From: dseeman@novell.com (Daniel Seeman)
Newsgroups: sci.physics
Subject: Re: Gravity & Rubber Sheet Analogy Problem
Keywords: gravity, general relativity
Date: 12 Jan 93 17:59:47 GMT
Distribution: usa
Organization: Novell Inc., San Jose, Califonia

In article <79814@hydra.gatech.EDU> gt1057a@prism.gatech.EDU (gt1057a JOHNSTON,KEITH) writes:
>In almost all explanations of gravity as warped space, the analogy
>used is two-dimensional.  A mass deforms a "rubber sheet", causing
>a depression in the two dimensional space.  Then, when an object 
>approaches the mass, it takes the shortest straight line on the
>sheet, which looks like a curved path to the people living in the
>two dimensional universe.
>
>But what if the first mass is Earth, and I set the moon in its
>depression, with no initial velocity.  What would pull it "down"
>toward the Earth, whicsits at the b bottom?  Why wouldn't it
>just sit there in the depression?  Unless there is some other force
>pushing it down the slope, which would mean an external "gravitational"
>force outside the rubber-sheet universe, why would it move?
>
>						Keith J
>
I'll take a crack at this one...

The "rubber sheet" example is just an analogy used to show what the deformation
of space MIGHT look like.  The near earth gravitational force is essential to 
making this analogy work in that it pulls the model earth and moon down into
the sheet so as deform the sheet.  Therefore, when the larger earth model
is placed on the sheet a large deformation is made so that when the moon is
placed on the sheet (a proportional distance from the model earth), it is 
already on a sloped surface.  This sloped surface has a tendancy to pull the
model moon toward the model earth.  It is important to note the weights of the
models (to a large degree) determines the "strength" of the "attraction."  For
example, if the model earth is too much heavier than the model moon, the model
moon will accelerate directly over to the model earth when placed on the sloped
rubber sheet.  The model moon must be heavy enough to deform the fabric enough
so that it will remain in the same area (or orbit) that it was originally 
placed.  I have seen a good model like this and we were actually able to get the
moon to circle about the earth a couple of times in what appeared to be a
"stable orbit."

The point is that the "rubber sheet" analogy is just that.  It is sort of a koan
or a thought experiment used to show what space might look like if you could
actually see it (when deformed by massive objects).  If the sheet were not in
an external gravitational field (due to the massive earth), the models would not
be pulled down into the fabric and no deformation would occur.  In this case,
the model would not work so well (if at all).  So for this analogy to work, you
need the external gravity since that is what is acting to force the sheet's
deformation.  Gravity also pulls the weights down the sloped surface of
the deformed sheet.  In reality the two massive objects are pulled together due 
to the attractive gravitational force that each exerts on the other.  But for
"small" masses (ie. smaller than the earth and moon---for real) it is really
hard to observe this phenomena without specialized equipment (or a trained eye)
because the gravitational force is pretty weak.

I hope that is clear and correct...

Other explanations or discussions are invited.  If you have other thoughts, 
please do tell ;-)

dks.