How much is space actually bent by mass?

[techwonder]

Is there a formula that readily says how much space is bent? I'm thinking of a formula that for example would give the length from A to B when there is a mass in line-of-sight between A and B.

What is that (or similar) formula?

I'd prefer a non-tensor answer, if possible ...

Thanks is advance

 

[chroot]

The only way to measure lengths involves a metric, which is a tensor.

- Warren

 

[marcus]

Is there a formula that readily says how much space is bent?

You want a simple formula that gives some idea of how much a given mass will bend space.
A partial answer is to assume there is a spherical mass M and a lightray that passes within a distance R (of the center) of the object. then there is an extremely simple formula that tells the ANGLE the ray is bent by the thing's gravity. Perhaps you already know that formula and want something fancier. but if not it certainly gives some idea of the size of the geometrical effect of a concentration of matter


the angle in radians is

$$\frac{4GM}{c^2R}$$

for the sun the quantity

$$\frac{4GM}{c^2}$$

is 6 kilometers, so if a ray of light passes 6,000,000 km from sun center
then it will be bent by an angle of 6/6,000,000 radians
or 1/1,000,000 of a radian.

you can plug in different masses for M, like mass of a galaxy or mass of the Earth, and see what angles light is bent

it gives a way of appreciating how very very slight the effect on the geometry of spacetime is, from even real hefty concentrations of matter

if you keep asking, chroot will probably tell you more of the story, but this is at least a start

[edit: thanks Labguy! I have edited this to conform with Labguy's pointer, originally I had R an order of magnitude smaller]

 

[Labguy]

so if a ray of light passes 600,000 km from sun center

That would be hard to do since the diameter of ther sun is ~1,390, 000 km, ~695,000 km Radius... :zzz:

 

[techwonder]

Thanks a lot!

the formula given is exactly what I looked for