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Canis Lupus
2017-Jan-20, 10:24 PM
Hi,

I'm very interested in Laplace resonance as a phenomenon.

I wish to appreciate it particularly as possibly some type of perfect example of orbital resonance and what it might reflect or imply about orbital resonances generally.

Hornblower
2017-Jan-21, 02:06 AM
https://en.wikipedia.org/wiki/Orbital_resonance

A Laplace resonance is a special case of orbital resonance in which three satellite bodies are locked into a 1:2:4 orbital period pattern. The classic example consists of Io, Europa and Ganymede in their orbits around Jupiter. It appears to be stable.

Canis Lupus
2017-Jan-21, 02:22 AM
https://en.wikipedia.org/wiki/Orbital_resonance

A Laplace resonance is a special case of orbital resonance in which three satellite bodies are locked into a 1:2:4 orbital period pattern. The classic example consists of Io, Europa and Ganymede in their orbits around Jupiter. It appears to be stable.

... and being stable would seem to represent some sort of ideal state?

tusenfem
2017-Jan-21, 10:09 AM
... and being stable would seem to represent some sort of ideal state?

Not an ideal state, it is just that in this resonance between the three bodies, each moon is making sure the other's are behaving well.
The fact that it is stable is (as far as we know) is interesting because there is also Callisto which is not in resonance (9.2 times Io's period), which would be a disturbing force.
I remember having read a good paper on Laplace resonances, but I cannot come up by whom. Maybe later.

Canis Lupus
2017-Jan-21, 11:15 AM
Not an ideal state, it is just that in this resonance between the three bodies, each moon is making sure the other's are behaving well.

That implies an ideal state but I could be accused of being pedantic pointing it out, I'm sure.


The fact that it is stable is (as far as we know) is interesting because there is also Callisto which is not in resonance (9.2 times Io's period), which would be a disturbing force.
I remember having read a good paper on Laplace resonances, but I cannot come up by whom. Maybe later.

i think it a subject underrepresented in the peer reviewed literature - or anywhere else for that matter.

Any scraps you find would be fine by this wolf.

Hornblower
2017-Jan-21, 12:27 PM
That implies an ideal state but I could be accused of being pedantic pointing it out, I'm sure.



i think it a subject underrepresented in the peer reviewed literature - or anywhere else for that matter.

Any scraps you find would be fine by this wolf.

What is the standard for what you would consider to be satisfactory representation?

grant hutchison
2017-Jan-21, 03:15 PM
i think it a subject underrepresented in the peer reviewed literature - or anywhere else for that matter.Well, it's pretty much a fixture in the textbooks: Murray and Dermott's Solar System Dynamics, Roy's Orbital Motion, for example.
For something that's simple and well understood, the textbooks are where you need to be - you're unlikely to find a steady stream of new papers on a topic like that, apart from the occasional review article like the one tusenfem mentions.

Grant Hutchison

chornedsnorkack
2017-Jan-21, 03:23 PM
Why is 1:2 Laplace resonance stable, if 1:2 Kirkwood gap is not?

tusenfem
2017-Jan-21, 09:22 PM
i think it a subject underrepresented in the peer reviewed literature - or anywhere else for that matter.


I greatly dispute that, searching on ADS for papers with Laplace Resonance in the title gives me a list of 19 peer reviewed papers (http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PHY&db_key=PRE&qform=PHY&arxiv_sel=astro-ph&arxiv_sel=cond-mat&arxiv_sel=cs&arxiv_sel=gr-qc&arxiv_sel=hep-ex&arxiv_sel=hep-lat&arxiv_sel=hep-ph&arxiv_sel=hep-th&arxiv_sel=math&arxiv_sel=math-ph&arxiv_sel=nlin&arxiv_sel=nucl-ex&arxiv_sel=nucl-th&arxiv_sel=physics&arxiv_sel=quant-ph&arxiv_sel=q-bio&aut_logic=OR&author=&ned_query=YES&sim_query=YES&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=AND&title=laplace+resonance&txt_logic=OR&text=&nr_to_return=200&start_nr=1&jou_pick=NO&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1), and I am sure if you search for papers with that in the abstract the number will be greater (indeed 528 papers).

tusenfem
2017-Jan-21, 09:24 PM
Why is 1:2 Laplace resonance stable, if 1:2 Kirkwood gap is not?

That's above my pay grade, I am just a simple plasma astrophysicist.

Canis Lupus
2017-Jan-21, 09:48 PM
I greatly dispute that, searching on ADS for papers with Laplace Resonance in the title gives me a list of 19 peer reviewed papers (http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PHY&db_key=PRE&qform=PHY&arxiv_sel=astro-ph&arxiv_sel=cond-mat&arxiv_sel=cs&arxiv_sel=gr-qc&arxiv_sel=hep-ex&arxiv_sel=hep-lat&arxiv_sel=hep-ph&arxiv_sel=hep-th&arxiv_sel=math&arxiv_sel=math-ph&arxiv_sel=nlin&arxiv_sel=nucl-ex&arxiv_sel=nucl-th&arxiv_sel=physics&arxiv_sel=quant-ph&arxiv_sel=q-bio&aut_logic=OR&author=&ned_query=YES&sim_query=YES&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=AND&title=laplace+resonance&txt_logic=OR&text=&nr_to_return=200&start_nr=1&jou_pick=NO&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1), and I am sure if you search for papers with that in the abstract the number will be greater (indeed 528 papers).

Thank you. I will check. Keep in mind that I am coming at the resonance from a particular angle. However, if there are that many papers, then I'm sure to come across one which deals with some of the issues I have percolating in the muddle I call my mind.

Whilst the focus of this thread is Laplance resonance, it is what this may reveal about all orbital resonances and their tendencies that I'm chasing.

I was ecstatic to read some time ago that a star's planetary system had been discovered which conformed to the Laplace resonance. The fact that we have two examples of it now is telling us something important I believe. The real answer I am seeking is what.

Canis Lupus
2017-Jan-21, 09:56 PM
That's above my pay grade, I am just a simple plasma astrophysicist.

You plasma astrophysicists are all the same - always putting yourself under intense pressure, balancing the positive and negative, spreading yourself seemingly everywhere, and from time to time coming up with something glaringly new. :)

You definitely deserve more pay, that's for sure.

Shaula
2017-Jan-22, 07:06 AM
I was ecstatic to read some time ago that a star's planetary system had been discovered which conformed to the Laplace resonance. The fact that we have two examples of it now is telling us something important I believe. The real answer I am seeking is what.
Interesting that when I gave you two examples of things you said couldn't exist, in another thread, I got the reply:

Without going into the details, we seem to have a few explainable odd-bods without discovering the many systems we ought to be observing.

So ... why is this different? And why is the Plutonian resonance (11:9:6) not as significant or ideal?

Canis Lupus
2017-Jan-22, 07:35 AM
Interesting that when I gave you two examples of things you said couldn't exist, in another thread, I got the reply:

This system is orbiting around a nomad planet or a star?



So ... why is this different? And why is the Plutonian resonance (11:9:6) not as significant or ideal?

Didn't state it wasn't.

Attribute what is fair, not make believe, is all I respectfully request.

Shaula
2017-Jan-22, 08:14 AM
Didn't state it wasn't.
Attribute what is fair, not make believe, is all I respectfully request.
Just trying to understand your question better. Resonances happen, and happen at all kinds of combinations of orbit ratios and numbers of bodies. They often don't include all the interacting bodies in a system (as in the Galileans) We only see a couple of examples of the Laplace one. So we have a rare resonance amid a number of other ones, I just want to understand why you think it is so significant? As in, what properties does it have that make it stand out as 'ideal' or 'perfect'? Or do you consider all resonances ideal/perfect?

Canis Lupus
2017-Jan-22, 08:13 PM
Just trying to understand your question better.

That is fair enough and very much appreciated.


Resonances happen, and happen at all kinds of combinations of orbit ratios and numbers of bodies. They often don't include all the interacting bodies in a system (as in the Galileans) We only see a couple of examples of the Laplace one. So we have a rare resonance amid a number of other ones, I just want to understand why you think it is so significant? As in, what properties does it have that make it stand out as 'ideal' or 'perfect'? Or do you consider all resonances ideal/perfect?

If there is a mathematical relationship between these different resonances and their ratios, it's not so much that anyone can think it significant, it's screaming something out to us. There must be something deeply significant between these ratios.

One of the problems I believe is that the ratios are being obscured in their purities by trends either away or towards a pure ratio. From my reading on this issue, I believe, that this is an issue in science, whether orbital resonances which appear close to pure ratios are trending away from the ratio or towards it. You might appreciate that if such trends exist, then that may have implications for plantary migrations. Since we live on a planet this is not only a scientific issue but an environmental one. Now that I have used that word "environment" how many boxes were just opened in areas of science which are forever refining theories?

I don't wish to appear too tangential here, but one cannot possibly be accused of wondering about something insignificant when attempting to understand Laplace resonance. It is the closest, most observable pure ratio we have to examine and work out. It is so important, I am amazed that it doesn't receive more public attention. It almost appears tucked away.

Canis Lupus
2017-Jan-22, 08:35 PM
One thought I had about this issue is that different ratios may apply, or trends towards different ratios may apply, depending upon the predominant element being used to create the resonance. For example, in a star which is burning mainly hydrogen, one type of ratio will be trended towards. In another burning more helium, another ratio applies.

If the above were true, then, by first determining the age of a star, we can understand better what will occur with its planetary system as the resonances continue to trend. Naturally, this application applies equally to the Sun.

Hornblower
2017-Jan-22, 08:52 PM
One thought I had about this issue is that different ratios may apply, or trends towards different ratios may apply, depending upon the predominant element being used to create the resonance. For example, in a star which is burning mainly hydrogen, one type of ratio will be trended towards. In another burning more helium, another ratio applies.

If the above were true, then, by first determining the age of a star, we can understand better what will occur with its planetary system as the resonances continue to trend. Naturally, this application applies equally to the Sun.

The forces in the orbital resonance situations are purely gravitational. The nature of the furnace in the core of the star should be immaterial. Why do you think we should expect otherwise?

Canis Lupus
2017-Jan-22, 09:01 PM
The forces in the orbital resonance situations are purely gravitational. The nature of the furnace in the core of the star should be immaterial. Why do you think we should expect otherwise?

I can't tell anyone what to expect until I have satisfied myself the data points to a connection. The example I gave was theoretical to illustrate potential importances. Under present understanding of gravity as energy and correlating with Mass, it can't be ruled out.

Shaula
2017-Jan-22, 09:07 PM
If there is a mathematical relationship between these different resonances and their ratios, it's not so much that anyone can think it significant, it's screaming something out to us. There must be something deeply significant between these ratios.
Why? This is the crux of it. We see 2:3s, 3:5s, 4:7s, 1:2s, 2:5s among TNOs. Which means we have 4:7:8:10:12 going in there. We have resonances and resonance gaps in the asteroid belt. We have all kinds of fun going on around Saturn. Resonances are not uncommon - and the fact that we only see one Laplace one seems to argue that it is not that special or perfect.


I don't wish to appear too tangential here, but one cannot possibly be accused of wondering about something insignificant when attempting to understand Laplace resonance. It is the closest, most observable pure ratio we have to examine and work out. It is so important, I am amazed that it doesn't receive more public attention. It almost appears tucked away.
It is hardly tucked away - but why would it be the subject of so much attention? It is just a resonance. There are loads of them out there. They are just a fact of orbital dynamics. They can be stabilising or de-stabilising.

Do you have any focused questions about these resonances? Maybe that could help us understand why you regard them as so important.

Canis Lupus
2017-Jan-22, 09:26 PM
Why? This is the crux of it. We see 2:3s, 3:5s, 4:7s, 1:2s, 2:5s among TNOs. Which means we have 4:7:8:10:12 going in there. We have resonances and resonance gaps in the asteroid belt. We have all kinds of fun going on around Saturn. Resonances are not uncommon - and the fact that we only see one Laplace one seems to argue that it is not that special or perfect.


It is hardly tucked away - but why would it be the subject of so much attention? It is just a resonance. There are loads of them out there. They are just a fact of orbital dynamics. They can be stabilising or de-stabilising.

Do you have any focused questions about these resonances? Maybe that could help us understand why you regard them as so important.

Yep, they are everywhere.

I'll apply my interpretation of your post to Matter. Matter is everywhere, therefore, searching for an understanding of a pure form of Matter informs us of nothing about the Matter which is everywhere.

I'm sure all those physicists who cracked the nature of the Atom would enjoy the logic.

I have not read any rule of Q & A that questions must be narrow, confined and focused, but I would welcome the education on this point.

Hornblower
2017-Jan-22, 11:25 PM
Yep, they are everywhere.

I'll apply my interpretation of your post to Matter. Matter is everywhere, therefore, searching for an understanding of a pure form of Matter informs us of nothing about the Matter which is everywhere.

I'm sure all those physicists who cracked the nature of the Atom would enjoy the logic.

I have not read any rule of Q & A that questions must be narrow, confined and focused, but I would welcome the education on this point.

My bold. Perhaps not a requirement, but it might help us in our attempts at ascertaining your line of thought.

Hornblower
2017-Jan-22, 11:28 PM
That is fair enough and very much appreciated.



If there is a mathematical relationship between these different resonances and their ratios, it's not so much that anyone can think it significant, it's screaming something out to us. There must be something deeply significant between these ratios.

One of the problems I believe is that the ratios are being obscured in their purities by trends either away or towards a pure ratio. From my reading on this issue, I believe, that this is an issue in science, whether orbital resonances which appear close to pure ratios are trending away from the ratio or towards it. You might appreciate that if such trends exist, then that may have implications for plantary migrations. Since we live on a planet this is not only a scientific issue but an environmental one. Now that I have used that word "environment" how many boxes were just opened in areas of science which are forever refining theories?

I don't wish to appear too tangential here, but one cannot possibly be accused of wondering about something insignificant when attempting to understand Laplace resonance. It is the closest, most observable pure ratio we have to examine and work out. It is so important, I am amazed that it doesn't receive more public attention. It almost appears tucked away.
I would venture a guess that Laplace and those mathematicians and orbital mechanics experts who stand on his great shoulders have thought of every issue that you have raised, and then some, and evaluated them.

Jens
2017-Jan-22, 11:59 PM
Yep, they are everywhere.
I'll apply my interpretation of your post to Matter. Matter is everywhere, therefore, searching for an understanding of a pure form of Matter informs us of nothing about the Matter which is everywhere.
I'm sure all those physicists who cracked the nature of the Atom would enjoy the logic.

He's asking you why you are particularly interested in that resonance. I don't see why it merits such a seemingly snide response. Clearly there is something that you're thinking, and it would help everybody to understand if you ask questions that are a bit more focused. OK, I'll go out on a limb and imagine that possibly what you're thinking is that a hydrogen-burning star is equivalent to a hydrogen atom on a larger scale, and a helium-burning star to a helium atom, etc. But that's just my wild guess.



Do you have any focused questions about these resonances? Maybe that could help us understand why you regard them as so important.


I have not read any rule of Q & A that questions must be narrow, confined and focused, but I would welcome the education on this point.

Here again, the question made it clear that it would be helpful for understanding, but you responded with something about rules. Nobody said it was against the rules. I'm not sure why there is a need to be defensive.

Geo Kaplan
2017-Jan-23, 12:04 AM
Yep, they are everywhere.

I'll apply my interpretation of your post to Matter. Matter is everywhere, therefore, searching for an understanding of a pure form of Matter informs us of nothing about the Matter which is everywhere.

I'm sure all those physicists who cracked the nature of the Atom would enjoy the logic.

I have not read any rule of Q & A that questions must be narrow, confined and focused, but I would welcome the education on this point.

Historically, beginning with some mystical beliefs and trying to use inductive reasoning to create a universe has a poor track record, I recommend first studying how the universe actually behaves, and then applying deductive reasoning so that your imagination is appropriately grounded in empirical evidence. "Outside of the box" thinking is not nearly the virtue that is held by many non-scientists. One must, at minimum, know where the box is. Feynman said it well when he asserted that science is about imagination in a strait-jacket.

In this case, you should know that "digital orreries" successfully predict the observed motion of celestial bodies. The inputs do not include the composition of the bodies, so as far as all the evidence shows, there is no need to consider what the bodies are made of. We just need to know the total size, the mass, and how that mass is distributed. Newton does quite well for the most part (that's how we are able to launch probes through and outside of our solar system with great success), with the full power of GR being needed for the rest.

Finally, resonances are an extremely common feature of dynamical systems. Masses suspended from springs, swinging pendulums, violin strings, brass instruments, etc., all show resonant behavior. Coupled dynamical systems continue to show resonances which, thanks to the coupling, can often produce eigenmodes that are related by more-or-less fixed ratios. Laplacian resonances are but an infinitesimal subset of a much broader set of phenomena that occur throughout nature.

Canis Lupus
2017-Jan-23, 12:50 AM
Historically, beginning with some mystical beliefs and trying to use inductive reasoning to create a universe has a poor track record ...

Except maybe with Einstein who appeared to start with a mystical belief in a space.time fabric, then went on to show how the data was consistent. He had to couple his inspirations and work with a mathematician to make it complete, but ah in the end he did it all via the method you are now advising against.

That's not to state that this method does not have its traps. Every method does, and I'm certainly not Einstein. But as a matter of principle, I cannot agree with your slant. On the other hand, I will concede it all has to do with the execution of the method as to whether it comes astray or not. This position, I believe, represents are better picture than the one above - a finer appreciation of the principle.



I recommend first studying how the universe actually behaves

I'll overlook the implications of this statement for the sake of civility on this forum but that is what I am attempting to do. If I thought a theory or hypothesis was the way in which the universe behaved, my way of expressing myself would be radically different. In fact, I don't think I would even bother with this forum with its focus on mainstream science.



and then applying deductive reasoning so that your imagination is appropriately grounded in empirical evidence.


Not going to even bother with this part of your post, except to state I am not going to bother with it. Others will find it interesting no doubt, especially the advocates of dark matter.


"Outside of the box" thinking is not nearly the virtue that is held by many non-scientists. One must, at minimum, know where the box is. Feynman said it well when he asserted that science is about imagination in a strait-jacket.

Yep, that is exactly how mainstream feels to me, like a straight jacket. Nonetheless, here I am working, not so much my imagination on it, but natural visualisation and geometric skills combined with reason referenced to the data. Different way of looking at it than what you are portraying by the loaded term "imagination", but again, like the last point a more accurate refinement.

Finding a box can be a difficult thing, I agree. If it is ok with you, I'll find the box by reference to other boxes and objects in the room and the room itself. I'd hate to be trying to find a box without knowing that its even in a room or some other general reference point.




In this case, you should know that "digital orreries" successfully predict the observed motion of celestial bodies. The inputs do not include the composition of the bodies, so as far as all the evidence shows, there is no need to consider what the bodies are made of. We just need to know the total size, the mass, and how that mass is distributed. Newton does quite well for the most part (that's how we are able to launch probes through and outside of our solar system with great success), with the full power of GR being needed for the rest.

That's all very well, but I would insist you miss the point of where I am coming from and possibly going to. But there will be other occasions to flesh this issue out.


Finally, resonances are an extremely common feature of dynamical systems.

Sure ... so?



Masses suspended from springs, swinging pendulums, violin strings, brass instruments, etc., all show resonant behavior.

Very good, and I'm sure that particular point is relevant to some debate somwhere.



Coupled dynamical systems continue to show resonances which, thanks to the coupling, can often produce eigenmodes that are related by more-or-less fixed ratios. Laplacian resonances are but an infinitesimal subset of a much broader set of phenomena that occur throughout nature.

But do they occur in conjunction with a large Mass known as a planet called Jupiter, which orbits a star called the Sun, affecting four other masses known as moons?

Geo Kaplan
2017-Jan-23, 01:09 AM
You missed several key takeaways, so I will repeat them.

Resonances are very common phenomena. Therefore, choosing one and calling it special (and using terms like "ideal" without defining the term) is an arbitrary act. You have ignored the "digital orreries" part. It tells you that there is no scientific rationale for invoking new physics to explain Laplacian resonance, as it is already explained as just another of a vast array of identical phenomena found throughout nature. New explanations have the burden of explaining all that is already explained (that is the strait-jacket part), while also doing something better. Most out of the box proposals do the easy part ("I have a theory, which feels good to me"), but dispense with the former ("All I need to do is some maths bits").

And yes, a straitjacket is indeed confining, because the universe's actual behaviour confines what our theories must predict. One's personal aesthetics have to take a back-seat.

Einstein knew very well where the box was, and how firm the walls were (and weren't). That's the key part that is too often ignored. Feynman's comment is all about knowing the difference.

Canis Lupus
2017-Jan-23, 01:32 AM
You missed several key takeaways, so I will repeat them.

Resonance are very common phenomena. Therefore, choosing one and calling it special (and using terms like "ideal" without defining the term) is an arbitrary act. You have ignored the "digital orreries" part. It tells you that there is no scientific rationale for invoking new physics to explain Laplacian resonance, as it is already explained as just another of a vast array of identical phenomena found throughout nature. New explanations have the burden of explaining all that is already explained (that is the strait-jacket part), while also doing something better. Most out of the box proposals do the easy part ("I have a theory, which feels good to me"), but dispense with the former ("All I need to do is some maths bits").

And yes, a straitjacket is indeed confining, because the universe's actual behaviour confines what our theories must predict. One's personal aesthetics have to take a back-seat.

Einstein knew very well where the box was, and how firm the walls were (and weren't). That's the key part that is too often ignored. Feynman's comment is all about knowing the difference.

We are in complete agreement then, particularly my takeaway dish I have placed in bold which you eloquently articulated for me. Thanks for your help. It is has been illuminating, particularly in understanding the limitations mainstream thinking imposes. I see it as a pleasant discipline to work with. Growing up with two very competitive brothers in our litter close to my age meant "challenges" were never far away. I embrace it as a sharpening tool.

Canis Lupus
2017-Jan-23, 02:04 AM
He's asking you why you are particularly interested in that resonance.

I provided an answer for that question.


I don't see why it merits such a seemingly snide response.

I reject 100% that I was snide. Please report my post if you think it was. In fact, I might do it myself now that you have made the accusation. I took the principle being applied to my enquiry and applied it to another situation to demonstrate it was not valid. Snide would feel complimented by your accusation, but I certainly don't!


Clearly there is something that you're thinking, and it would help everybody to understand if you ask questions that are a bit more focused. OK, I'll go out on a limb and imagine that possibly what you're thinking is that a hydrogen-burning star is equivalent to a hydrogen atom on a larger scale, and a helium-burning star to a helium atom, etc. But that's just my wild guess.

Thanks for the effort and there is something in what you state, but you see I used the example as a theoretical one to justify my interest in the phenomenon, not to provoke a debate on the issue and what it may imply.


Here again, the question made it clear that it would be helpful for understanding, but you responded with something about rules. Nobody said it was against the rules. I'm not sure why there is a need to be defensive.

I really want to, like all genuine enquirers ought, know as much about the phenomenon as possible, particularly by reference to the peer reviewed literature. If, after that process of investigation and research is conducted (with the helpful guidance of those here to some extent), something appears to me which I think very important, I will have more questions that will be undoubtedly specific and focused.

It is not me who is defensive.

Geo Kaplan
2017-Jan-23, 02:06 AM
We are in complete agreement then, particularly my takeaway dish I have placed in bold which you eloquently articulated for me. Thanks for your help. It is has been illuminating, particularly in understanding the limitations mainstream thinking imposes. I see it as a pleasant discipline to work with. Growing up with two very competitive brothers in our litter close to my age meant "challenges" were never far away. I embrace it as a sharpening tool.

I wish you all the best in your quest!

Canis Lupus
2017-Jan-23, 02:10 AM
I would venture a guess that Laplace and those mathematicians and orbital mechanics experts who stand on his great shoulders have thought of every issue that you have raised, and then some, and evaluated them.

Last time I checked this isn't a forum about guessing.

Canis Lupus
2017-Jan-23, 02:10 AM
I wish you all the best in your quest!

Much appreciated

Canis Lupus
2017-Jan-23, 02:18 AM
My bold. Perhaps not a requirement, but it might help us in our attempts at ascertaining your line of thought.

I have given my line of thought. If you want an ATM, I don't have one to give. Maybe in the future, of course, but that should apply to everyone as a matter of principle.

Canis Lupus
2017-Jan-23, 02:24 AM
Yep, they are everywhere.

I'll apply my interpretation of your post to Matter. Matter is everywhere, therefore, searching for an understanding of a pure form of Matter informs us of nothing about the Matter which is everywhere.

I'm sure all those physicists who cracked the nature of the Atom would enjoy the logic.

Ok, as foreshadowed elsewhere, the post above has gone to the third umpire as we say in cricket.

Hornblower
2017-Jan-23, 02:25 AM
I have given my line of thought. If you want an ATM, I don't have one to give. Maybe in the future, of course, but that should apply to everyone as a matter of principle.

It is not clear to me just what you mean by terms such as ideal, perfect or pure for a Laplace resonance as compared with other well known and well studied resonances. Is it an aesthetic appeal of some sort, or is there an explicit mathematical feature here?

Canis Lupus
2017-Jan-23, 02:40 AM
It is not clear to me just what you mean by terms such as ideal, perfect or pure for a Laplace resonance as compared with other well known and well studied resonances. Is it an aesthetic appeal of some sort, or is there an explicit mathematical feature here?

Note this:


Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter (https://en.wikipedia.org/wiki/Jupiter)'s moons Ganymede (https://en.wikipedia.org/wiki/Ganymede_(moon)), Europa (https://en.wikipedia.org/wiki/Europa_(moon)) and Io (https://en.wikipedia.org/wiki/Io_(moon)), and the 2:3 resonance between Pluto (https://en.wikipedia.org/wiki/Pluto) and Neptune (https://en.wikipedia.org/wiki/Neptune).

Then note this:


In general, an orbital resonance may

involve one or any combination of the orbit parameters (e.g. eccentricity (https://en.wikipedia.org/wiki/Eccentricity_(orbit)) versus semimajor axis (https://en.wikipedia.org/wiki/Semimajor_axis), or eccentricity versus orbital inclination).
act on any time scale from short term, commensurable with the orbit periods, to secular (https://en.wikipedia.org/wiki/Secular_phenomena), measured in 104 to 106 years.
lead to either long-term stabilization of the orbits or be the cause of their destabilization.



https://en.wikipedia.org/wiki/Orbital_resonance

Ideal means stable - what orbital resonances may be trending towards or away from or have achieved.

AS an aside, given that it seems that only Pluto and Neptune have achieved a stable (ideal) resonance, putting aside the moons of Jupiter for a moment, there appears an implication don't you think?

Swift
2017-Jan-23, 04:10 AM
I have not read any rule of Q & A that questions must be narrow, confined and focused, but I would welcome the education on this point.
From one of the Q&A stickies:

This section of the forum is for astronomy and space exploration questions with straightforward, generally accepted answers.

Questions that are likely to lead to extended discussion about the correct answer, or that have no clearcut correct answer, should be posted in the forum most appropriate to the topic of the question. If a question does lead to such discussion, it may be split off or moved entirely to a more appropriate forum by a moderator. Since it's hard to tell how a discussion will go, posting such questions will generally be treated as a judgment matter and not a rule violation.

Questions taking issue or raising concerns with the mainstream viewpoint should be posted in the ATM forum. Posting questions along these lines will generally be treated as a rule violation.

You've been given the mainstream answers, yet you continue to argue about it, and apparently not for clarification, but to advocate an ATM idea.

One thought I had about this issue is that different ratios may apply, or trends towards different ratios may apply, depending upon the predominant element being used to create the resonance. For example, in a star which is burning mainly hydrogen, one type of ratio will be trended towards. In another burning more helium, another ratio applies.

If the above were true, then, by first determining the age of a star, we can understand better what will occur with its planetary system as the resonances continue to trend. Naturally, this application applies equally to the Sun.
Given all this, the trend is closed. You're getting a zero pointer to help you remember all this. Next time, the infraction will be for points.