensions, let alone imagining "warps" in these dimensions. So the analogy reduces the warping to a 2 dimensional object (a sheet of rubber) so that we can visualize something, instead of having to talk in abstract mathematical terms all the time. It is analogous only in that respect.