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..

 

[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..

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.

 

[Quaoar]

Ah, thanks for clearing that up pervect. Well, here's a method that will make the Sun's gravity disappear: Detonate a gigantic bomb at the center of the Sun so that the vast majority of its mass is ejected isotropically at nearly c. That way, in 8 minutes, all of the Sun's mass will fly past the Earth's orbit, leaving nothing for the Earth to orbit around (thanks to Gauss' law). Voila! :)

 

[Danger]

That way, in 8 minutes, all of the Sun's mass will fly past the Earth's orbit, leaving nothing for the Earth to orbit around

Of course, that would also leave no Earth.

 

[ZapperZ]

This thread has degenerated into "pointless speculation". Thus, all of you should know what happens to such threads.

Zz.

 

[pervect]

"Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) . The wiki article talks about pulsating stars, but the same argument applies to spherically symmetric explosions as it does to spherically symmetric pulsations - they don't emit gravitational radiation. The only reason there would be any gravity waves at all is because the sun has some angular momentum.

Hence, the first change in gravity in this thought experiment would occur when the debris physically passes the Earth. One can use spherical symmetry, Newtonian theory, and Gauss's law to get an approximately correct answer in this case (because of the aforementioned lack of gravity waves). The total gravitational force towards the point where the sun used to be will be proportional to the amount of mass remaining within a sphere of the radius of the Earth's orbit (assuming for simplicity that the Earth's orbit is essentially circular).

 

[Quaoar]

This thread has degenerated into "pointless speculation". Thus, all of you should know what happens to such threads.

Zz.

Not sure I agree it has degenerated to "pointless speculation." Pervect was explaining why having the mass disappear was unphysical...I don't see what's wrong with him setting the record straight.

 

[rbj]

"Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) .
...
Hence, the first change in gravity in this thought experiment would occur when the debris physically passes the Earth. One can use spherical symmetry, Newtonian theory, and Gauss's law to get an approximately correct answer in this case (because of the aforementioned lack of gravity waves).

not knowing GR well enough to do mathematics in it, that makes perfect sense. but what about an explosion (of energy comparable to novae) that spews at nearly c nearly all of the sun's matter out of the top and bottom along the axis of the orbital plane? that should send out a gravitational wave. does it beat the electromagnetic wave?

 

[pervect]

In GR, gravity waves travel at 'c' in a vacuum, just like light. Of course the interstellar media isn't quite a perfect vacuum. More on this later.

You will generate gravity waves when you have systems that are not spherically symmetric. An axis-symmetric explosion like the one you describe would indeed cause gravity waves to be emitted. It's not clear to me how to generte such a non-symmetric explosion. One way of generating gravity waves would be to implode the sun into a black hole, rather than exploding it. I'd suggest using the same x-ray implosion techniques that we use in H-bombs on a much larger scale. (I haven't really worked out the details.) The rotation of the sun would make the resulting implosion spherically assymetrical (it would only be axis symmetric) so that it would generate gravity waves.

Exploding the rotating sun in this way doesn't provide much in the way of gravity waves, as I mentioned. It turns out emitted power (luminosity) for rotating systems scales something like (M/2r)^5 in geometric units. Because M/2r is about 200,000 for the sun, we would be talking about a 10^25 or more increase in gravity wave production with the implosion technique - or alterantively, a 10^25 reduction factor if we just explode the sun.

People haven't seriously studied the idea of imploding the sun, of course, but they have started to study the expected gravity wave signatures from supernovae due to rotating core collapse (see for instance http://www.ligo.caltech.edu/docs/G/G020075-00.pdf ).

Offhand, I would expect that the interstellar medium would slow light down slightly, while not affecting the propagation speed of gravity nearly as much - because gravity interacts much more weakly with matter than electromagnetism does. So for a distant enough supernova, I'd expect that the gravity waves would arrive first, probably about the same time as the neutrino pulse, and the light would arrive later. The gravity waves and the neutrinos would essentially travel at c, the light would be slightly slowed down by its interaction with the interstellar medium.

We've already seen this effect when we happened to catch a neutrino pulse and the optical pulse from the same supernova. This took a little bit of luck. Of course, we haven't seen any gravity waves from Ligo yet, so we don't have any similar data on their timing.

If we do detect supernova with Ligo or Lisa, and detect the same supernova optically, we will probably be able to get some experimental data on the speed of gravity. Until then, I don't think we'll have much in the way of observational evidence. I think it was mentioned earlier in this thread that some experiments have been done, but on review it seemed questionable as to what the experiments had actually measured. A measurement of a gravity wave pulse and an optical pulse from a cosmic catastrophe would be much more direct.

 

[MeJennifer]

So does a rotating star generate gravity waves?

 

[Garth]

So does a rotating star generate gravity waves?

No, symmetric models do not produce gravitational waves, antipodal mass contributions cancel each other out.

Garth

 

[MeJennifer]

No, symmetric models do not produce gravitational waves, antipodal mass contributions cancel each other out.

Garth

Wait so an exploding rotational ball would not generate gravitational waves while a collapsing rotational ball would?
How come there is no symmetry between those situations? what is different?

It must be me not understanding all this but it is confusing to say the least:

Blowing up the sun" is a much more sensible thought experiment than making the sun disappear. It's totally impractical, of course, but it doesn't involve violating physical law. If the explosion is spherically symmetric, there will not be any significant gravity waves emitted when blowing up the sun because of Birkhoff's theorem, see for example http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) .

So here I am led to believe that an exploding rotating ball does not generate gravitational waves.

One way of generating gravity waves would be to implode the sun into a black hole, rather than exploding it. I'd suggest using the same x-ray implosion techniques that we use in H-bombs on a much larger scale. (I haven't really worked out the details.) The rotation of the sun would make the resulting implosion spherically assymetrical (it would only be axis symmetric) so that it would generate gravity waves.

But apparently a rotating ball that is imploding does generate gravitational waves because it is rotating.

Exploding the rotating sun in this way doesn't provide much in the way of gravity waves, as I mentioned. It turns out emitted power (luminosity) for rotating systems scales something like (M/2r)^5 in geometric units. Because M/2r is about 200,000 for the sun, we would be talking about a 10^25 or more increase in gravity wave production with the implosion technique - or alterantively, a 10^25 reduction factor if we just explode the sun.

Now I am led to believe that a rotating ball does generate gravity waves but is just not much.

So how about getting this in the form of a simple schema folks so that all those people who lack understanding, people like me, can get this right.

And let's agree on that does not generate any gravitational waves means not even if the amount is very very tiny.

So we have:

1. A rotating ball
2. A rotating exploding ball
3. A rotating collapsing ball

For any of those three situations do we have gravitational waves?

Furthermore does a rotating ball have a spherical shape in GR?
Furthermore what is the relationship (if any) between gravitational waves in rotating scenarios and the, sometimes called gravitomagnetic, Lense-Thirring effect and "geodetic" precession?

 

[LURCH]

A symetrical rotating star does not generate gravity waves. A symmetrical rotating star that is exploding is a very different scenario; one that most certainly does generate gravity waves.

 

[MeJennifer]

A symetrical rotating star does not generate gravity waves. A symmetrical rotating star that is exploding is a very different scenario; one that most certainly does generate gravity waves.

So, a rotating black hole does not generate gravitational waves either?

But is a rotating star symmetrical in GR?
In other words does GR predict rotating balls to be symmetrical, e.g. no bulge on the equator?

For instance neutron stars generate gravitational waves and they rotate.

 

[LURCH]

I've never heard that rotating eutron stars generate gravity waves. It is predicted that two neutron stars (or two black holes) orbitting very close to each other would produce them, I've not heard of any prediction that a single star rotating on its own axis could.

GR does predict that a rotating sphere will bulge at the middle, but this does not make it asymmetrical. It is symmetrical if you use the axis of rotation as the plane of reflection.

The idea behind gravitational waves is that they require some location within space to undergo a drastic change in gravitational field. The gravitational field around our Sun for example, is fairly homogenous no matter where one measures it. If you drew lines of longitude on the surface of the Sun, you would see them complete one revolution about every 25 days. But the force of gravity is nearly identical over all the lines of longitude, so the gravitational field is not fluctuating. Therefore, the Sun is not expected to generate any measurable gravitational waves.

 

[MeJennifer]

GR does predict that a rotating sphere will bulge at the middle, but this does not make it asymmetrical. It is symmetrical if you use the axis of rotation as the plane of reflection.

So then a rotating ball with an equatorial bulge is considered spherical symmetric?

 

[selfAdjoint]

So then a rotating ball with an equatorial bulge is considered spherical symmetric?

Not spherical. It has axial or cylindrical symmetry. That's appropriate, since it's rotating.