Can We Understand Axis Tilts in Planetary Systems?

[marcus]

http://physicsweb.org/articles/news/10/4/15/1?rss=2.0

"New Light on Giant Tilts"

It's a major unsolved problem in planetary system dynamics. Anybody want to discuss?

 

[tony873004]

It would be interesting to read the Nature paper, as this articles doesn't go into any details.

...Jupiter and Saturn then became immersed in a disk of thousands of tiny balls of rock and ice, known as planetissimals.
The combined gravitational effects of these balls, which lay in a disk beyond Neptune, caused the position of the planets to migrate...

If they're beyond the orbit of Neptune, then why are only Jupiter and Saturn immersed? I imagine there would have to be a lot more than "thousands" of them to explain any significant migration of the gas giants.

...Saturn moved slightly away from the Sun, while Jupiter moved slightly towards it. This process eventually resulted in Saturn having an orbital period that was exactly twice that of Jupiter's...

But Saturn has a period of ~33 years, and Jupiter has a period of ~12 years. That's not 2:1. Or did Saturn continue to migrate beyond the Jupiter's 2:1 exterior resonance zone, in which case, what's the relavance of that sentence to this article?

To expand upon this a little, I believe the reason that Jupiter would migrate in, and Saturn migrate out has to do with Jupiter's greater ability to eject things from the solar system. As Jupiter or Saturn gravitationally perturb an object into a higher orbit, they must migrate inward. And if they perturb something inward, they must migrate outward. Objects that get perturbed still have a Jupiter or Saturn crossing perihelion or aphelion, and ultimately return to get perturbed again. The net bias is 0 minus the bias from any object that gets ejected from the solar system, never to return to get re-perturbed again. Jupiter has only one way of ejecting objects, so it migrates in. Saturn has two ways of ejecting objects: do it itself, or perturb it inward and let Jupiter eject it. Since Jupiter is much more massive than Saturn, the latter is far more efficient. So Saturn, with a net bias of perturbing objects inward, migrates outward. Uranus and Neptune also have a net bias that causes their orbits to expand. And Jupiter with a net bias of perturbing objects outward, migrates inward.

His results suggest that the giant planets' obliquities might have been fixed into their present-day positions by gravitational interactions between the planets during this migration.

How? I wish the article elaborated a little more on this. The Nature article should explain it. I'll have to look at it the next time I'm in the library.

 

[tony873004]

Here's a link that goes into a little more depth.
http://www.planetary.org/blog/article/00000553/
It answers some of the questions I posted above, but leaves me wondering about something else.

Jupiter and Saturn start out at roughly 5 and 8 astronomical units; Uranus and Neptune begin much closer to the Sun than their current positions, at about 13 and 14 AU. They stay pretty comfortably in those positions for about 100,000 years. Then, quite suddenly, that 1:2 resonance is reached.

5 AU and 8 AU are wider than the 2:1 resonance SMAs. The ratio of SMAs for a 2:1 resonance is about 1.587, while 8/5 is 1.6. This means that the orbits of Jupiter and Saturn would have to approach each other, rather than move away from each other. But how can this be with Jupiter's orbit shrinking and Saturn's orbit growing? Maybe the Nature paper explains it better. Perhaps its the way the author of the article rounded his numbers, since 4.6/8.4 rounds to 5/8 and 4.6/8.4 is smaller than the spacing required for a 2:1 resonance.

 

[tony873004]

Uranus and Neptune begin much closer to the Sun than their current positions, at about 13 and 14 AU. They stay pretty comfortably in those positions for about 100,000 years.

I wonder if he's misquoting the Nature paper.

I tried simulating this. I wanted to see the effects Jupiter and Saturn in a 2:1 resonance had on Uranus and Neptune at 13 and 14 AU, and then compare it to the effects if Jupiter and Saturn slightly missed the 2:1 resonance. I found that if the resonance were perfect, Uranus and Neptune do indeed get perturbed. However, they get perturbed if the resonance isn't perfect either. And they even get perturbed if Jupiter and Saturn are deleted from the simulation. Uranus and Neptune perturb each other. They don't sit comfortably at those distances for 100,000 years. They sit comfortably at those distances for a few decades until they reach their first conjunction. In one of my simulations, a close pass 150 years after the simulation begins causes them to cross orbits.

Screen shots:

http://orbitsimulator.com/PF/un1.GIF

http://orbitsimulator.com/PF/un2.GIF

http://orbitsimulator.com/PF/un3.GIF

 

[tony873004]

I wonder if he's misquoting the Nature paper. quoting myself

He wasn't misquoting the Nature letter. I read the Nature letter today in the school library. This data showing the 13 & 14 AU distances were in the form of a graph. I'm not sure about the 100,000 years though. I don't think I understand the x-axis of the graph. I wish I could post a picture here. It seems to imply < 10 years, which makes no sense. But the context of the article implies 100,000s years, rather than ~10 years. Maybe I need to re-read it more carefully.

This brings me back to my original question. I've experimented myself, and found that a 13 AU Uranus and a 14 AU Neptune are not stable for more than ~1 century. So how can the author of the letter to Nature claim through a graph that Uranus & Neptune were happily co-existing in a 13:14 sma ratio for hundreds of thousands of years? Perhaps Uranus & Neptune weren't fully formed at the time, and had only a fraction of their present masses?

 

[SpaceTiger]

"New Light on Giant Tilts"

Astronomers...

 

[Chronos]

Planetary axis tilts could result from any number of effects. I am more surprised that any two planets would have remarkably similar alignments after ~5 billion years.