all the way up to 1 if you're on a parabolic orbit.
Notice that it goes up to 1 right here, although nothing is on a parabolic orbit.
And you can be greater than 1 if you're on a hyperbolic orbit.
Remember, hyperbolic orbits are ones that are not even bound to the Sun.
Finally, you have the inclination, if I take this orbit and I look at it sideways,
here's the Sun, here's the orbit let's say of the Earth out here at 1 AU,
going in this disc.
Inclination is this angle with respect to the Earth or in this case with
respect to a slightly different angle but we'll just call it the Earth of the orbit.
Something that's down here at 0 is going to be in the plane of the solar system.
Things up here as high as 40 degrees are going to be quite tilted
with respect to the plane of the solar system.
Let's see what we have.
Well, first off remember, we have the Earth.
The Earth is at 1 AU and it has essentially 0 eccentricity and
zero inclination, so this is the Earth.
The other thing that's on this plot or
at least the region of it on this plot is Mars.
Mars, Mars is out here at about 1.52, a little more eccentric,
not really very inclined.
So Earth and Mars, and
then all the asteroids that are out there, where are they?
Well, for the most part, you can see these dots are between Mars and Jupiter.
Jupiter would be out here at 5.2 AU on it's circular un-inclined orbit.
And there are a few asteroids scattered out throughout here that you don't but
the population is not very big.
What you mostly see is a ton of asteroids between about 2 AU and
about 3, 4 AU, this is called the main asteroid belt.
And as you can see it's not just a random collections of things in random orbits,
there's quite a bit of structure in through there.
Let's talk about where that structure is, when is comes from.
The first thing to notice is there's these labels.
3:1, I'll call that 3 to 1, 5 to 2, 2 to 1.
Those labels are things that are the resonances with Jupiter.
A resonance is when an object in an orbit goes around a precise number
of times compared to another object.
It's 2 to 1, that means that the asteroid which is closer here,
it's around 3.5 AU, asteroid goes around twice, one,
two, for precisely every one time that Jupiter goes around.
Why it does matter?
Well, notice first that it seems to matter a lot, 2 to 1, 5 to 2, 3 to 1.
These are regions where there are essentially walls in the distribution
of asteroids, where asteroids clearly aren't allowed to live, why.
Why?
Because if Jupiter goes around, let's talk about the 2 to 1, if Jupiter goes around
one time and this object goes around some random number of times.
Let's not have it in the 2 to 1 resonance.
Let's just have it in somewhere here where it goes around maybe 2 and
a half times 2 and a quarter times.
No nothing, no round number goes around once, goes around again and
it ends up right here, Jupiter is back here.
Next time it ends up here, next time here, next time here, next time here,
next time here.
Every time the asteroid and Jupiter go around
they meet each other in random locations, where they meet each other matters a lot.
Every time the asteroid and Jupiter line up with respect to the Sun, the closest to
each other if we lived on the asteroid we would call that Jupiter is at opposition.
Every time Jupiter is at opposition for that asteroid
the asteroid gets a little bit stronger tug by Jupiter than it would otherwise.
That little tug modifies the orbit ever so slightly.
Now as long as those tugs are happening at random times in random locations,
they sort of cancel each other out.
You do have wobbling of the orbits around changing around a little bit but
over long periods of time, they basically don't change.
What happens though if Jupiter is here, goes around once, shows up here, and
in that time this object goes around precisely twice, shows up right here.
Next time, that gets a little tug.
Next time, does it again.
It's another little tug exactly in the same direction.
Next time, another little tug exactly in the same direction.
Eventually, you can imagine that this is going to elongate the orbit of this object
until eventually, something bad is going to happen.
It's going to cross Jupiter's orbit, it's going to be ejected from the solar system.
It's going to get pushed into the Sun,
it's going to impact the planet, something bad is going to happen.
Living inside of one of these resonances is a bad, bad thing, it's so
bad that it doesn't happen.
Notice that there's nothing inside these resonances at all, there's one other one.
Notice this envelope, right here, where things for the most part,
the main part of the asteroid belt doesn't exist above this
envelope unless it's well above this envelope.
This is called, this one's a little bit more obscure.
This is called the new six resonance.
The six refers to more or less, the sixth planet, Saturn.
So this is due to the effect, believe it or not, of Saturn.
And it's a little bit complicated, it's because Saturn is not
on a perfectly circular orbit, it's on an eccentric orbit.
And like everything in the solar system or in mechanics that's on an eccentric orbit,
that orbit precesses.
It's a complicated theory to explain exactly how it precesses and how fast and
why but it precesses.
So imagine Saturn is precessing, everything else is also precessing and
it turns out that an object that was on this red line here would have a precession
rate exactly the same as Saturn's.
So though it's not lining up time, after time, after time, after time, after time,
over a long period of time the orbit of this, the, an object right here and
the orbit of Saturn would be aligned as they both precess around the Sun.
That effect, over enough times,
would eventually do the same thing that these resonance here,
these are called mean motion resonances instead of secular resonance.
That would do the same thing, it would eject the object from the solar system.
So we have this envelope, you're not allowed to be in this area,
you're not allowed to be inside these resonance.
And other than that, do we fill things uniformly?
Well, this area looks pretty unifromally filled.
This is often called the inner main asteroid belt and
through here you'll see sort of clumpy things.
There's a clump, there's a big clump, be clumped into here.
We'll look very detailed at some of these clumps in a minute.
Down here, you know, there's not much in this region at all except for
this little clump down through here.
And then there's some clumps here, clumps here, it's a very structured region.
It'll be important if we could understand why.
Before we do that, let's look though at things beyond the main asteroid belt when
we say asteroid belt, these are the objects we mean.
These are the objects we mean but
there are other things out there that are beyond the main asteroid belt.
Some of them are in the same semi-major axis range as the main,
main asteroid belt.
But they are way up here in eccentricity and important things happen.
If you have eccentricity above this line and the semi-major axis where you are,
that means that your closest approach to the Sun is within the Earth's orbit.
All of these objects above here are Earth-crossing asteroids,
near Earth asteroids, we call them.
All these objects, which are inside the Earth's orbit are eccentric enough that
their most distant approach from this on crosses the Earth's orbit.
Everything in this ridge has the ability to impact the Earth.
These are the objects that are the source of impacts.
These are the objects that are the source of meteorites.
These are the objects at the source of big craters that we can see on the Earth and
on the Moon.
Interestingly, the numbers of objects in through here is relatively small.
Relatively small compared to the numbers that are here.
Relatively small compared to their lifetime.
You can imagine that things like this will not exist in these orbits for very long.
You can't exist in an orbit very long if you come close to planets.
Why is that? Well, you could impact a planet,
you'll be removed or you could just have a close encounter with a planet.
And that close encounter can give you a gravitational slingshot which again,
will push you maybe out towards Jupiter.
Getting near Jupiter, always a bad idea maybe push you in towards the Sun.
Getting too close to the Sun, also a bad idea.
So these things have short lifetimes, short dynamical lifetimes.
Short doesn't mean ten minutes but
it means much shorter that the age of the solar system.
If you have a population with short fly times,
there needs to be a way to get that population there.
Where do these object come from?
What is the replenishment of these objects?
The obvious source is of course the main asteroid belt but
how do you get things from the main asteroid belt to here?
In particular, the main asteroid belt, the reg,
regions where things survive in the main asteroid belt are where they are stable.
Most of these objects in the main asteroid belt will be in exactly the same
place if you came back after another 4.5 billion years.
Their orbits do not change significantly just like
the planets are in relatively stable orbits.
Yes, they have eccentric orbits.
Yes, they have inclined orbits because they did
interact with planets in the past.
But one of the reasons they're alive now is because they are,
the small fraction of things that are stable.
So how do you get these near Earth asteroids?
How do you get the meteorites delivered to us?
A clue comes from looking in more detail at these clumps in the asteroid belt.
