Gravitational waves in elsewhere of light cone

[PhysicoRaj]

Hello every one,
This might sound as much stupid as it is confusing for me.
Suppose the sun vanished right now (that would not happen practically, but I'm not concerned with that), then it will not be less than approximately a little more than eight minutes for us to know that the sun has gone out, since at that time the Earth would be in the elsewhere position in the light cone graph. But since there is no mass in the focus of the Earth's orbit, the gravity of sun ceases. This should affect the earth, and the Earth should fly off, owing to it's orbital velocity, which was when the sun was existing. But my question is, which will happen first? I mean, as soon as the sun vanishes, would the Earth experience the absence (in terms of gravity), or will that even take eight minutes? Because gravitational waves travel at the speed of light.

 

[sweet springs]

Hi. It will take eight minutes because gravitational waves travel at speed of light.
Regards.

 

[PhysicoRaj]

Hi. It will take eight minutes because gravitational waves travel at speed of light.
Regards.

Are you sure? Because if that was the case then it would be FANTASTIC to view it from space. First mercury would fly off, then venus, then earth, mars,...!

 

[sweet springs]

Hi.

I am sure. You see anything uncomfortable there?

regards.

 

[PhysicoRaj]

No. Only that it sounded fantastic
Thank you

 

[Drakkith]

Are you sure? Because if that was the case then it would be FANTASTIC to view it from space. First mercury would fly off, then venus, then earth, mars,...!

It would be quite a sight indeed! One I hope to never witness!

 

[willem2]

Are you sure? Because if that was the case then it would be FANTASTIC to view it from space. First mercury would fly off, then venus, then earth, mars,...!

They will just continue to fly on in a straight line. It will take some days before the lack of acceration will become visible. The apparent movement in the sky because of the rotation of the Earth of the planets is much bigger than the movement in the sky because of the velocity of the planets.
It's most likely that the planets will just slowly become smaller, and continue to move across the sky just as they do now. If it happens at just the right time however, it's possible that some of the planets will come much closer before moving away for good.
A collision seems impossible because the planes of the orbits aren't the same.

 

[Nabeshin]

Because if that was the case then it would be FANTASTIC to view it from space. First mercury would fly off, then venus, then earth, mars,...!

Perhaps fantastic, but I don't think for the reasons you think. Mercury is ~ 3 minutes from the sun, so after 3 minutes Mercury begins its inertial motion. But we here on the Earth are ~5 minutes away from Mercury, so for us to see Mercury deviate from its course requires the full 8 minutes! The same with Venus. In effect, if we could immediately notice the deviation from their orbital paths induced by such an effect (we can't), we would see the two inner planets begin such a deviation at exactly the same time.

Realistically, we would notice the deviation from the orbits first for Mercury simply because its orbit is a smaller circle, and the deviation grows faster.

 

[George Jones]

Hi. It will take eight minutes because gravitational waves travel at speed of light.
Regards.

Yes. The situation is actually fairly subtle. What follows is my attempt at a non-technical explanation. I probably have introduced some inaccuracies.

Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed.

As the Earth orbits the Sun, the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve.

In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity.

As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit.

Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves.

These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago.

What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.

 

[cosmik debris]

Using GR to explain an event that can't happen in GR is a little paradoxical don't you think?

 

[George Jones]

I forgot to reference Carlip's paper,

http://arxiv.org/abs/gr-qc/9909087.

 

[Steely Dan]

Yes. The situation is actually fairly subtle. What follows is my attempt at a non-technical explanation. I probably have introduced some inaccuracies.

Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed.

As the Earth orbits the Sun, the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve.

In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity.

As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit.

Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves.

These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago.

What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.

One does not need to understand GR to understand that there is a difference between a field existing (which gives rise to the force) and changes to the field propagating at some finite speed. These are both things which can be understood in purely pre-GR terms, in analogy with electromagnetism (although of course Newtonian mechanics provides no way for us to know what that signal speed for field changes actually is, even though in principle one could test that empirically). Naturally what GR helps us do is interpret what the meaning of that field is (i.e. the value of the field corresponds to the local geometry of space).

 

[PhysicoRaj]

Perhaps fantastic, but I don't think for the reasons you think. Mercury is ~ 3 minutes from the sun, so after 3 minutes Mercury begins its inertial motion. But we here on the Earth are ~5 minutes away from Mercury, so for us to see Mercury deviate from its course requires the full 8 minutes! The same with Venus. In effect, if we could immediately notice the deviation from their orbital paths induced by such an effect (we can't), we would see the two inner planets begin such a deviation at exactly the same time.

Realistically, we would notice the deviation from the orbits first for Mercury simply because its orbit is a smaller circle, and the deviation grows faster.

Yeah. I had thought of it. It would be weird to view from earth. But to view it from space, means to increase the distance and hence the weirdness..

 

[PhysicoRaj]

Yes. The situation is actually fairly subtle. What follows is my attempt at a non-technical explanation. I probably have introduced some inaccuracies.

Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed.

As the Earth orbits the Sun, the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse?

To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve.

In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity.

As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit.

Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves.

These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago.

What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.

Boy, that is great. The "apparent" force is because this situation itself is apparent! So, can't we have graphs of gravitational cones in space time?