The sun's gravitational pull on the earth

[Mono182]

if the sun was to vanish, what would happen to the earth. I've been told that the Earth would still rotate around as if there was a sun, was atleast 8 minutes because that's the time it take for the sun's light to reach the earth. Since nothing is faster than the speed of light, the Earth will stay in orbit. is that statement true or is there a better way of explaining it?

 

[billiards]

I think that might be true, of course there would be no way to tell that the sun had vanished before those 8 minutes were up, and besides, stars don't just vanish like that.

 

[Danger]

True, it's an impossible situation. Gravity does travel at the speed of light, though, so any disturbance in the sun's field would take 8 minutes to be noticed here.

 

[Mono182]

so gravity does have a speed?

 

[scott1]

so gravity does have a speed?

In Genreal Realtivity the speed of light is also the speed of gravity

 

[Labguy]

In Genreal Realtivity the speed of light is also the speed of gravity

Which is exactly what became several L-O-N-G threads on the General Astronomy forum. Check over there for about all the opinions and questions you would ever want to read...

 

[Danger]

Thanks. I knew there was at least one around somewhere, but I couldn't remember where.

 

[George Jones]

In Genreal Realtivity the speed of light is also the speed of gravity

This is very https://www.physicsforums.com/showpost.php?p=886267&postcount=12".

 

[Labguy]

Full flaps, dammit! That's a tennis court!

Try putting an F-18 down on a rolling Carrier...

 

[Danger]

No thanks; I get seasick.

 

[mijoon]

May I add that the Earth would be squished by the tidal forces at around the 8 minute mark.

 

[Danger]

You lost me on that one. If there is no gravitational source, there are no tidal forces.
By the bye, it's nice to see someone finally spell our country properly.

 

[Labguy]

You lost me on that one. If there is no gravitational source, there are no tidal forces.
By the bye, it's nice to see someone finally spell our country properly.

Not squished necessarily, but total disaster. As of now, the Earth is "compressed" by tidal forces between Sun and Moon in a vectored direction.

If the Sun's gravity were to "let go" 499 seconds (mean) after the Sun disappeared, the tidal forces would be instantly gone and the Earth's crust, et. al. would "spring out" and tear the hell out of about everything..:yuck:

 

[Danger]

Hmmm... I don't even know whether that would fall under astronomy or planetology or what, but it completely escaped my home-made education. I would have expected the opposite effect, as in the compressive force of gravity no longer being counteracted by tidal force, but with the rotation still keeping the planet 'expanded'. At most, I figured that there would be a slight inward settling of the crust (still devestating to civilization, of course).
Thanks for the tune-in.

 

[Labguy]

(still devestating to civilization, of course).

That's about all I really meant.

 

[LURCH]

Not squished necessarily, but total disaster. As of now, the Earth is "compressed" by tidal forces between Sun and Moon in a vectored direction.

If the Sun's gravity were to "let go" 499 seconds (mean) after the Sun disappeared, the tidal forces would be instantly gone and the Earth's crust, et. al. would "spring out" and tear the hell out of about everything..:yuck:

But would this cause the Earth's crust to move any more than it does on a daily basis? Tidal forces compress and extend the crust once for each planetary revoltion, don't they?

 

[Labguy]

But would this cause the Earth's crust to move any more than it does on a daily basis? Tidal forces compress and extend the crust once for each planetary revoltion, don't they?

Yes, but slowly, not instantly..

 

[rbj]

so gravity does have a speed?

In Genreal Realtivity the speed of light is also the speed of gravity

so think of $c$ as not simply the "speed of light" or the "speed of electromagnetic propagation" (which is where it came from originally), but as the speed of propagation of all things "instantaneous".

whether you and your signalling partner are each holding an electric charge (and you're wiggling them back and forth to signal the other) or you and your signalling partner are holding planets and wiggling them around to send "gravity signals", any instantaneous action from whatever source moves at a speed of $c$.

 

[sdemjanenko]

would we even feel the "release" i mean as it is we are falling anyway. If there is no gravity we just feel like we are falling. So if we get released i don't think the Earth would react in any significant and disasterous way.

 

[russ_watters]

Correct. It is a little bit of a tricky thing: when you are in orbit, you are falling towards the object you are orbiting and feel nothing. If the object blinks out of existence, you no longer orbit and you feel no forces pulling you toward something that doesn't exist. So you'd notice no change in the forces on you.

 

[LURCH]

Yes, but slowly, not instantly..

Oh yeah, hadn't thought of that.

But then again, from what I've heard the Earth is still bouncing back from deformations caused by the last Ice Age, so the subsidence of the tidal bulge might be a very gradual thing, taking thousands of years.

 

[Quaoar]

Pretty sure the sudden absence of the Sun would NOT cause catastrophic rebound from the disappearance of the tidal forces. Quoth http://en.wikipedia.org/wiki/Tidal_acceleration" :

Earth's net equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.

...for the moon. If you do the math, the Sun's tidal forces are about half as strong. So basically, the sudden disappearance of the Sun would result in an elevation drop of no more than 1.6cm, which would also not be instantaneous due to the Earth's elasticity. In addition, the difference between local elevation changes would be tiny (Probably on the order of nanometers for two sides of an Earthquake fault).

 

[Mono182]

hmm, since gravity travels at the speed of light, if the sun disappeared the Earth would still orbit as if the sun was still there for atleast 8 mins, then we would feel the effects?

 

[Danger]

Correct, but relax: it can't happen.

 

[rbj]

hmm, since gravity travels at the speed of light, if the sun disappeared the Earth would still orbit as if the sun was still there for atleast 8 mins, then we would feel the effects?

Correct, but relax: it can't happen.

but, even so, since orbiting or free-falling toward a graviational source is just an inertial movement from the perspective of GR, we wouldn't even feel the effects after those 8 minutes. the folks on the near side of the Earth would miss the sunlight, but the folks on the far side wouldn't know any difference (except from communications) until the sun fails to rise when it's expected to.

what would be perceptually immediately remarkable is an observer near the axis of the Earth's revolution around the sun, equidistant from the Earth and sun, and far enough away to see the circular or elliptical path of the Earth around the sun would see the Earth continue in its elliptical orbit for 8 minutes after the sun was observed to disappear. that is a different observation than if the speed of gravity was infinite and the Earth was observed to be moving in a straight line immediately after the sun disappears. that's the salient kernel of this thought experiment.

 

[LURCH]

No, I think an observer equidistant between the Earth and Sun would "see" the Sun's dissaperance and the Earth's change of course simultaneously, wouldn't they?

 

[Mono182]

something amusing:

i asked this same question to a group of my friends a while back (then came here for answers) and today it randomly appeared on one of my friend's Earth and space science test. After he read it he was like crap, i should of listened!

 

[pervect]

The speed of gravity is talked about at great length in
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

If you look for this link in the physics forums, you'll find where this issue has been discussed in the past.

The correct answer to "what happens if the sun dissappears" according to General relativity is "the sun can't disappear". This sitaution is quite analogous to the question of "what happens according to Maxwell's equations if a charge disappears". The conservation of charge is _built into_ Maxwell's equations, and they do not have a sensible solution where charge disappears. Similarly, the conservation of energy and momentum is _built into_ the theory of General Relativity (in the form of certain differential conservation laws - while these laws don't generalize to the usual intergal form that's another topic.). These differential conservation laws would be violated if the sun suddenly disappeared, so General Relativity does not make any prediction as to what would happen in that event. Instead, it says that that event cannot happen.

If you want to measure the speed of gravity, you need to set up a thought experiment that can actually be performed. The answer in theory is fairly simple and similar to the way we measure the speed of light. You acclerate a mass, to measure a gravitational wave (just as accelerating a charge generates an electromagnetic wave) - then you measure the propagation speed of the wave, i.e. how long it takes to arrive. Unfortunately, gravitational radiation is so weak that we currently cannot detect natural events expected to cause it, nor can we generate enough of it to be detectable. We have indirect observations of binary inspiralling stars that convinces us that energy is being carried away by graviational radiation but we cannot measure the radiation directly currently. This may change with Ligo and Lisa, two projects dedicated to detecting natural sources of gravitational radiation (like binary inspirals that generate black holes).

You do _not_ measure the speed of light by making a charge disappear, because this cannot be done. Mathematically, attempting to do this gives nonsense results. Similarly, you do _not_ measure the speed of gravity by making mass disappear, because this cannot be done. You use the mass to generate gravitational waves (or the charge to generate electromagnetic waves) and you measure the speeds of the wave.

 

[rbj]

No, I think an observer equidistant between the Earth and Sun would "see" the Sun's dissaperance and the Earth's change of course simultaneously, wouldn't they?

why? the Earth (or half of it) would remain illuminated for 8 minutes after the disappearance of the Sun for such an observer. even though it does not change the argument, i was not implying that the observer was between the Earth and Sun in the orbital plane, but far off in space, reasonably close to the axis of revolution of the Earth's orbit (the line going through the sun that is perpendicular to the orbital plane of the Earth) and equidistant from the Earth and Sun. connecting the three, it would be an isosoles triangle with a very acute angle at the observer.

 

[Quaoar]

The correct answer to "what happens if the sun dissappears" according to General relativity is "the sun can't disappear".

I don't know if I agree with this. I can think of some really ridiculous ways for the sun to disappear that are HORRIBLY unlikely but not ruled out by relativity. For instance, what if the mouth of a wormhole suddenly opened up and sucked the Sun to the different part of the universe, and then the wormhole instantly evaporated? What if we measure the Sun where it is today, and then, by the uncertainty principle, the next time we measure it it has moved 10 light years away (the odds are incredibly tiny, but still, non-zero). I don't think that GR specifically prohibits these scenarios...and I'm sure there are others that would facilitate the Sun's sudden disappearance.

 

[pervect]

I don't know if I agree with this. I can think of some really ridiculous ways for the sun to disappear that are HORRIBLY unlikely but not ruled out by relativity. For instance, what if the mouth of a wormhole suddenly opened up and sucked the Sun to the different part of the universe, and then the wormhole instantly evaporated? What if we measure the Sun where it is today, and then, by the uncertainty principle, the next time we measure it it has moved 10 light years away (the odds are incredibly tiny, but still, non-zero). I don't think that GR specifically prohibits these scenarios...and I'm sure there are others that would facilitate the Sun's sudden disappearance.

If you imagined a sphere in 3d space enclosing the sun and the wormhole, the total mass enclosed by the sphere would be the same before and after the sun passed through the wormhole.

I see that you've added the idea that the wormhole "instantly evaporates". This is no more possible than the sun "instantly evaporating".

As far as the wormhole part of the physics goes, here are a few popular references:

http://www.npl.washington.edu/AV/altvw69.html

If a positive electric charge Q passes through a wormhole mouth, the electric lines of force radiating away from the charge must thread through the aperture of the wormhole. The net result is that the entrance wormhole mouth has lines of force radiating away from it, and the exit wormhole mouth has lines of force radiating toward it. In effect, the entrance mouth has now been given a positive electric charge Q, and the exit mouth acquires a corresponding negative charge -Q. Similarly, if a mass M passes through a wormhole mouth, the entrance mouth has its mass increased by M, and the exit mouth has its mass reduced by an amount -M.

Another source:

http://golem.ph.utexas.edu/string/archives/000550.html

An interesting fact about wormholes is that they change in mass as an
object passes through them. To see this, imagine a wormhole connecting
two distinct asymptotically flat spacetimes. In each spacetime, the ADM
mass is conserved. Thus, if we pass an object of mass m through the
wormhole, from A to B, the ADM mass on either side
cannot change. This means that the mass of the mouth A
increases by m and the mass of mouth B decreases by m. In
other words, the wormhole has measured the mass of the object. Note
that this argument applies in any dimension in which the ADM mass makes
sense.

Note that you can read the original Suskind paper and Suskind's own rebuttal to his paper at http://arxiv.org/abs/gr-qc/0504039 http://arxiv.org/abs/gr-qc/0503097. This paper is not directly concerned with the topic, however, though it mentions the particular point I wanted to make, that when a mass passes through a wormhole, the entrance mouth gains the appropriate amount of mass, to satisfy the conservation laws.

The differential conservation law that prevents the sun from disappearing is $$\nabla_a T^{ab} = 0$$. This is the differential form of the conservation of energy and momentum. Essentially, you can move the sun around, but you just can't make it vanish.

More formally, as the second reference metions, the point is that the ADM mass (assuming an asymptotically flat background space-time, i.e. an isolated system) is conserved. This is analogous to the way that charge is conserved in classical E&M.

Just because you can imagine things happening doesn't make them physically possible. The proof of the impossibility is in the details of the conservation laws. Conservation of energy in GR is a bit trickier than the conservation of charge in E&M, but it's still not possible to make the sun instantly disappear.

 

[Quaoar]

What if we position a wormhole next to the Sun, feed in another Sun-sized star into the other end, thus forcing the exit of the wormhole to acquire mass -M. Wouldn't we have a net total mass of 0 at the Sun's position?

 

[DaveC426913]

Pretty sure the sudden absence of the Sun would NOT cause catastrophic rebound from the disappearance of the tidal forces. Quoth http://en.wikipedia.org/wiki/Tidal_acceleration" :

Earth's net equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.

...for the moon. If you do the math, the Sun's tidal forces are about half as strong. So basically, the sudden disappearance of the Sun would result in an elevation drop of no more than 1.6cm, which would also not be instantaneous due to the Earth's elasticity. In addition, the difference between local elevation changes would be tiny (Probably on the order of nanometers for two sides of an Earthquake fault).

Well, it's not comparable to any old earthquake. It's the entire world.

Tornados can do a real number on a house, not so much because the winds are so high, but because they act across the entire surface of the walls at once and on the entire house at once.

Likewise, an earthquake acting locally will be dampened by all the ground around it abosorbing the motion, but one that that acts on every part of the Earth will be orders of magnitude larger.

 

[pervect]

What if we position a wormhole next to the Sun, feed in another Sun-sized star into the other end, thus forcing the exit of the wormhole to acquire mass -M. Wouldn't we have a net total mass of 0 at the Sun's position?

If we assume the wormhole was initially in a state where its exit mass was negligible compared to the sun, after the object of mass M passed through the wormhole you'd have the wormhole exit, with a mass of -M, the object that just passed through the wormhole, with a mass of +M, and the sun, with a mass M. Total mass = M.

This is the same as the mass near the exit of the wormhole before the object passed through (the inital exit mass of the wormhole, assumed to be negligible, plus the mass of the sun). If you assume that the mass of the exit of the wormhole is non-negligible, nothing much changes, except that the initial and final masses of the wormhole + sun are m_exit + m_sun. +M gets added to this because of the object passing through, and -M gets added to this because of the change in the exit mass of the wormhole.

You do need to assume asymptotic flatness to define the ADM mass in the first place (or an alternative would be to assume a static metric and replace the ADM mass with the Komar mass). Other than that there isn't much difference between the "disappearing charge" scenario and the "disappearing mass" scenario - neither one can actually happen. This becomes clearer when one tries to actually solve the problem rigorously by writing down the 4-potential for the E&M case, or the metric coefficients for the GR case.

 

[Danger]

Damn! A post that I entered about a page back seems to have disappeared, and now I can't remember what it was. :grumpy: