How quickly does the Earth feel the effects of a halved Sun's mass?

[Hak]

I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so. If, for example, we attach something to a spring and give a quick tug, the object doesn't immediately feel the force; so why should it be any different for gravitation?
Can you clarify this doubt? Thank you for any intervention.

P.S. You are very free to move this thread to another Forum if you feel that I have not posted it in the more appropriate one...

 

[phinds]

I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so. If, for example, we attach something to a spring and give a quick tug, the object doesn't immediately feel the force; so why should it be any different for gravitation?
Can you clarify this doubt? Thank you for any intervention.

P.S. You are very free to move this thread to another Forum if you feel that I have not posted it in the more appropriate one...

First off, you do not have a "doubt", you have a question. They are not at all the same.
https://www.physicsforums.com/threads/exploring-the-meaning-behind-the-phrase-have-a-doubt.607274/

Second, you are positing magic, so there is no answer to your question as asked.
https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

If what you want to know (and it pretty clearly IS) is whether or not gravitational effect from the sun to the Earth are instantaneous, then no, they most certainly are not. It takes about 8 minutes for the gravitational effect of the sun to travel to the earth.

 

[Hak]

First off, you do not have a "doubt", you have a question. They are not at all the same.
https://www.physicsforums.com/threads/exploring-the-meaning-behind-the-phrase-have-a-doubt.607274/

Second, you are positing magic, so there is no answer to your question as asked.
https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

If what you want to know (and it pretty clearly IS) is whether or not gravitational effect from the sun to the Earth are instantaneous, then no, they most certainly are not. It takes about 8 minutes for the gravitational effect of the sun to travel to the earth.

Thank you very much. If I understand what you are saying, it should depend on whether the propagation of information takes place at the speed of light or not: in this case, the information would take at least 8 minutes to arrive, not about 8 minutes, right? Where am I wrong?
Also, in what sense and how does the Earth (or a charged particle, I think the process is almost analogous) get ''informed'' that it is attracted? Thank you.

 

[phinds]

Thank you very much. If I understand what you are saying, it should depend on whether the propagation of information takes place at the speed of light or not: in this case, the information would take at least 8 minutes to arrive, not about 8 minutes, right? Where am I wrong?

I don't recall the exact amount, which is why I said "about 8 minutes". It's likely just under or just over 8 minutes.

Also, in what sense and how does the Earth (or a charged particle, I think the process is almost analogous) get ''informed'' that it is attracted? Thank you.

The Earth's attraction to the sun and a charge particle's attraction to something are TOTALLY different phenomenon. The first is caused by the geometry of space-time (what we call "gravity") and the second is electromagnetic attraction. There IS a gravitational compenent to electromagnetic attraction between two bodies that have mass but it is normally so tiny relative to the EM force that it is ignored.

 

[Hak]

I don't recall the exact amount, which is why I said "about 8 minutes". It's likely just under or just over 8 minutes.

The Earth's attraction to the sun and a charge particle's attraction to something are TOTALLY different phenomenon. The first is caused by the geometry of space-time (what we call "gravity") and the second is electromagnetic attraction. There IS a gravitational compenent to electromagnetic attraction between two bodies that have mass but it is normally so tiny relative to the EM force that it is ignored.

Thank you again. Is it possible to know more about this (gravitons, graviphotons or something else, which I don't know yet)?

 

[phinds]

Thank you again. Is it possible to know more about this (gravitons, graviphotons or something else, which I don't know yet)?

Yes, you need to study General Relativity if you want to understand space-time geometry. Newtonian mechanics says that gravity is a force but that is incorrect. Newtonian gravity is a trivial sub-set of General Relativity, which shows that what we call "gravity" is not a force at all, it is space-time geometry.

BUT ... if you are new to this stuff, you are a LONG way from being ready to study GR. Start with Special Relativity.

 

[Hak]

Yes, you need to study General Relativity if you want to understand space-time geometry. Newtonian mechanics says that gravity is a force but that is incorrect. Newtonian gravity is a trivial sub-set of General Relativity, which shows that what we call "gravity" is not a force at all, it is space-time geometry.

BUT ... if you are new to this stuff, you are a LONG way from being ready to study GR. Start with Special Relativity.

Thanks. Yes, I'm new to this stuff, I am aware that I am not yet ready for General Relativity, but I would like to know more about this theory. Could you recommend me some paper source, book or other in which these topics (in particular, those related to my initial question in the OP) are covered? I promise I will be very cautious in tackling them, I am aware of my abilities and know how to give weight to the difficulty of the topics. Thank you.

 

[berkeman]

Could you recommend me some paper source, book or other in which these topics (in particular, those related to my initial question in the OP) are covered?

I did a search in the Academic Advising forum for threads with Relativity in the title, and got lots of hits. Maybe have a look through these threads for advice on resources for starting to study the subject:

https://www.physicsforums.com/searc...1&c[nodes][0]=139&c[title_only]=1&o=relevance

 

[Hak]

I did a search in the Academic Advising forum for threads with Relativity in the title, and got lots of hits. Maybe have a look through these threads for advice on resources for starting to study the subject:

https://www.physicsforums.com/searc...1&c[nodes][0]=139&c[title_only]=1&o=relevance

Thank you. But are there no Insights on the specific problem I submitted (combined with GR)?

 

[Orodruin]

Suppose the mass of the Sun halves in an instant

Just to expand on this. Assuming we are talking about GR (gravity in Newtonian gravity acts instantaneously), the assumption that the Sun’s mass would halve in an instant is fundamentally contradictory to GR. It simply cannot happen. This is why asking what GR would predict if it happened is moot. You cannot use any theory to predict what would happen if that theory is not valid. The answer may as well be ”purple”.

 

[Hak]

Just to expand on this. Assuming we are talking about GR (gravity in Newtonian gravity acts instantaneously), the assumption that the Sun’s mass would halve in an instant is fundamentally contradictory to GR. It simply cannot happen. This is why asking what GR would predict if it happened is moot. You cannot use any theory to predict what would happen if that theory is not valid. The answer may as well be ”purple”.

I understand, that's why I want to learn some basics of GR (I don't pretend to start studying it well: someone told me that many things in GR seem to make no sense and be counterintuitive).

 

[Hak]

@PeroK Why are you skeptical?

 

[PeroK]

I understand, that's why I want to learn some basics of GR (I don't pretend to start studying it well: someone told me that many things in GR seem to make no sense and be counterintuitive).

The Sun cannot suddenly lose half its mass in either Newtonian physics or GR. But, you could have a star of half the mass of the Sun and a body with initial orbital conditions equal to the Earth's solar orbit and study its subsequent trajectory using either theory. Newtonian gravity would give you a good enough approximation for most purposes.

That said, studying this problem would require some mathematics, which is generally in short supply in your posts.

 

[PeroK]

@PeroK Why are you skeptical?

I'm generally skeptical of hearsay. Let your friend join PF and say what he has to say about GR.

 

[Hak]

I'm generally skeptical of hearsay. Let your friend join PF and say what he has to say about GR.

I too am skeptical of hearsay. A professor told me this some time ago, although he did not go into detail, perhaps because he thought it was not appropriate. He is supposed to be a reliable source: I remember him telling me that if one were to try to give a reasonable and sensible justification for all the theories of GR, one would spend a lot of time without getting satisfactory results.

 

[berkeman]

I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so.

To try to give you a better physical scenario and also make it easier to visualize, suppose that the Sun exploded all of a sudden and broke into two hemispheres that flew apart at high velocity, with the 2 halves moving perpendicular to the Solar System's orbital (ecliptic) plane.

The change in the Sun's gravitational field would propagate outward at the same velocity as the light from the Sun, so the changes in the gravitational field from the Sun would be "noticed" on Earth at the same time that we "saw" the two hemispheres separating and flying apart.

(and a little while later we would all get cold and die...)

 

[Hak]

The Sun cannot suddenly lose half its mass in either Newtonian physics or GR. But, you could have a star of half the mass of the Sun and a body with initial orbital conditions equal to the Earth's solar orbit and study its subsequent trajectory using either theory. Newtonian gravity would give you a good enough approximation for most purposes.

That said, studying this problem would require some mathematics, which is generally in short supply in your posts.

You are right. Maths is scarce in my posts because I don't know how to apply it well to SR, GR, QM, cosmology, QFT, etc.... I only apply it to problems in classical mechanics, thermodynamics, Electromagnetism, etc., where even quantitative analysis and evaluation of the precise symbolic expression is required, and not qualitative questions that primarily involve advanced theoretical knowledge and not so simple mathematics. However, if you give me some premise or hint to carry out this problem you have proposed, I can try.

 

[Hak]

To try to give you a better physical scenario and also make it easier to visualize, suppose that the Sun exploded all of a sudden and broke into two hemispheres that flew apart at high velocity, with the 2 halves moving perpendicular to the Solar System's orbital (ecliptic) plane.

The change in the Sun's gravitational field would propagate outward at the same velocity as the light from the Sun, so the changes in the gravitational field from the Sun would be "noticed" on Earth at the same time that we "saw" the two hemispheres separating and flying apart.

(and a little while later we would all get cold and die...)

Thank you for your contribution.

 

[Ibix]

Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?

This scenario violates local conservation of stress-energy. GR says this is impossible, so this question has no answer.

More generally, no causal influence can propagate faster than light. So there is a lower bound on how long it would be before the Earth's orbit was affected of about eight minutes in the solar system rest frame. However, depending on the exact change to the mass distribution, the delay can be considerably longer, or there may be no effect.

 

[FactChecker]

EDIT Gravity Gravitational waves travel at the speed of light. The LIGO results confirmed that.

 

[Ibix]

Gravity waves travel at the speed of light. The LIGO results confirmed that.

I think you mean gravitational waves, not gravity waves. Gravity waves are a kind of water wave.

And yes, they do travel at the speed of light, but not all mass distribution changes emit them. For example, a spherically symmetric non-rotating mass can expand and contract without changing the orbits of satellites, unless the expansion carries some matter past the orbit of one of the satellites.

 

[timmdeeg]

And yes, they do travel at the speed of light, but not all mass distribution changes emit them. For example, a spherically symmetric non-rotating mass can expand and contract without changing the orbits of satellites, unless the expansion carries some matter past the orbit of one of the satellites.

And in addition a spherically symmetric rotating mass doesn't emit gravitational waves, right? It matters whether a rotating system has a time-varying quadrupole moment.

 

[Orodruin]

And in addition a spherically symmetric rotating mass doesn't emit gravitational waves, right? It matters whether a rotating system has a time-varying quadrupole moment.

Indeed. The spherically symmetric case only has a (constant) monopole moment. Thus no gravitational waves.

 

[Vanadium 50]

Perhaps more to the point, a spherically symmetric mass, even if rotating, is a static situation: one cannot ask how fast changes in the gravitational field change if the source does not change. There are no changes in that case.

 

[PeterDonis]

Moderator's note: Moved thread to relativity forum.

 

[PeterDonis]

Suppose the mass of the Sun halves in an instant

It can't; this would violate local conservation of stress-energy. So this scenario is not valid; it breaks the laws of physics, and it makes no sense to ask what the laws of physics say about a scenario that breaks the laws of physics.

As for the more general question of how fast gravity propagates, see this classic paper by Carlip (which has been discussed in multiple previous PF threads):

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

The short answer is that gravity propagates at the speed of light, but testing that is not as easy as you might think because of energy conservation; you can't just turn a source of gravity on and off the way you can a source of a non-gravitational interaction such as electromagnetism.

 

[renormalize]

you can't just turn a source of gravity on and off the way you can a source of a non-gravitational interaction such as electromagnetism.

Yes, and the closest electromagnetic analogy is to ask at what speed the disturbance in the coulomb field around a charge propagates when the charge suddenly disappears. That scenario is similarly unphysical due to charge conservation.

 

[Dale]

Suppose the mass of the Sun halves in an instant

This is premise not compatible with general relativity, so any conclusion based on this premise will not be compatible with general relativity either.

Thank you. But are there no Insights on the specific problem I submitted (combined with GR)?

Of course not, the specific problem you submitted is fundamentally incompatible with GR. You need to ask a different problem, the specific one you asked is a dead-end.

For a bare-bones introduction to General Relativity it is hard to beat Carroll's No Nonsense Introduction:
https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf

 

[Hak]

Of course not, the specific problem you submitted is fundamentally incompatible with GR. You need to ask a different problem, the specific one you asked is a dead-end.

Sorry, we probably had a misunderstanding. By 'specific problem' I meant whether or not the gravitational effects from the Sun to the Earth are instantaneous, certainly not 'if the Sun's mass halved'.

 

[Dale]

Sorry, we probably had a misunderstanding. By 'specific problem' I meant whether or not the gravitational effects from the Sun to the Earth are instantaneous, certainly not 'if the Sun's mass halved'.

You do have to be a little careful defining what you mean by "gravitational effects". Gravitational waves propagate at $c$. The word "effects" seems maybe too broad. Probably some things can be thought of as a gravitational effects that don't propagate at all.

 

[PeterDonis]

By 'specific problem' I meant whether or not the gravitational effects from the Sun to the Earth are instantaneous

I answered this in post #26. Note, though, that another caveat is that if the system is stationary (i.e., the gravitational field does not change with time), then there is nothing to "propagate", so it makes no sense to ask how fast gravity "propagates" under such circumstances.

 

[pervect]

I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so. If, for example, we attach something to a spring and give a quick tug, the object doesn't immediately feel the force; so why should it be any different for gravitation?
Can you clarify this doubt? Thank you for any intervention.

P.S. You are very free to move this thread to another Forum if you feel that I have not posted it in the more appropriate one...

As others have pointed out, it's not possible for the sun to lose half it's mass in an instant. Thus, asking what the equations of GR say in this case is like asking what Maxwell's equations say about the electric field of a disappearing charge. The answer is similiar - Maxwell's equations aren't consistent with charges just vanishing, and the equations of GR aren't consistent with mass vanishing.

To get around this, it's been suggested that you rephrase the question, though if someone has recommended exactly how, I haven't seen it.

I'll fill in this lack by suggesting how you can rephrase the question. While you can't make matter magically disappear, you can re-arrange it. Specifically, you can (in theory) blow up or explode the Sun.

The exact answer to your question will then depend on "how did I blow up the Sun"?

The easiest case to answer is if the explosion is spherically symmetrical. Note that to keep energy conserved, you'll need to include the source energy of the explosion in your calcuations. The "biggest boom" woud occur if the mass of the sun were totally converted to radiation in an instant, via a distributed, idealizazed, matter/anti-matter reaction.

There is an interesting question here - I was planning to invoke Birkhoff theorem, but when I looked at the fine print, this may not quite do the job, as it's not static. Which hapens I think because it's not a vacuum solution, either. :(.

However, I believe we can say that a spherical solution won't generate any gravitational waves, though I don't have a specific reference handy to shore up my recollection. And what I expect to happen in this case is that until the expanding wavefront of the exploding matter of the explosion reaches the observer, therre won't be any impact on the gravitation. If we imagine the "total conversion" explosion, this means there is no effect until the radiation from the explosoin reaches the observer.

IIRC - and again I don't have a specific reference - a non-spherical explosion does have the possibility of converting some of the energy of the explosion into gravitatioanl waves, so it becomes a harder problem.

A technical note - I'm assuming an asymptotically flat space-time, which is more-or-less required to talk about energy conservation in General Relativity.

 

[PeterDonis]

I believe we can say that a spherical solution won't generate any gravitational waves

That is correct. Any such waves would have to be monopole, and the lowest non-vanishing order for gravitational waves is quadrupole. This is well known and substantiated in the literature. (The basic reason is that gravity is spin-2; for spin-1, such as electromagnetism, the lowest non-vanishing order for waves is dipole; and you need spin-0 to get non-vanishing monopole waves.)

 

[renormalize]

the lowest non-vanishing order for gravitational waves is dipole.

Quadrupole.

 

[PeterDonis]

Quadrupole.

Oops, yes, thanks! Fixed now.