March 15, 2013 report

# Physics duo discover 13 new solutions to Newtonian three-body orbit problem

(Phys.org) —Physicists Milovan Šuvakov and V. Dmitrašinović of the Institute of Physics, Belgrade in Serbia have discovered using computer simulations, 13 new solutions to the three-body problem—predicting patterns that describe how three bodies will orbit around each other in space in a repeating pattern. The two describe how they came up with their solutions using computer simulations in their paper published in *Physical Review Letters*.

When two bodies in space orbit one another, such as a planet and a star, their paths can be easily described by Newton's laws of gravity—they are elliptical. When another body is introduced, however, things become so complex that scientists have not been able to find a way to predict the sorts of patterns that are possible for a stable system (where they don't run into one another eventually) to come about. Until now, just three families have been identified: The Lagrange-Euler, the Broucke-Hénon, and the figure-eight.

To discover a repeating pattern that describes how three bodies will orbit one another in stable fashion requires some degree of luck, the Lagrange-Euler family for example was discovered by the mathematicians for whom it is named and is demonstrated by the way the sun, Jupiter and the asteroid Trojan orbit one another. Another way requires some degree of brute force—that's the approach taken in this new effort. The two researchers started with a known solution then changed some of the parameters in their computer simulations and ran the results to see what would happen. As it turned out, their way resulted in the discovery of 13 new families of patterns—stable orbits that eventually lead to all three bodies existing in the same place as they were when the simulation started.

Because they found so many new solutions, the two came up with a way to classify them using what they call a shape-sphere to graphically show what the orbits look like and then gave each a name, based on what they thought they resembled: yarn, butterfly, goggles, etc.

Thus far, the 13 new families haven't been tested thoroughly enough to verify that their orbits would remain stable over long periods of time (which would mean holding their pattern despite slight perturbations), however—the researchers plan to do just that as part of their next effort. If it turns out some or all of them can withstand the test of time, then scientists can begin looking for instances of them in real systems and perhaps learning more about those systems as a result.

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**More information:**Three Classes of Newtonian Three-Body Planar Periodic Orbits, Phys. Rev. Lett. 110, 114301 (2013) DOI:10.1103/PhysRevLett.110.114301 (on ArXiv)

**Abstract**

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits' geometric and algebraic symmetries. In each class we present a few orbits' initial conditions, 15 in all; 13 of these correspond to distinct orbits.

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**Citation**: Physics duo discover 13 new solutions to Newtonian three-body orbit problem (2013, March 15) retrieved 19 September 2019 from https://phys.org/news/2013-03-physics-duo-solutions-newtonian-three-body.html

## User comments

antialias_physorgBirgerEl_Nosebut an orbit is stable -- the definition of orbit inplies stablity, and since that definition was applied to these bodies, I have trouble understanding your real question

gwredeBoy, was I wrong. Now it seems like (to me anyway) that computer cycles are used for spam, youtube, porn, facebook, twitter, viruses, phishing, espionage, and bomb building instructions. Those are not why I got into computers.

El_NosePkunk_I haven't yet come across a single concrete experiment that proves without any doubt. There is no guarantee that the speed of propogation of gravity "waves" or a gravitational field is bound by C .

To conclusively prove this would probably require some sort of multiple satellite experiment that tests gravity propagation over a multiple AU distance.

Q-StarLeaving "guarantees" aside, have ya "yet come across a single concrete experiment that" EVEN SUGGESTS that gravity operates at some speed other than c? Assuming c has been correct in all the phenomena observed to-date.

It would be much easier to prove it doesn't than it would to that it does. And since it's easier, ya should offer to "prove" it doesn't. Or at least offer "a single concrete experiment" that suggests there is a reason to question it.

Lobo TommyECOnservativeantialias_physorgWe'll know more when the data from the Advanced LIGO experiment - which is set up to precisely look for this - comes in.

Whydening GyreTake a look at the article on complex systems...

ValeriaTantialias_physorgLurker2358LIGO is built next to a rail road where local vibrations are far, far larger than the anticipated data vibrations would be.

There is no way to know for sure whether a "result" is just some local phenomenon, because it could be anything from a pogo stick to a train...

It's a waste of resources.

antialias_physorgI think you might read up a bit on how (and where) LIGO is constructed, firts, before making such statements

Pogo stick vibration do not travel at c. It is comparatively easy to filter any results out that aren't in the expected range.

alfie_nullGood point. I'd generalize it to "computers are largely, and increasingly used as entertainment devices". But also consider that the commoditization of computers has made them more easily available to many more researchers to do work like this.

Torbjorn_Larsson_OM@LT:

Look in the "resulted" link.

@AP: We do know the speed of gravity.

It is the universal speed limit. General relativity ensures it is so for all physical interactions, the gravitational interactions observed ensures it is so for the relevant "gravitomagnetic" changes (see here: http://en.wikiped..._gravity ), and the low energy approximation of a gravitational field tests that in the limit (field changes mediated by gravitons).

Maybe you are thinking of inflation, which makes spacetime expand superluminally in the presence of a gravitational potential (which must be there to balance particle field et cetera energies). But that is no interaction, no "gravity" speed. It is a spacetime "speed".

Torbjorn_Larsson_OMThe problem comes if we want to call that "gravity", or "physical interactions". It isn't, we can't signal with it and we can't move masses with it. (Cf Alcubierre's drive, which is created superluminally and can't be populated with particles to transfer and/or signal with. It isn't "driving" anything.)

baraknYou were wrong. Only L4 and L5 are "stable" in the manner you suggest, because of the Coriolis force (for those of you incapable of comprehending a rotating reference frame, yes, it's a pseudoforce). L1, L2, and L3 are truly unstable and an object trying to stay at one of them will require energy and fuel to do so. The speed of gravity is a red herring - discussions of Lagrange points typically only involve Newtonian gravity.

nugeNot quite the same. There is no way you can have three bodies which are mutually attracted to one another in EM.

Reg MundySethDYou'd think computer simulations are for modelling, not discovering.

EverythingsJustATheoryYes, yes. We all understand that Einstein disproved Newton's definition of gravity. Reg, can we move on to an issue rooted in this century?

avengersAnd how did he do that? I thought he just expanded on it mathematically, and gave his own view of what gravity is.

Which we now know was wrong. The notorious "Standard Model" isn't playing well either...

avengersGood catch! But also from the physical point of view: you can't solve the famous Newton's problem, you can only model it.

Serbs and science... They make such blunders because they abandoned teachings of their greatest mind ever Nicola Tesla, and are now trying to talk the talk and walk the walk of his haters and mockers from the wild wild west. What a junk paper.

Reg MundyThat's the real problem, EJAT. Moving on based on false assumptions is counter-productive. When something doesn't work, it is often best to reconsider basics rather than keep sticking bits of plaster over the cracks. We gotta ask the fundamental questions, like why the models based on, for example, gravity, do not work.

antialias_physorgSometimes you get discoveries using computer models. Computer models are based on algorithms that work with well established (i.e. often observed) phenomena. So you plug those algorithms into your simulation to see what happens.

The thing is: you always have boundary conditions/rare cases for which you don't know whether the algorithm holds. With a simulation you can always take an easy look at those conditionsbecause nulike in reality setting up a rare set of conditions isn't any harder than setting the 'usual case'.

Sometimes you'll see something surprising happen in the simulation. So then you do an experiment if it's really just the simulation being applied to conditions it isn't suited for - or whether that weird behaviour actually manifests.

If it does indeed occur you have made a discovery via a simulation.

EverythingsJustATheoryMuch more than an expansion, Einstein completely redefined it. And as far as I know, General Relativity has stood up to every test not at the quantum level. I wouldn't call it wrong, just incomplete at the smallest scales.

Netwon was describing the effect we observe, but his reason why it was occuring was incorrect (attractive force).

Einstein showed that matter warps spacetime itself, and that this causes the effect (attractive force) we observe. The earth is moving in a straight line in the sun's warped spacetime, which causes it to orbit. The force is being exerted on the earth from spacetime itself, not any attraction from the sun.

Reg, I guess I was wrong about everyone knowing.

SethDIt claims to be universal, so if it's "incomplete" then it's wrong in it's major claim. Not just any claim...

"Spacetime" is a mathematical construct, so far no physical meaning. So matter doesn't "warp" (whatever that means) an idea which stays firmly in someone's head.

For example your mind is twisted enough already.

EverythingsJustATheoryhttp://en.wikiped...lativity

avengersSo true, yet people tend to forget it all the time!

avengersAm pretty sure Seth understands it. Indeed, as he correctly noted: "spacetime" exists only if you imagine it. Which makes it totally useless for universal considerations. You can't warp something around nothing.

Get it? I doubt you ever will.

Reg MundyEinstein didn't "show" anything, he theorised. His theories have stood up remarkably well, but in the final analysis he "invented" the space-time continuum then "warped" it. It has been a superb tool for handling reality, just as Newton's law of gravity is, but there is no "proof" that any of it is any more "true" than a dozen other theories. The bit about "everyone knowing" illustrates the problem, they only THINK they know without actually THINKING about it. The likelihood of there being warps in space-time is about the same as there being a Father Xmas, and more people KNOW he exists.

EverythingsJustATheoryGravitational lensing has been observed countless times, which pretty much proves that spacetime is warped in the presence of matter.

So your claim that there is just as much evidence for the existence of Santa Clause is total bullshit.

Q-StarProves is a strong word, but it does say that Einstein's model concerning spacetime warping is more accurate as to what we actually see than any other so far proposed. Newton would have the photon possessing mass, and falling toward the lensing object, not steered around it.

It shows the opposite. That light does not act like any other solid object. By the fact that the lensing does not attract the light toward the massive object, but bends it around the massive object.

Anything else would be pulled toward the center of mass. But spacetime itself is warped, as far as the light is concerned, it is still traveling in a straight line.

Q-StarAttracted into? Yes I'm claiming it can not. Light(photons) is a massless particle, it doesn't respond to gravity, in the same way an object with mass does, it responds to the spacetime that the massive objects warps.

For photons to be attracted TO mass, then ya would have to propose a mechanism for light to have it's velocity to change in a vacuum of spacetime, but we are very certain that "c" is a universal constant. So far no observations have hinted otherwise. It's one of the most precise & invariant constants we've ever measured.

Black holes can't suck light in, "c" is too great for that. Light can not escape the event horizon because the required escape velocity at that point is greater than "c".

Reg MundyThere is no "proof" that gravitational lensing is not actually refraction. It has not been possible to model the effect by positioning mass, normal matter and/or dark matter, to achieve the observed results.

PS Sorry to upset you about Santa Claus, but your mother should have told you before you went to big school.

EverythingsJustATheoryUnfortunately for your argument, Newton's prediction for the bending of light by a massive object was only half the value observed in reality. Einstein was the first to correctly calculate the value for light bending using General Relativity.

Not been possible to observe the effects?

Arthur Eddington - 1919

Lick Observatory - 1922

Yerkes Observatory - 1953

University of Texas - 1973

As for Santa, I figured that one out myself when I was five when I found hidden presents a day or two before Christmas that were 'From' Santa

EverythingsJustATheoryDo you not understand what refraction means? Refraction is when light waves change direction due to traveling through a different medium. What medium change would be present for refraction to occur other than warped spacetime?

Are you suggesting that the density of space inside our solar system varies from one side of the sun to the other? Because the Sun most definitely bends light so that stars that should be not visible (blocked by line of sight) are, and the amount of bending is twice what Newton predicted.

nxentWhydening GyreWow, Q. That is as correct a statement as I will ever read(at least in my left-handed mind). (cont)

Whydening GyreYour described bond tween photons and "space/time" is exactly the way I see it. Gravity has nothing to do with lensing, but the warping of space time with matter does - yowza. Makes the thought of gravity being a property of matter interacting with other matter, as opposed to the idea of gravity already just being there, even more appealing...

Reg MundyIf you think about the density of matter in the vicinity of, say, a black hole, it stands to sense that you will encounter more matter, e.g. hydrogen, if you are near to it than if you were further away. Classic lens formation from a gas.

Same applies to increasing gas density on approaching Sol.

Incidentally, I hope you can think back to when you discovered the presents under the tree "from Santa", 'cos that's the feeling you're gunna get when the penny drops about gravity... but in spades.

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