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After all, ignorance is not always bliss...8)

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- Thread starter Muon12
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After all, ignorance is not always bliss...8)

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selfAdjoint

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Usually in relativity the spatial components are measured in lengths of some kind, and the time component is -- also measured in length. They multiply its time units by a speed - length unit per time unit - to convert it. The speed they use is the speed of light.

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Doesn't the body's density also affect how the body affects space time?

From what I understand, something can have a low mass, high density, and therefore make a huge "pit" in space-time.[b(]

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chroot

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Yes, density affects the so called "surface gravity." Cosmic strings (if they exist) are infinitely thin yet very massive, and thus would have surface gravity tending towards infinite.Originally posted by photon

Doesn't the body's density also affect how the body affects space time?

From what I understand, something can have a low mass, high density, and therefore make a huge "pit" in space-time.[b(]

- Warren

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so would that make time infinite around the object or on the object? how does that work?

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If you consider the universe as a whole - it has the correct mass for a black hole having a size equal to the Hubbe radius. Again - the affect upon space is:

delta r = MG/3c^2 - nothing to do with density per se

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marcus

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Originally posted by selfAdjoint

The expression you are thinking of is called the Schwartzschild metric. It describes the curvature of spacetime (not just space) in the vicinity of a gravitating mass. This works if the mass is not rotating and doesn't have an electric charge. There are other metrics that describe the curvature in those cases.

...

selfAdjoint and Yogi have already answered this question. I can add a concrete example to illustrate.

Muon's question is: "Is there an exact known ratio for the curvature of space-time in relation to an object's mass? In other words, is there a value or equation that is used to determine how relatively distorted space will be due to an object's gravitational pull?"

Well one way of measuring how distorted space is to say how much a ray of light will be bent as it passes a massive object.

It depends on the mass and on how close the ray of light comes to the mass, and a formula rather like the one that Yogi wrote can be used

If something has mass M then a handy length to calculate (if you want to say how much it bends space) is GM/c

For the mass of the sun it comes to 1.5 kilometers or a bit less than a mile.

you can calculate it yourself by looking up in a book to find the mass of the sun in kilograms and the speed of light in meters per second and the constant G (in kilograms, meters, and seconds). A lot of stuff cancels and it boils down to 1.5 kilometers.

The angle a ray is bent when it passes within distance D of the (center of the) sun is some very small number of radians---a tiny fraction of a radian actually---which you calculate very easily. It is just 4 x this length divided by D.

So since the length is 1.5 kilometer, 4 x the length is 6 kilometer.

And if the light passes within 6 million kilometers of the sun, then the angle is just 6 divided by 6 million-------a millionth of a radian.

If the light passes within 800,000 km of the sun, then the angle of bending is just 6 divided by 800,000-----6/8 of one 100,000th of a radian.

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