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Lecture 3.04: The surface density of the solar system
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来自 Caltech 的课程
太阳系科学
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从本节课中
Unit 3: Big questions from small bodies (week 1)
与讲师见面
Mike BrownProfessor
Planetary Astronomy
Before we go on and talk about the different
populations of small bodies individually, I want to do one
more general thought experiment that will help us set
the stage for what these small bodies really are like.
Alright, here's what I want you to picture.
I want you to picture the eight planets going around the sun and
think about how much mass it took to make each of those eight planets.
Now, think about the fact that that mass is all distributed in
a disk of material that would eventually coalesce to form those, into those
eight planets, okay so do this, go to each of the planets, go
to Jupiter, smash flat, spread it out into an annulus around the sun.
So, let's put the sun here and Jupiter used to be here, we smashed it flat and we
spread it out and make that annular extend from
where Jupiter is to where Saturn is, but smash Saturn.
So, Saturn has been smashed too, also has an annulus.
Uranus and Neptune smash, smash and annuli there too.
And, of course, all of the mass in the asteroid
belt in here, smash, Mercury, Venus, Earth, Mars, smash, smash, smash.
All these annuli here.
When you've done that, you have created a disk
out of material of the planetary system and you've almost
figured out how much material you needed to have
had to begin with, except for a couple of problems.
One big problem is that you know that
Jupiter and Saturn and Uranus and Neptune have all
the gas, have, have the hydrogen and helium,
even if Uranus and Neptune don't have as much.
But they have, they have all the hydrogen and helium that
would have been around that the terrestrial planets did not acquire.
We don't have large masses, large
atmospheres of hydrogen and helium around here.
The original hydrogen and helium that went with the
solid materials that are now the earth and the terrestrial
planets, that initial hydrogen and helium got blown away from
the sun, and is now off in interstellar space somewhere.
So, what you need to do is, go back and
take your hydrogen and helium shaker, and sprinkle in the
amount of hydrogen and helium that you still needed to
have to account for all the mass that was in here.
When you do that, and you spread all that hydrogen and helium out in here, you have
something that looks sort of like the original
disk of material from which the solar system came.
And I say sort of like, because we don't
really know, we don't know how much extra material
the planetary system needed to form the planets and
that, in which, how much of that material was ejected.
We don't really know what the exact distribution of the materials was.
But you have something that is not far
off from what the original mass of material was.
When you do this exercise, when you spread all these annuli around and add in
the extra hydrogen and helium, you're left with
something that's called the minimum mass solar nebula.
Why minimum mass solar nebula?
Minimum mass is, this is, you couldn't have had less
material than this, if you wanted to form the planetary system.
You might have had more, but this is the minimum mass solar nebula.
Nebula just means that cloud around the sun and this is our best
simple reconstruction of what the planetary nebula
was like before all the planets formed.
Okay.
When you do that, what does it looks like?
Well, by what does it look like, I mean, what is the density of material
in this disk if I am setting about it like we are here and looking down.
So, if I look in a little square centimeter patch right here and I
look straight through and I count up the entire mass in a square centimeter patch.
It's not density, because I don't really care about the height.
I don't care if some of it's high and some of it's low.
I'm just looking down into that square centimeter.
So, I'm going to look at it in units of grams per square centimeter, and I'm
going to do that at every square centimeter
of the patch all the way around here.
And I'm going to then have a profile which says, from sun all the
way out, what is the number of grams per centimeter squared in this disk.
What does it look like when I do that?
It looks something like this, where I have labeled all
the planets and just because it's an interesting historic progression, I
labeled Pluto on here and the rest of the Kuiper
belt in, with the question mark of what happens beyond it.
But, let's look what we see.
Jupiter, Saturn, Uranus and Neptune.
It's funny to see Jupiter down here, below the Earth.
When I speak of the annulus that, that Jupiter came from was so big,
that the total amount of material in
grams per centimeter squared was still relatively small.
Something like 100 grams per centimeter squared.
If you were in the middle of this nebula and the sun were over here and you
looked straight up and you looked straight down and
you calculated all the material above and below you.
And you were in one square centimeter you'd only have 100 grams of material.
It's a pretty thin disk of material.
Over here, by the Earth, you're above 1,000, quite a bit more.
Venus, still more.
The interesting things about this plot, and the reason I'm showing you this
plot is because it fits mostly a nice straight line in through here.
Now this is a log log plot.
This is the logarithm in units of, going up
by factors of ten here, factors of ten here, so,
what that log log plot means is that this line
is not a straight line but it's a power law.
That means that the, you can write that the surface density is equal to some
number times radius to some power, in this
the power is something like minus three half.
It's sort of pleasing to see because power
laws, power laws like this abound in, in astronomy.
Partially because astronomers plot on these log, log
scales because that compresses out all the areas.
You don't really see anything, but also because a lot
of things really do sort of follow these power laws.
So, we have a nice power law that fits the Venus and
Earth, the big terrestrial planets, all of the giant planets out through here.
Pretty cool.
What doesn't it fit very well?
Well, the glaring problems are of course, the asteroid belt,
where the amount of material in the asteroid belt is
down by a factor of, well that's 10 to the
3rd, this is down here below ten to the zero.
This has depleted.
The asteroid belt is depleted by a factor of at least
1,000, compared to what you could have thought should have been there.
And the other interesting place.
Well, first, it was interesting that Pluto was so far below this.
Pretty good indication that something funny was going on with Pluto early on.
When the Kuiper belt first started being discovered.
There were people who unwisely speculated that the total mass might eventually
come up here like this, and of course the answer is no.
The Kuiper belt, even the Kuiper belt is quite
depleted compared to what it, what it might have been.
It might have been somewhere around one, it's down here around at 10 to
minus 2, so it's depleted by a factor of something like 100 to 1,000.
Of the material that you would get, it's not that we know this material here, but
the material that you would get if you
just continued this extrapolation on the straight line.
Also down, of course, is Mars and Mercury.
And we talked about that last time, that they
are a little bit under massive if you start
out with a disk that is, really fits this
power law, this minimum mass solar nebula, like this.
You predict always that you have bigger Marses and bigger Mercurys.
But this leads us to one of the critical things about the small
body populations is that unlike the giant
planets, and at least these two terrestrial
planets, which seem to have acquired some good fraction of the material around them,
the asteroid belt, not only in to the asteroids and the Kuiper belt objects.
Not only did they never have a chance to become
large, they also, it appears that many of them were lost.
Why were they lost?
Well, they would have been lost because Jupiter was again
exciting those orbits and you saw, in those previous simulations,
how many of those objects just get ejected from the
solar system or sucked into Jupiter or pushed into the sun.
And it's factors of 100 or 1,000 in the mass of the asteroid belt.
Same problem with the Kuiper belt.
These objects that were out to here.
There probably were many more of them in
the past, and they were ejected by Neptune.
Or, in a much more crazy scenario we'll talk about, they were ejected when a, an
entire dramatic event happened in the solar system,
which made things go crazy all over the place.
It was an interesting speculation to make, sometime around the year 2000.
I think I actually made this plot around the
year 2000, and we don't have a Pluto for a
long time, the Kuiper belt had just been, being
explored and it was a really interesting question to ask.
We, we knew about this much of the Kuiper belt, out to about,
if you look at this number, this is 10, 20, 30, 40, 50.
Out to about 50 AU, the Kuiper Belt goes from something like 40 to 50 AU.
And now, beyond 50 AU, well we didn't know, the reason
we didn't know is because 50 AU is pretty far away.
It was just the early stages of discovering the Kuiper Belt.
No objects had been found out there beyond 50 AU.
And so, it was something that we could speculate about instead.
And so, one of the speculations was, well, perhaps, like the asteroid
belt, this goes down like this and then comes back up again.
And, because there's another mass out through here.
Now, maybe this depletion of the Kuiper belt was big and it went across like this.
Or, maybe it was really big and it went across like this.
But it was always possible that something could come up out through here again.
Maybe it didn't happen.
But we could at least speculate for fun, that maybe something like that did happen.
Of course, we spent a lot of that following decade looking
specifically for things, big things, out in this region through here.
And I'm sad to tell you that they're not
there, really it's true that the density comes down here.
At the location of the Kuiper belt and really just sort of plummets.
This is the edge of the main part of the solar system.
It's really the main collection of small bodies, all kind of in the same
place in here, and then there's very little material going out in this region.
Now, the fact that I say there's very little
material going out in this region doesn't mean that there
are not a lot of things, but it also means
that there's a lot of space for them to cover.
So, the density of the material out through here is really very small.
So, we're left with our dichotomy between planets,
either the giant planets or the terrestrial planets.
That collected most of the material around
them, allowed themselves to get big, and small
body populations, the asteroid belt, the Kuiper belt,
that never were allowed to get very big.
And that, in addition, had so much interaction with the giant
planets, either Jupiter, in this case, or Neptune in this case.
That much of their material was removed.
We're already starting to get a little bit of the flavor of the interesting
things that I told you about, why, why I find the small bodies so fascinating.
So, the small bodies, they're not very big.
Many of them have, have been gotten rid of by the giant planets.
But that entire process was because of the way that the giant planets formed.
Where they formed.
When they formed.
And, this removal of those factor of 1000 or factor of 100
to 1000 here or here are signatures of what the giant planets did.
So, even though they're small bodies, and they're, they're heavily
depleted from what they used to be, they really do
carry the story, the bigger story of how the solar
system put itself together, and how it's evolved since then.
