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.