# The Naked Scientists Forum

### Author Topic: Space bending formula?  (Read 3155 times)

#### 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?

#### 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.

#### 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!

#### 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

#### 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.

#### 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.)

#### 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.

#### 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?

#### 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 »