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Offline philogean

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Space bending formula?
« on: 25/01/2010 14:12:54 »
I'm curious to know if anyone knows the formula for the amount of "bend" a body of mass creates in space?

In other words... how much does space bend for a given mass?


 

Offline LeeE

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Space bending formula?
« Reply #1 on: 26/01/2010 01:16:54 »
I don't think you'll find that it's as simple as that; the shape of space due to the presence of matter changes depending upon where you're looking at it from and how fast you're moving relative to it.  For example, consider a pair of artificial satellites in orbit around the Earth, with one in a perfectly circular orbit and the other in a highly elliptical orbit.  Both satellites will 'think' they're moving in a straight line through space but their paths are both different even though the Earth is the same for both.  Then just for fun, add a fast moving object that comes from outside our solar system and falls through without being captured; that too is moving through the same space, but once again, on an entirely different path.
 

Offline namaan

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Space bending formula?
« Reply #2 on: 27/01/2010 05:19:08 »
Well, one might imagine that the amount of space bending to be proportional to the gravitational potential of mass m, and inversely proportional to distance r from the mass? If I use ~ for the proportionality symbol and p for gravitation potential, then perhaps something like:

Bend ~ p / r
p = G * m / r (guessing...or rather, borrowing from electrical potential)
Bend ~ ( G * m / r ) / r
Bend ~ G * m / r^2

This also happens to equal the gravitational field magnitude for a mass, so I guess:

Bend ~ Gravitation Field Magnitude of mass m

Well, I'm not at all qualified to write this, but it seemed like a fun exercise, so there you go!
 

Offline LeeE

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Space bending formula?
« Reply #3 on: 27/01/2010 18:47:34 »
What you're calculating there namaan is the acceleration due to gravity, not the shape of space, and you've omitted the leading '-' from the formula too, which ensures that the acceleration is towards the mass and not away from it  ;)
 

Offline namaan

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Space bending formula?
« Reply #4 on: 28/01/2010 01:10:25 »
Well, I should have added, that it was most likely wrong ;) That being said, I never intended it to be a 'formula', I was really only taking about relationships and proportionality. And I interpreted the question differently; I certainly wasn't trying to arrive at the shape of space (that just sounds nauseatingly complex).

Perhaps I'm thoroughly wrong, but I don't find it to be a far-fetched idea that the magnitude of space bending would be proportional to Fg or the gravitational force, and inversely proportional to how far away you are from the mass.
 

Offline JP

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Space bending formula?
« Reply #5 on: 28/01/2010 01:18:17 »
The equation for space bending is given by Einstein's field equation, which describes gravity through a bending of space.  This Wikipedia article goes into considerable detail.  As with everything GR, it's easy to say "gravity causes space-time to bend" and hard to understand the mathematics. 

Or, if you just want to see the equation:
,
where the first 2 terms on the left indicate the bending of space.  Or in a simplified version, by rearranging some terms and
choosing appropriate units

(Both of these were copied from the Wikipedia article.)
 

Offline LeeE

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Space bending formula?
« Reply #6 on: 28/01/2010 16:05:22 »
This plot shows the gravitational acceleration (which is perpendicular to the lines) around a number of bodies.  Note through, that it doesn't show how a body will move through this 'space', as that will obviously depend not only upon where and in which direction its moving, but also how fast its moving.
 

Offline yor_on

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Space bending formula?
« Reply #7 on: 31/01/2010 21:45:26 »
As time and gravity is so intimately connected, don't you have to say that it is SpaceTime that bends to gravity?
 

Offline LeeE

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Space bending formula?
« Reply #8 on: 31/01/2010 23:42:25 »
Yes, of course.
 

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Space bending formula?
« Reply #8 on: 31/01/2010 23:42:25 »

 

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