The April 27 issue of Nature has an article on how the outer planets got their tilts. The Planetary Society did a writeup on this article. You can find it here: http://www.planetary.org/blog/article/00000553/

from the Planetary Society article:
This doesn't make sense to me. Uranus and Neptune at 13 & 14 AU would very heavily perturb themselves. Their comfortably round orbits would last only until their 1st conjunction, and at those distances, they would have a conjunction about every 500 years. After passing conjunction, they pull each other out of round orbits, into orbits with high eccentricity, sometimes entering orbits that cross each other, and sometimes switching places. This is all within a few hundred years.

The Nature paper gives a diagram, showing that Uranus and Neptune peacefully co-exist in round orbits for about 100,000 years. Then it shows their orbits in utter chaos after Saturn and Jupiter migrate into a 2:1 orbital resonance. But my simulation shows the utter chaos beginning immediately, without the help of Jupiter or Saturn.

If they were less massive at that time, that might help explain things, but according to the Nature paper:

So it seems to me like the author of the Nature paper is considering fully or nearly-fully formed planets. But I find that even with half their present masses, Neptune and Uranus can not peacefully co-exist at 13 & 14 AU.

Any thoughts?

Here's some screen shots showing the paths of a fully-formed Uranus & Neptune starting in circular orbits at 13 & 14 AU from the Sun. Within a few hundred years, they've crossed each other's orbits and swapped places. This completely contradicts what the Nature paper diagram shows.

Well, nothing is as difficult as modelling the 3-body problem numerically. Let alone, if you want to model the whole solar system. I see only the two planets, where are Jupiter and Saturn? Did you use a good timestep for your numerical integration? Did you use a correct numerical integrator? etc. etc.

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I agree with 'tusenfem'. You can not discount Jupiter or Saturn in these calculations. They were there exerting a great deal of influence over the early solar system. Whats wrong with the idea that the planetary disk just condensed the way it is ? No amount of modeling can for see what may have actually happened in the early years of this system.

Tony, I wonder if the fact that Uranus and Neptune were orbiting within a debris disk is relevant here: that has a powerful circularizing effect on orbits, as the planets exchange energy with the disk as well as with each other.

Grant Hutchison

Yep, here we go. The caption to the first graph in Brunini's letter to Nature includes the following detail of the simulation parameters: "The orbits were circularized as though dynamical friction by the planetesimal disk were operating while the planets were immersed in the planetesimal disk ..."

Grant Hutchison

Yeah, the Neptune/Uranus conjunctions happen about half a dozen times less often than resonant conjuctions with Jupiter and Saturn, but are much closer, so it's not obvious which would be more important. Until you throw in the fact that the resonant effects always happen at the same place in the orbits of Neptune and Uranus. So if Grant is right, what must be happening is that the random kicks by Neptune/Uranus get smoothed over by the circularizing effects of the debris disk, whereas the resonant kicks have a chance to cause a gradually increasing orbital radius even in the presence of the circularization. I'm not really sure what causes that difference, but that's the big deal with resonant interactions. Also, I'm personally a bit surprised that the circularization could be so strong as to act on tony873004's 500 year timescale, but I can't think of any better suggestion than Grant's. It does seem pretty mysterious to me.

Thank you for the replies.

I'm not trying to model the whole solar system. I'm only trying to see if a fully formed Uranus & Neptune can peacefully co-exist for 100,000 years while seperated by only 1 AU. Originally, I did have Jupiter and Saturn in the simulation, I placed them at 5 & 8 AU as shown in the Nature diagram. This is just beyond the 2:1 resonant point. You have to look really close at figure 1 so see that Saturn migrates ever so slightly towards Jupiter which brings it into the 2:1 resonant point, where their combined gravity will now point in a specific direction rather than random directions at conjunction, as Ken describes.

With Jupiter and Saturn in the simulation, the results were similar, and the chaos in Uranus' and Neptune's orbits began right away. Wanting to know the sourse of chaos-producing pertabutions, and suspecting that Uranus & Neptune were doing it to each other, I deleted Jupiter and Saturn.

I used a timestep of 65K seconds, less than 1 day. I only need to go 500 - 1000 years to get my results.


The problem with the planetary disk condensing the way it is is that orbital periods are quite slow at the distances of Uranus & Neptune, and the disk material is theorized to have been too thin at that distance that the lifetime of the solar system is not long enough to have allowed Uranus & Neptune to accrete. This suggests they formed closer to the Sun, and migrated out to their current positions.

In the particular case of this Nature paper, the author's concern about the planets forming in their current locations is that it doesn't explain the tilts of the gas giants, especially Uranus. If Uranus were knocked on its side by a giant collision, there's no reason to believe that the orbital planes of its moons would have enough time over the life of the solar system to catch up with the planet's equator. So he speculates that if Uranus got tipped on its side gradually over the course of hundreds of thousands of years, that the moons orbital planes would be able to keep pace with the changing orientation of Uranus' equator. Although he doesn't say so in the paper, it seems to me that unlike the impactor theory, the planatary pertubation theory would provide torque to the planes moons' orbits as well as Uranus' equator.

Although no amount of modeling can forsee what may have actually happened in the early years of this system, that's not really the goal of these kinds of simulations. These simulations are only trying to spot trends. The author performed about 30 different simulations varying his starting conditions each time. He's not trying to find the smoking gun that says "Jupiter started exactly here, Saturn exactly there, this produces the exact obliquities observed today." He's simply trying to show that close planetary encounters can affect the obliquities of the planets, and that a 2:1 Jupiter Saturn orbital period ratio can disrupt the orbits of Uranus and Neptune enough to cause these close planetary encounters.

I'm glad you've got the Nature paper, Grant. It makes it much easier to discuss. The part you quote is followed by:

"...( the disk is assumed to start just beyond the initial orbit of the outermost planet)..."

which I take to mean that Uranus & Neptune were not in the disk at the time. And the part you quote is preceeded by the description of the changes in their orbits and obliquities following the migration of Jupiter and Saturn into the 2:1 resonance.

So I think the part you quote is referring to how their orbits circularized into the orbits we see today, [i]after[/] Saturn migrated beyond the 2:1 resonant point, rather than how they remained circular during the first 100,000 years before any of them ventured out into the planetisimal disk.

As Ken pointed out, the dynamical friction would have to be very strong to continuously circularize the orbits of planets that are pumping full AUs into each others perihelions and aphelions every 500 years.

I've taken it to mean that Jupiter, Saturn, Uranus and Neptune are all initially embedded in the simulated disk (which "starts" just beyond Neptune and extends all the way to the sun). The initial migration of the planets is then driven by the disk. But when Jupiter and Saturn hit resonance, they begin "pumping" the rest of the solar system.

Grant Hutchison

But they're not, if they're embedded in a disc. They're pumping a momentum change for a relatively short period of time once every 500 years, but the disc acts to damp that momentum change for the whole of those 500 years. And such planet-disc interactions can be fierce: some simulations show Jupiter-mass objects moving from 5AU to striking the central star in the order of 100,000 years. That's a big transfer of angular momentum.

I pulled the paper in the library at lunchtime today, but didn't copy it. However, my recollection is that the graph didn't have the resolution to show spikes in eccentricity followed by prompt damping with a time constant of a century or so.

Grant Hutchison

Shouldn't "starts" be referring to its inner edge and not its outer edge? When talking about the present day Kuiper Belt, we would say it starts just beyond the orbit of Neptune and ends at 50 AU, rather than saying it "starts" at 50 AU and ends at the orbit of Neptune.

But, you're right, he could mean it the way you say since there's probably no definitive way to use the words "starts" and "ends" when referring to orbiting disks.

However, I still think he means it extends away from Neptune, not towards the Sun. The 4 gas giants would have swept the area interior to Neptune clear during their formation, but further than Neptune, where orbital velocities ,and hence accretion, are slower, there is still abundent mass is still in the form of planetesimals.

In figure 1, there's virtually no migrating going on in the 1st 100,000 years. I'd expect migration during this period if the planets were embedded in the disk during this period. This period of almost no migration lasts until a very small migragion by Saturn places it in the 2:1 resonance and kicks Uranus and Neptune outward into the disk of planetesimals. Then once inside this disk, they scatter the disk and their migration accelerates as a result. They kick some objects in towards Jupiter and Saturn, which causes them, especially Saturn, to migrate as well. Just my guess...

That really surprises me, since the disk is also orbiting and it is much easier to see how disk interactions could cause circularization than it is to see how they cause the "death spiral", and so quickly. It sounds like this is telling us that circularization happens very fast, and is due to interactions with disk material at the same distance to the Sun as the planet, whereas there is a slower (but not a lot slower!) interaction with disk material that is preferetially farther out (which is what you need to extract angular momentum from the planet). Note these "death spiral" models need the disk to continue down toward the Sun, whereas the outward migrations need the disk to extend outward away from the Sun (you have to keep the planet immersed in the disk to keep circularizing the orbit). So the Neptune/Uranus conjuctions must not do that much since they can't make both planets migrate outward (perhaps it helps separate the two orbits, though) whereas the resonant interactions with Saturn and Jupiter can cause an outward spiral even in the presence of the circularization.

I didn't notice Grant's post #9 until Ken quoted it. I guess that's because it came while I was typing my reply. I appreciate you taking the time to look up the paper.

I'd have to agree with you that if the orbits were being constantly circularized that the graph doesn't have the resolution to show it. In fact, in my astronomy class we were talking about this. Graphs are often tiny because the author has to pay by the page to have his work submitted. I'm not sure if this works for the Letters to Nature or only journal entries.

But if Uranus & Neptune were immersed in a disk thick enough to smooth out the rough edges, often exceeding 1 AU, then it seems to me that they should be doing some migrating during this period.

In my simulations, Uranus and Neptune are not just affecting each others' eccentricity, but they're affecting each others' semi-major axes as well. In some runs of my simulation, it only takes two conjunctions to make Uranus & Neptune switch places. You could still have migrating semi-major axes while retaining a relatively circular orbit. But in the author's diagram, their semi-major axes hold steady during the first 100,000 years.

In my screenshots above, I simply show the results after the first two conjunctions. But if I let it run for thousands of years, Uranus and Neptune will have an encounter close enough to eject one of them, and send the other one on a Jupiter-crossing orbit with a perihelion near the Sun. Even if a planetesimal disk could circularize this orbit, it would be far from the original orbit.

If I understand the paper correctly, Jupiter and Saturn are not causing the outard spiral. Jupiter and Saturn, while teamed up in the 2:1 resonance are only exciting the eccentricities of Uranus and Neptune, causing their aphelions to wander out into the planetesimal disk. It is there that the migrating happens.

I've found something else that confuses me about the author's model.
Jupiter and Saturn perturb each other and do not stay at the 2:1 resonant positions for any extended period of time. If I place them perfectly at 2:1, after their first conjunction, they're not at 2:1 anymore. They're close, but close isn't good enough as it causes the longitude of their conjunction to drift. It's important for his model that the longitude of conjunction remains stationary, so the pertabutions to Uranus and Neptune build upon each other, rather than average out.

In my simulation, with Jupiter and Saturn placed perfectly in 2:1, ( 5AU & 7.9370388140957004 AU) their resonance jumps to 2.01 : 1 after one conjunction, and after 10 conjunctions, it is 2.03 : 1, and the longitude of conjunction has drifted ~30 degrees.

Objects can librate periodically around a 2:1 mean-motion resonance, swinging through a range of values of a and e. This is much more common in the wild, I understand, than an exact, unchanging resonance. Again, the author may be showing you mean values over a longer time period.

Grant Hutchison

The underlying physics is beyond me, but the inward movement occurs because of an asymmetry in the way angular momentum is transferred between the planet and its inner and outer Lindblad resonances in the disc. There are varying regimes of migration, depending on the mass of the planet.
Nelson et al's paper The Migration and Growth of Protoplanets in Protostellar Discs gives the details.

Grant Hutchison

PS: Bad memory strikes again. That paper relates to a dense viscous gaseous disc, so the dynamics are rather different from a planetesimal disc. Planetesimal discs also causes inward migration for Jupiter in simulations, but evidently to a much lesser extent.

Oh, and you're probably aware that 2:1 resonances can be either stable or unstable, depending on the relative orientations of the orbits, and relative positions of the planets. Is it possible you're setting up an unstable resonance as your starting point?

Grant Hutchison

Probably. I just put them in circular orbits, which would probably produce an unstable resonance to begin with. Watching it over a period of time showed me that the advance of the conjunction point did slow a bit, as if it were going to stop and reverse. But then it picked up speed and continued forward. I take this to mean that it is almost locked into a resonance. Starting it out with some eccentricity for Saturn will probably lock it into the resonance. Then the longitude of conjunction would librate back and forth around a point. This is interesting because that means that it's not only the longitude of Jupiter & Saturn's conjunction that causes instability to Uranus & Neptune, but the longitudes of the places that the conjunction never visits.

Thanks, Grant. That hadn't occured to me.
_________________________________________
Here's an animation of Jupiter and Saturn, in circular orbits at 2:1. This is not a rotating frame. It is a Kepler's pretzel centered on Jupiter. Rotating frames don't show much if the orbits are round.


Purple: Jupiter; Red: Sun; Yellow: Saturn
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This rotating frame animation isn't of Jupiter and Saturn, but of 2 hypothetical objects locked in a 2:1 resonance. But it serves to show qualitatively what is happening. If the resonance in the Jupiter & Saturn simulation did lock, the conjunction point would librate around a larger portion of the circle than this animation.

Yellow: Sun; Purple: Planet; Red: test particle with significant eccentricity

[QUOTE=tony873004]
The problem with the planetary disk condensing the way it is is that orbital periods are quite slow at the distances of Uranus & Neptune, and the disk material is theorized to have been too thin at that distance that the lifetime of the solar system is not long enough to have allowed Uranus & Neptune to accrete. This suggests they formed closer to the Sun, and migrated out to their current positions.
(eddit to add end quote here)

(i havent seen anyone suggest this apart from one other person who was to put it mildly rather `strange')got any links?


In the particular case of this Nature paper, the author's concern about the planets forming in their current locations is that it doesn't explain the tilts of the gas giants, especially Uranus. If Uranus were knocked on its side by a giant collision, there's no reason to believe that the orbital planes of its moons would have enough time over the life of the solar system to catch up with the planet's equator. So he speculates that if Uranus got tipped on its side gradually over the course of hundreds of thousands of years, that the moons orbital planes would be able to keep pace with the changing orientation of Uranus' equator. Although he doesn't say so in the paper, it seems to me that unlike the impactor theory, the planatary pertubation theory would provide torque to the planes moons' orbits as well as Uranus' equator.


ummm


by exactly what mechanism would a planatary impact (changing its axis of rotatation or not) have any ef(F)ect on the moons orbits anyway??

seems like either you i or both have misunderstood him-or he really has no idea about planets,orbits or anything else to do with planetary movement or newtons `laws'

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Surely if you are going to start a conspiracy theory it is best to start with something that might have a grain of truth or reality in it. To start with the preposterous and go downhill from there is just stupid. steve(primus) (Avatar)

During all of this orbital dancing, Brunini says, the planets exchange a great deal of angular momentum. In particular, the very close approaches of Uranus to Saturn causes them to exchange momentum, which, over time, changes their axial tilts. Now, this process is relatively fast, happening over a few hundred thousand years, but it is much slower than a single humongous impact tipping over a planet. The slower pace of the process that Brunini proposes means that as the planets slowly tilt, their satellite systems can actually follow the change in tilt. (All of these planets are fatter at the equator than at the poles, a geometry that tends to make their satellites' orbits flatten out into their equatorial planes over time.)

ok i see he has addressed that problem


ill say

shrug i dunno

ill wait for the brainy ones to nut it out

in 5 years time he'll be either right(ish) or wrong(ish)

id be wary of using simulations to `prove' anything tho

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Surely if you are going to start a conspiracy theory it is best to start with something that might have a grain of truth or reality in it. To start with the preposterous and go downhill from there is just stupid. steve(primus) (Avatar)

[QUOTE=http://www.chron.com/content/interactive/space/astronomy/news/1999/solarsys/991209.html]
That's the problem Brunini has with the impact theory. Uranus' moons orbit in the plane of Uranus' equator. If Uranus was knocked on its side by a giant impact, there's no reason to believe that the moons should have followed the equator.

It's not the purpose of the simulation to 'prove' that things happened the way Brunini it theorizing. The purpose of the simulation is to demonstrate that what he proposes is possible.

It might be a little tricky to get a letter published in Nature if this were the case.

Grant Hutchison

So, the initial protoplanetary disk was more massive on the outer side of Uranus/Neptun since they migrated outwords even the disk was less dense then inner disc from wich all inner planets were formed and despite majority of debris disk's mass (Jupiter/Saturn et al.) was located in the place between the Sun and U/N system? (Do I smell Dark Matter here? :-))
The planets swept out traces of the debris disk, how come they forgot the Asteroid Belt?
What is the relevancy of something "that could happened" in the context of science? (I thought it was art that is dealing with that.)
I mean, is Nature some sort of "popular science"?
Recently, in arxiv, a paper popped up, where it was shawn that Jupiter could travel through the solar system end cause Asteroid Belt formation, tilt of Uranus end Gud knows what else..
Really, isn't it just a matter of choice of initial conditions (i.e. stable and unstable resonance)?

if hes right-others will agree
if hes not-others wont

(thats the good thing about science-you can hypothenis all you like-but the data will finally show through)

all i was saying was i havent seen many others promoting the `pinball' theory and the ones that have have fallen by the wayside

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Surely if you are going to start a conspiracy theory it is best to start with something that might have a grain of truth or reality in it. To start with the preposterous and go downhill from there is just stupid. steve(primus) (Avatar)

Not necessarily (and apparently not in the case of this paper). It's possible that Jupiter and Saturn could have given Uranus and Neptune energy in a resonant "kick" that would send them to a larger orbit. (Think Earth-moon system.)