Spacetime and gravity: question about how they work together

[byrdawg]

Hello, I have had this lingering curiosity for a while. I read through https://www.physicsforums.com/showthread.php?t=5732" thread a second ago and would like to kind of take it a step further on a tangent.

I have only read about gravity effects and space-time as such they are "fabric-like", and seen many picture as http://images.google.com/imgres?img...rg.mozilla:en-US:official&sa=N&start=42&um=1". Which to me is very easy to understand, but I have never seen this model with a secondary satellite.

Imagine our sun in the center and the Earth being the satellite in orbit, then the "ripple" in space-time that the Earth generates would be "inclined" or "tilted" as to that of the Suns "ripple". Now I am curious how this model encompasses the Moon. When the moon rounds the Earth towards the Sun the inertia and "downhill" momentum from the "tilted ripple" is not going to be the same as when the moon rounds the Earth away from the Sun ("uphill"). This would cause the Moon to rather trail into the Sun or Crash into the Earth.

I know the above is not correct, and that space-time is not actually an entity. Can someone set me straight on how the spacetime model woul encompass the moon orbiting?

 

[A.T.]

I have only read about gravity effects and space-time as such they are "fabric-like", and seen many picture as http://images.google.com/imgres?img...rg.mozilla:en-US:official&sa=N&start=42&um=1". Which to me is very easy to understand,

This picture might be easy to understand but has little to do with the mass attraction model of General Relativity. The curved grid doesn't represent spacetime, just space. There is no time dimension shown there. See links in this post for better pictures:

https://www.physicsforums.com/showthread.php?p=2046692

 

[Dale]

Don't take the stretchy fabric model very seriously. It is a weak and flawed analogy that is barely even suitable for pop-sci documentaries.

 

[rplatter]

I think one thing people forget is that, In the Earth moon scenario, they are orbiting each other.
It's just that one party is significantly more massive than the other, so it doesn't get deflected as much.
Both the Earth and the moon orbit around their common center of gravity.

To see an example of this tie two masses together and throw them.
Similar masses like two tennis balls will swing around the center of the connecting string. If you make one a baseball, the center point of the spinning will be closer to the baseball. If you make the baseball a bowling ball, the center point will be inside the bowling ball, but not at the center of the bowling ball.

The rubber sheet analogy is usefull in that it demonstrates how a vector is changed by a mass. The closer you get to a mass the more you are affected by its 'funnel'. The moon is actually falling to earth, but because it is moving at a rate perpendicular to the surface of the Earth at a speed similar to how fast it is falling, it never hits the earth.

Take a cannon ball.
If you drop it it falls at a certain speed.
If you fire it out of a cannon perpendicular to the ground, it will fall at the same speed, but will hit the Earth a distance away because of the sideways acceleration.
If you fire the cannon ball fast enough, the rate it will travel far enough around the Earth that the curve of the Earth will drop as fast as the cannon ball does.
If you fire it faster than that the Earth will drop away faster than the cannon ball does, and you have achieved escape velocity.
(all the above assuming no drag from air friction and not obsticals in the way)

The moon is just a larger cannon ball..

 

[A.T.]

The rubber sheet analogy is usefull in that it demonstrates how a vector is changed by a mass.

That is so general, it could be an analogy for anything.

The rubber sheet analogy has nothing to do with the gravity model of GR, which is geodesics in curved spacetime. It contains neither spacetime nor geodesics.

Take a cannon ball.
If you drop it it falls at a certain speed.....

That is all very nice but irrelevant to visualizing curved spacetime. You can use the rubber sheet analogy to visualize the Newtonian gravitational potential:
http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity