Space Warping & Mass: Is There an Equation?

[Jake Minneman]

Is there an equation directly incorporating the mass of an object to the speed at which it warps space? Or do all object warp space at the speed of light?

If there is could one provide me with said equation.

An example of an equation directly incorporating mass is the schwarzschild radius where the mass of the figure is a variable that is required to calculate.

Thank You,

 

[Jake Minneman]

I know that the closer you get to the speed of light the more mass
you gain...so if you get infinitely close to that speed than you have infinite
mass or something like that.

 

[Pengwuino]

Is there an equation directly incorporating the mass of an object to the speed at which it warps space? Or do all object warp space at the speed of light?

The warping of space-time occurs at the speed of light.

 

[Jake Minneman]

If that is true and gravitational waves propagate at c, does this mean that if the sun were to explode we would be shot form orbit the exact time we saw the explosion? 8 minutes after. (That is of course if we are looking up.)

 

[WannabeNewton]

Yes sir but remember that only gravitational waves with sufficiently weak amplitudes propagate at c.

 

[PAllen]

If that is true and gravitational waves propagate at c, does this mean that if the sun were to explode we would be shot form orbit the exact time we saw the explosion? 8 minutes after. (That is of course if we are looking up.)

Roughly speaking, yes. But note that to a first approximation, attraction is to center of mass. Thus if the sun split in a few fragments, by the time the gravitational ripple of the explosion (and light) reached us, the center of mass of the fragments would still be the same, so our motion would not be dramatically affected. Only when the fragments reach 'near' the Earth's orbit would this break down, which would be much later than the explosion. If the fragments were moving at e.g. 50% speed of light, our orbit would really go haywire about 20 minutes after the explosion, more from the motion of the fragments than the propagation delay (though propagation delay would be an important secondary effect).

 

[PAllen]

Actually, there is a further complication in the exploding sun example, making it hard to detect any effects of propagation delay except as high order corrections to the Newtonian action at a distance picture. This is because the direction of attraction to a *moving* body is not to its retarded postion but to the quadratically extrapolated retarded position. Thus, after explosion, with fragments moving inertially, the attraction would be exactly as if action at a distance occurred (except for high order corrections).

This difficulty is why there is, at present, no experimental measurement of the speed of propagation of gravity (there is a measurement of the velocity dependent component of the Shapiro time dely by Fomalont and Kopeikin that the authors claim measures the speed of gravity; other authors (Clifford Will, Steven Carlip) believe that this experiment does not measure the speed of gravity; Neither set of author's has accepted the other's arguments).

 

[Jake Minneman]

What if perhaps instead of exploding the sun "hypothetically" vanished. Would this then follow the principals i have listed above.

 

[PAllen]

What if perhaps instead of exploding the sun "hypothetically" vanished. Would this then follow the principals i have listed above.

Well, a little yes, mostly impossible. Yes, if that were somehow possible, there would be propagation delay. However, it would be impossible to express such a thing in GR - mass/energy cannot disappear in a solution of the GR field equations. Maybe something that could be hypothesized: suppose 10 Jupiter's worth of anti-matter were brought near the sun, and fired at it in a controlled way such that the sun moved with rapidly increasing *acceleration* for a significant period of time. Then, the Earth's orbital changes would substantially lag the sun's position, distinguishable at the first order from Newtonian gravity.