Learn about the science behind the current exploration of the solar system in this free class. Use principles from physics, chemistry, biology, and geology to understand the latest from Mars, comprehend the outer solar system, ponder planets outside our solar system, and search for habitability in our neighborhood and beyond. This course is generally taught at an advanced level assuming a prior knowledge of undergraduate math and physics, but the majority of the concepts and lectures can be understood without these prerequisites. The quizzes and final exam are designed to make you think critically about the material you have learned rather than to simply make you memorize facts. The class is expected to be challenging but rewarding.
Lecture 3.18: Dynamical instabilities
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From the course by Caltech
The Science of the Solar System
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From the lesson
Unit 3: Big questions from small bodies (week 2)
Meet the Instructors
Mike BrownProfessor
Planetary Astronomy
You've now learned some of the things that the outer solar system is telling us about
the migrations of the giant planets, how things moved around,
how the small bodies and the Kuiper belt themselves got pushed around.
Now it's time to realize some of the things they tell us about
why some of our ideas might be wrong.
You remember the elegant story we put together about the migration
that had to do with where the objects in resonances were.
And as I'll remind you the story, Neptune moves its way out
by scattering planetesimals and moves its way out, pushes things into higher
eccentricity orbit, captures things into these beautiful resonances and
makes a very discernible pattern of objects in the outer solar system which
looks a lot like the discernible pattern that we see here.
But it does one other thing that we didn't talk about.
Remember that process we talked about earlier about dynamical friction where you
have large bodies, a sea of small bodies, large bodies interact,
small bodies interact, and over time the small bodies end up going fast.
The larger bodies end up slowing down and slowing down and
that's because of, well we had a lot of different ways of describing it.
Equal partition of energy or that process by which large basketballs and
small ping pong balls are all inside of a big container.
If you shook them around the ping pong balls go fast,
the basket ball will go slow.
All that's the same sort of process.
If you remember, when we were talking about the formation of planetesimals,
what that really meant in practice is that
the large objects got on increasingly circular orbits,
their eccentricities got lower and lower, their inclinations got lower and lower.
While the small objects end up with very high eccentricities,
very high inclinations.
You can watch this process happen again if we go through this again and
watch these again.
These are the small bodies are getting up on this very high eccentricities.
You would see them up on high inclinations too.
You don't see anything happening to Neptune in this particular
stimulation because Neptune is actually not interacting with these particles.
It's just being physically shoved out by the computer and
not actually because of the interactions here.
But you can imagine that the interactions of these small bodies with this large one
would serve to circularize Neptune's orbit and to keep it at very low inclination.
If we looked at Neptune today, it should indeed be very circular and
very low inclination through this process.
So there's been nothing else since this time that
would have led it to have a high eccentricity.
So, what does it look like?
Here's a simulation now that does the entire job right.
It takes the planetary system of Jupiter's Saturn, Uranus, Neptune.
It allows those bodies to interact with the small bodies.
Recall, as they interact Neptune moves out, Uranus moves out, Saturn moves out,
Jupiter moves out.
All of these large bodies are interacting with the small bodies.
All of them will have their eccentricities dropped to nearly zero
in a way that looks like this.
If you start them out at pretty high values, and a 0.05,
5% eccentricity means that Jupiter is 5% further when it's its furthest,
5% closer when it's its closest, and that's the current value today.
And Saturn is about the same, it's a little bit higher right now.
If you start these out at these very high values,
the dynamical friction from interacting with these small bodies quickly drops
these eccentricities to very, very small by users for Jupiter, there's for Saturn.
I can show you Uranus and Neptune, they would be the same.
Jupiter and Saturn which we think of on, as on a very nice circular orbits and
they are on a very nice circular orbits, 5%, 6%.
They're still significantly more eccentric than they should be.
They had gone to this process of driving the planetesimals out of the solar system.
This is not the only problem.
There are couple of other inconsistencies in our whole story that don't quite
fit right.
It's hard when you come up with a very elegant theory like planetary migration
that fits some of the observations so well.
You want it to be the right answer but
you can't force it to make things true that aren't true.
That planetary migration scenario would make these eccentricities quite low and
they're simply not.
So what's going on?
Spectacular solution to this problem has been proposed recently by a group
working out of Nice, France.
Therefore, goes by the name the Nice model.
And it goes something like this.
We know that right now Jupiter,
here the distance Jupiter is at 5.2 AU, Saturn's at 9.2AU.
Jupiter goes around 11.6 years.
Saturn goes around 29.5 years.
Jupiter and Saturn are close, 2:1 resonance.
If Saturn were a little bit closer and if it were 23.7 instead of 29.5,
they would be in a 2:1 resonance.
The fact that they're even this close causes a lot of sort of wobbling of
the solar system as these come close and go far away in sequence over the years.
Imagine what had happened though if early on Saturn actually had formed closer.
Imagine that Jupiter's out here at about 5.6 AU with a 13.2 year period and
2:1 then is 26.5 year period.
It will be at 8.8 AU.
Saturn is a little bit closer, it's inside the 2:1 resonance.
With the shorter period, remember we are hypothesizing that the entire solar system
formed more compact and spread out and
this is just looking at the consequences of that action.
Jupiter and Saturn formed closer, Uranus and Neptune are still out there delivering
particles in planetesimals into Jupiter and Saturn.
So, Saturn is moving outward, Jupiter is moving inward.
And look what's going to happen.
Jupiter's period is going to get shorter,
it's going to go from 13.2 years eventually down to 11.6.
Saturn's period is going to get longer.
At some point, these two are going to cross the 2:1 mean motion resonance.
When that happens, bad things happen.
Jupiter and Saturn are the dominant members of our solar system and
if those two objects were in a mean motion resonance, you remember how I described to
you when the asteroids were in a mean motion resonance with Jupiter,
they came around three times for every time Jupiter went around once.
They eventually got their eccentricities pumped up across the orbit of Jupiter and
injected from the solar system.
Imagine what would happen to Jupiter and Saturn.
Jupiter gets a pole from Saturn, Saturn gets a pole from Jupiter.
They both start to get eccentric.
These two objects so large and so much mass in our solar system becoming
eccentric start to shake the entire solar system.
And as you'll see in this pretty simulation I'm about to show you,
when that happens they raise the eccentricities of Uranus and
Neptune, and then I'll just show you what happens.
Here's a simulation where we start out with Jupiter, Saturn.
Notice that they're closer together now.
Currently Saturn's more like here.
Uranus is more like here.
And Neptune is more like here.
The Kuiper belt is out here and we have everything in closer.
Let's let time go forward a little bit and
this is just at the moment when Jupiter and Saturn have hit the 2:1 resonance.
So you'll start to see excitation happen very quickly.
Notice the eccentricity of Saturn getting pumped up very quickly.
Uranus is the same way.
Uranus gets popped back down.
Saturn is going up.
They start to wobble around a lot, so they don't always go uniformly up, more up.
And notice what happens.
Saturn got a little bit of a shove inward.
Uranus is getting even higher eccentricity and
in about one time step, and a dynamical explosion is going to occur.
Suddenly, I'm going to go backwards one.
Suddenly you go from an eccentric orbit, well, look at this,
this eccentric orbit is so eccentric it almost crosses the orbit of Neptune.
These two things cross and once they cross, they might even cross the orbits of
Saturn and they get tossed out into where the Kuiper belt used to be.
Notice this thing has an eccentricity of 0.3, something with the eccentricity of
0.3 something major access of 15 means that it's uphilling.
That's farthest away from the sun is more like 20 AU's.
So it's an invading all the way to out here.
It goes up to here now.
And eccentricity of 0.5 and 20 AU, that means,
it's uphilling all the way out here.
There's no way these objects can survive while these very eccentric
objects are making their way through there.
Plus, these two objects are crossing their orbits, it's crazy.
The eccentricities of the Kuiper belt get very quickly raised up, and
that whole Kuiper belt gets essentially destroyed.
In the meantime, the eccentricities of Uranus and Neptune,
by scattering all these things out of the solar system, or into Jupiter and Saturn.
The eccentricities that Uranus and Neptune start to drop,
the inclinations start to drop, the simulation doesn't continue
on to where they finally drop down to their present values.
But they will.
They have a lot of material to scatter out.
Dynamical friction is very powerful.
They will drop back down and as they drop down to their present locations and
present values they will eject everything from the solar system except for
things that are in these mean motion resonances or
things that are far enough away that they're not affected.
And we will end up with something that looks an awful lot like the Kuiper belt.
Okay, so this, maybe, doesn't seem that much different.
Jupiter, Saturn, Uranus, Neptune form in close, and they either smoothly push their
way out, or Uranus and Neptune get tossed out there, and eject things.
These are, in fact, however, profoundly different.
It's a difference between a very smooth migration of all the planets and
a very orderly reshaping of the outer solar system versus a sudden dynamical
explosion which shakes the entire solar system ejects stuff all over the place.
Now, this sudden shaking of the solar system doesn't happen
necessarily right at the very beginning of the solar system.
It happens whenever Jupiter and Saturn cross that 2:1 resonance.
So, it could be time,
we don't know when it happened if it happened, but it could've happened
something like 600 million years after the formation of the solar system.
Why do I say 600 million years to the formation of the solar system?
Well, that's a special time.
Remember there are all the material in the outer part of the solar system,
all that shaking caused it to be
spewing all over the solar system including the inter solar system,
including the moon, including what could be the late heavy bombardment.
These Kuiper belt objects from further out
could have been the things that hit the moon for the late heavy bombardment.
Plus, Jupiter and Saturn becoming very eccentric would
dislodge many of the asteroids in the asteroid belt.
They would hit the Earth, they would hit the moon, they would hit Mars.
This could be an explanation not just for
that mundane sounding thing of the eccentricities of the planets but for
this, again, profound thing, this late heavy bombardment.
There are few more things of this model predicts or
explains depending on how you want to look at it.
And one of them is the presence of
two of the small body populations we haven't talked much about.
One of them is the irregular satellites.
Remember that Jupiter, of course, has couple of regular satellites.
Io, Europa, Ganymede, Callisto, pretty close to Jupiter, pretty big.
Regular we call them because they are nice regular circular orbits around Jupiter.
But it has a whole host of irregular satellites, really far away,
eccentric orbits.
Going all over the place, tiny things.
And these have always been understood to be captured.
It was just never clear where they were captured or when they were captured,
or what sorts of objects they were before they were captured.
In this Nice model, these things have to be Kuiper belt objects.
They have to have come from the outer part of the disk and
as this big instability is going on, well the Kuiper belt is the most massive,
small body population at the beginning of the solar system.
And so when there are millions and millions
of objects flying around the solar system, they are mostly capable objects.
So what is their most link to be captured, mostly Kuiper belt objects.
One of the interesting questions to find out is
if we could look at some of these small, irregular satellites,
are we going to find out do they look just like a Kuiper belt object would look?
I'm actually trying to do that project right now and
answer some of these questions about some of these irregular satellites.
There's a second population that we haven't talked much about but
it's another population of what are called asteroids.
And these are trojan asteroids.
These are asteroids that are on an orbit either 60 degrees in front of Jupiter or
60 degrees behind Jupiter.
And sort of like the regular satellites these had to have been captured
into this peculiar orbit.
They're stable in that orbit because the forces from the sun, and
from Jupiter cancel out and let them be very stable right there.
So they will stay there forever.
And the question is how did they get there and, where did they come from.
For years it was thought they had come from the asteroid belt in here, and
somehow migrated their way out to there and become part of the Trojan population.
So if we could look at Trojan asteroids in detail we would find out that they
are just like the outer parts of the asteroid belt.
The Nice model, on the other hand,
proposes that these things came from the Kuiper belt.
In that same period when everything was flying around everywhere Kuiper belt
objects were flying everywhere and
they would have been the things that have been captured in.
If we could get to these Trojans and see what they're made out of, and
see that they're made out of the same materials as Kuiper belt objects.
See that they're made out of materials that we only expect to form in this
outer part of the solar system,
I think we will have answered an incredibly profound question.
Because, remember this is Jupiter, there's Saturn, there's Uranus, there's Neptune.
There are a lot of giant planets between the Kuiper's belt and the Trojans.
There's no reasonable way that we could get Kuiper belt objects in here to
the Trojans if we had smooth migration of all these planets inward and outward.
The only way we can get these outer parts of the disk into the inner part of a disk
is through this one sort of dynamical explosion.
So, in some ways I believe that these Trojan asteroids are the key
to understanding if this amazing story that the Nice model tries were opposed.
This amazing story is really true.
How would you do it.
Well, we have some ideas.
NASA is very interested in sending spacecraft to Trojan asteroid.
I think this would be a really good idea as long as it doesn't have a lame acronym.
And we have some tricks.
We're trying to use telescope on the ground to try to connect
to see if we can find similarity between these objects.
In these subjects, and best I can tell you is that this is what I worked on earlier
this week and you have to stay tuned, I'm going to let you know.
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