Re: two questions on the bend of the space



Hi, Kara,


> Is it known or can you calculate the radius of the bend of the space?


I've been struggling, trying to give you a number you can grab hold of,
and have just got an answer.

My problem was that the curvature tensor has lots of different
components, which are different in different coordinate systems. I
think what you are looking for is an order of magnitude, and the best I
have been able to come up with is via the Kretschmann invariant,
defined in:

http://www.answers.com/main/ntquery?method=4&dsid=2222&dekey=Schwarzschild+metric&gwp=8&curtab=2222_1

which is sort of the modulus-squared of the curvature tensor.

First, what is the value at a distance from the sun equal to that of
the earth. The Schwarzschild radius for the sun is ~ 3 km, and the
orbital radius of the earth is ~ 150 Gm. This gives a
root-Kretschmann-invariant of 3e-30 m^-2. If you want to compare it to
that of a sphere, the curvature of space is comparable to one of radius
5.6e14 m, i.e. 3000 times the orbital radius.

Next, what about at the surface of the earth. The Schwarzschild radius
for the earth is 9mm, and the surface radius is 6.4 Mm. This gives a
root-Kretschmann-invariant of 1.2e-22 m^-2, comparable to a sphere of
radius 92 Gm, 15000 times the surface radius.

Cheers,

Zigoteau.

.

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