Question about the space-time fabric

[TheJoninator]

Ok, I sort of understand the space-time fabric but there's one thing that bugs me. In this picture, how does the satellite orbit the earth? I know it's because of gravity but how is affected by the curvature of the space-time? It's not touching the curved part. Or does the curvature go all around the earth?

http://1.bp.blogspot.com/-Yd6pNvjyRIc/TaF_oQuUAeI/AAAAAAAABYU/SSZDkK3gqwc/s1600/gravity-1.jpg

 

[Naty1]

Orbits in GR are accounted for according to the curvature of space-time...orbits follow geodesics...the world line of a free falling object. In your link, an orbit is a line of latitude...
A satellite is in free fall...hence astronauts "float"...(are not accelerating in GR)


A close approximate force-based theory equates centripetal force with gravitational force.

More here: (and a diagram)
http://en.wikipedia.org/wiki/Satellite_orbit#Understanding_orbits

 

[TheJoninator]

What I don't get is that you know the curvature that's under the Earth in the picture I gave, is the curvature only under it? Or is it everywhere around it?

 

[cosmik debris]

That picture you gave is wrong in so many ways.

 

[WannabeNewton]

Think of the geometry of space - time around the Earth as approximately that of a 4 - sphere that does not rotate and does not change with time. A particle would follow an orbit of constant latitude along the respective geodesic of the curved space - time (the 4 - sphere). So yes, in a way, if you take a hyper surface of constant time the curvature would be "all around" it.

 

[DaveC426913]

What I don't get is that you know the curvature that's under the Earth in the picture I gave, is the curvature only under it? Or is it everywhere around it?

That picture is completely abstract (and misleading, since it's showing a 2D field with 3D objects). The curvature is in all three physical dimensions and extends to infinity.

 

[eloheim]

That picture is completely abstract (and misleading, since it's showing a 2D field with 3D objects). The curvature is in all three physical dimensions and extends to infinity.

Yea the curvature is 3-dimensional (spatially, that is). I think what you're doing is kind of making it more complicated than it is. The relativity theories are amazing because (among other things) they put movement through time and movement through space in a single coherent framework, but your question about how/why satellites orbit the Earth is focused only on the spatial aspects of the theory (as far as I can tell).

The "time" part of "space-time" for an orbiting satellite concerns things like how the mass of the satellite dictates the apparent slowing of time from the view of someone on it or on the earth, along with the other relative observables like the length of the object and all that.

The long answer is that you're trying to separate things that are, kind of 'by definition,' inseparable (space-time). The short answer though is that for the rough model you have in your head, you need to realize that the Tron-like picture of space as a flat neon grid spackled with gravitational divots is only a 2-D approximation of the actual 3-D reality we live in. In the real world space is curved 3-dimensionally, with the divots funneling towards mass-ive objects from ALL directions.

The full insights of Einstein's theories would tell you not only how an already orbiting satellite will move into the future, but also how much force, and it what direction it would need to be applied, to get said object INTO orbit. But for the purposes of the picture in your head that we probably all started with, that information is really excess.

(P.S. If anything I've said is grossly wrong please correct me, as my goal is to learn about how the universe works, not look cool. )

 

[Naty1]

Or is it everywhere around it?

It IS everywhere, and as Dave posted, and does extend asymptotically to infinity...BUT as the illustrations above imply, the curveature is much less prounced at greater distances... what that means, of course, is that if a spaceship passes close to Earth at some firxed velocity it's path is affected a lot more than if it were to pass by but,say, in another galaxy.

As another example, the massive black hole believed to be at the center of our own galaxy gobbles up lots of stuff nearby...but Earth at it's great distance is barely affected... eventually we might end up there too, except that probably our sun will engulf the Earth (erupting as a red dwarf) first and ruin all the fun.

Purists in these forums often HATE those diagrams...but I believe they are a good place to start recognizing their limitations...

Maybe a good next step is to look at world lines in special relativity...no curvature, no gravity: http://en.wikipedia.org/wiki/World_line

A major problem is that no one can visualize curved space..let aloe curved time...nor the way that space and time become intermingled in general relativity...they partially change into each other...One way to begin to understand some of that is to note that in a gravitational field, say of a planet, where space time curvature is prominent, time slows relative to a distant observer...gravitational potential affects perceived passage of time as does velocity...!

Both gravitational potential (GR) and velocity (SR) affect perceived spacetime...the latter via length contraction and time dilation...

 

[DaveC426913]

Your period key is stuck

 

[JesseM]

The "rubber sheet diagrams" showing spatial curvature around large bodies are potentially misleading because people tend to imagine that objects are pulled "down" into gravity wells, but really the diagrams are just meant to show how gravity distorts spatial distances from what they'd be in a flat plane, you could equally well flip them over so that the "gravity wells" become "gravity bumps" and they'd be just as accurate in representing distances along different paths (and perhaps less misleading). Also, although general relativity does explain the path of objects in the presence of gravity by saying they follow "geodesic" paths, these aren't spatial geodesics which would be the closest approximation to a "straight line" in curved space like what's shown in rubber sheet diagrams, instead general relativity says that objects follow the closest thing possible to a "straight line" in curved spacetime, which is rather different. In [post=2046692]this post[/post] A.T. gave some useful links which try to illustrate curved spacetime using curved surfaces where one dimension is supposed to represent space and the other is supposed to represent time:

http://www.relativitet.se/spacetime1.html
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.adamtoons.de/physics/gravitation.swf

 

[DaveC426913]

I draw your attention to a link JesseM provided:


http://www.relativitet.se/spacetime1.html

Also, here's a related PF discussion.
https://www.physicsforums.com/showthread.php?t=472256

 

[Naty1]

The "rubber sheet diagrams" showing spatial curvature around large bodies ... are just meant to show how gravity distorts spatial distances from what they'd be in a flat plane

yes, distortion of time is omitted...

Jesse, That's a great diagram...space and time... ...but what a mouthful this is:

The line of the steeper initial direction reaches a greater maximum height (the red before the green) - and takes a longer time to return

I had to read it five times to realize the author was NOT claiming red was not the steeper direction...and that term "direction" seems rather awkward when considering curvature of time..

 

[JesseM]

The line of the steeper initial direction reaches a greater maximum height (the red before the green) - and takes a longer time to return

I had to read it five times to realize the author was NOT claiming red was not the steeper direction...and that term "direction" seems rather awkward when considering curvature of time..

Yeah, I think "reaches a greater maximum height (the red before the green)" just means the red line reaches its maximum height at an earlier time than the green does. And "steeper" here is on a coordinate chart with one position dimension (height) and one time dimension, so a steeper slope would mean it has a greater initial velocity--its position rises more rapidly per unit of time.

 

[Naty1]

agreed...and maybe that's an indicaton why the less accurate rubber sheet has been a popular introduction diagram...