We did pretty well understanding 
terrestrial worlds which are relatively 
similar to Earth. 
Now we can get ambitious, we can see what 
we can say about the Jovian planets and 
see how much of what we've understood 
translates to these more interesting 
systems. 
looking at their motion in the solar 
system the things I'd like to point out 
is the inclinations of the orbits are 
very small. 
the periods of the orbits are 
interesting. 
Jupiter and Saturn are locked, as you can 
see if you do the calculation, into a two 
to five resonance. 
So, the one to two resonance that 
destabilize things has locked into a 
stable two to five resonance which is 
anchoring if, in some sense, the 
stability of the rest of the solar 
system. 
in terms of the rotation periods, the 
spin periods, notice how fast all of 
these objects spin. 
The slowest is Uranus with a seventeen 
hour, spin. 
Jupiter and its entire mass rotates about 
its axis every ten hours. 
If we think about these giant planets 
forming out of a gravitational collapse, 
a gravitational instability then we 
remember that this will acquire angular 
momentum from more distant parts of the 
cloud. 
This explains the rather rapid spinning 
motion and will have consequences as we 
go along. 
the other thing to note is that the tilt 
angles are moderate except for Uranus, 
which has a axial tilt of 97 degrees, 
which means its axis essentially is not 
perpendicular to the ecliptic but is 
essentially in the plane of the ecliptic. 
this gives extraordinarily 
marked seasonal effects on Uranus and 
even from observations from Earth will be 
able to remark those. 
Notice that those seasons are rather long 
since the year is 84 years long. 
And so in some sense, Neptune with the 
longest year was discovered about a year 
ago. 
This is what we see in terms of their 
motions. 
We talked about how they got there. 
looking at the surface or the atmosphere, 
which in these cases is the same thing 
since this atmosphere, primarily 
hydrogen, molecular hydrogen and helium, 
is all we're going to see because there's 
a sufficiently deep atmosphere in all of 
these that we cannot see through them. 
the atmospheres are always hydrogen and 
helium. 
Uranus and Neptune acquire their blue 
tint from traces of methane. 
What do we see looking at the surface? 
Well, the surface is the same as the 
atmosphere because all of these planets 
have sufficiently thick 
high atmospheres of hydrogen and helium 
that we cannot see through them with any 
instrument. 
And so, the atmosphere is what we see the 
atmospheres are hydrogen and helium. 
In the case of Uranus and Neptune a trace 
amount of methane tinges them blue. 
And what we see when we look at this 
wonderful image of Jupiter is the lines 
of latitude tracing convection cells the 
atmosphere is heated by the core from 
below, just as on Earth. 
This in conjunction with the more rapid 
rotation leads to these bands and zones 
which are tracing the patterns of the 
convection cells. together with the rapid 
rotation, you get very massive global 
winds. 
And at the interfaces between direct, 
differing directions of global winds, you 
get intense storms most famously the 
Giant Red Spot on Jupiter. A storm the 
size of the Earth which we conjecture has 
been ongoing for 100,000 years. 
but there are many other persistent 
storms on Jupiter. 
comparing this to an image of Saturn, we 
see similar things. 
We see the same band structure, although 
less pronounced. 
The dark coloring of some of the regions 
on Jupiter 
are 
is attributed to the rising of some form 
of complex. 
Perhaps, hydrocarbon molecules. 
But nobody's precisely sure what causes 
the coloring. 
And in particular, nobody can explain why 
once in a while, one of those dark belts 
disappears for a few months, 
as happened about six months ago. 
And then, reacquires its colors. 
It's not a change in the global 
circulation patterns. 
But something else, and nobody completely 
understands it. 
we see the same kind of storm pattern on 
Saturn. We see simliar effects on Uranus 
and indeed similar effects on Neptune. On 
Neptune, what we notice is the 
hemispherical variations with season. 
this happens on Uranus, 
it also happens on Neptune despite the 
tilt not being as extreme. 
Simply because the seasons are so long 
that global hemispheric effects take 
place in the course of the 164 year 
orbit. 
Looking inside the planets, well we don't 
do seismology on these giant planets. 
we conjecture the structure of their 
inside from modelling as we do for the 
terrestrial planets combined with 
measurements of the obliqueness, the 
rapid spin causes all of these planets 
like as indeed, the Earth does, to be 
slightly thicker around the equator than 
around the poles. 
This is because of the effect of spin. 
By measuring how ablate they are compared 
to how they spin, we can estimate produce 
some estimate of the internal structure. 
And the internal structure that seems to 
obtain for Jupiter and Saturn is that 
inside the external atmosphere of 
hydrogen and helium, is a mantle made of 
metallic hydrogen. 
Hydrogen, if you look at its place in the 
periodic table, the, should be a metal. 
Metallic hydrogen is certainly not found 
naturally on Earth. 
It occurs only under very, very high 
pressures it was only produced on Earth 
in I think the 80s.' 
and but it exists naturally under the 
extreme compression of the immense 
gravity and the immense weight of the 
heavy atmospheres of these planets. 
We have the usual hydro-dynamic 
equilibrium where pressures in the cores 
of these planets are very, very extreme 
and decrease as you move out. 
But since the atmosphere is thousands of 
kilometers thick and very heavy, even at 
the bottom of the atmosphere, pressures 
are intense. 
metallic hydrogen is a conductor. 
The rapid rotation leads to a strong 
dipolar magnetic field for all of these 
planets. 
in the case of the gas giants Jupiter and 
Saturn this magnet is aligned very nicely 
with the planet's rotation axis. 
in the case of Uranus and Neptune, the 
mantle is actually compressed ices. So 
water, ammonia, methane, etc., at high 
density. 
these too can conduct, but the mechanism 
is a little bit different. 
the understanding is incomplete but the 
one of the manifestations of the 
difference in the mantle is that the 
magnetic fields of Uranus and Neptune are 
60 degrees tilted relative to their 
direction of rotation. 
inside each of these is a core, the, 
presumably the seed that started the 
planet's growth. 
as you can see in this image, the core is 
roughly Earth-like in size probably more 
massive because compressed. And has an 
iron-rich inside, and perhaps a silicate 
outside if it chemically differentiated. 
so set, the core of each of these planets 
is about the size of Earth itself. 
Again, the interiors of these planets are 
both extremely compressed and very, very 
hot. 
in the case of these planets, much of the 
internal heat, remember the only the core 
is rich in heavy elements. 
Here this is a tiny fraction of the 
actual huge planet. 
and so, radioactivity does not play a 
large role in maintaining and producing 
internal heat. 
Internal heart is produced by Kelvin 
Helmholtz processes by precipitation and 
by increased continuing compression of 
the interiors of the planet. 
On the case, in the case of Saturn, 
precipitation of liquid helium. 
So, liquid helium rain at high pressure 
is the mechanism by which Saturn is 
chemically differentiating. 
And 
this is significant. If you do the 
calculation of surface temperature based 
on our black body calculation, compared 
to the measured temperature of the 
surfaces of these planets, you'll 
discover that both Jupiter and Saturn 
radiate about twice as much energy as 
they absorb from the sun. 
This is the difference is being made by 
continual heating from the core through 
mostly Calvin Helmholtz processes. 
And we have the strong magnetic field. 
This is an aurora on Jupiter's north 
pole. 
These are aurorae on Saturn's poles. 
And if we look for aurorae on Uranus, you 
can see that if you look at the ring 
structure that indicates the equator of 
the planet, this is not the pole. 
The pole is way over here to the left. 
And the aurorae are showing up at 
intermediate latitudes. 
This is indicating to you the offset of 
the magnetic field. 
indeed, this reminds us that the most 
impressive structures carried by these 
giant planets are their rings. 
And we understand, in some sense, where 
these might come from. 
These planets are formed by a 
gravitational instability in the nebula 
collapse. 
And the collapse will be accompanied by a 
flattening into an accretion disk from 
which the planet acquires gas and dust. 
near, some of this leftovers of the 
nebula will form moons. 
So, most of these planets have moons that 
orbit them in their equatorial plane. 
these moons formed within the accretion 
disk, just as the planets formed in the 
sun's accretion disk. 
but, 
close to the planet, tidal forces can 
prevent gravitational accretion. 
This would have been true in the case of 
the Sun as well, except that close to the 
Sun whatever didn't accrete into Mercury 
was blown away by T Tauri winds. 
Planets do not generate T Tauri winds. 
So whatever accreted near the planet, too 
close to form a star a moon will produce 
ring like structures. 
And they have ring structures around 
Jupiter, 
and ring structures around Uranus, 
and ring Neptune, 
and ring structures around Uranus. 
And the beautiful magnificent rings 
around Saturn. 
for reasons nobody completely understands 
the rings around all of the three giants 
other than Saturn are dusty and dim. 
Whereas, with Saturns rings are almost 
99.9% water ice. 
Water ice, as we know, is brilliant and 
shiny which is why the rings appear so 
bright. 
we see here that the rings are discrete, 
the large gap here, the Cassini gap, is 
visible in a moderate telescope from 
Earth. 
The slightly smaller gap farther out, the 
Enke gap, is visible with a more advanced 
telescope. 
But upon closer inspection, it turns out 
that these rings have a very, very fine 
internal structure. 
We'll get into that in a second. 
Let's understand what it is that I'm 
saying when I say that too close to a 
planet a moon cannot form. 
the limiting distance, the closest 
distance at which it can form is called 
the Roche Limit. 
it was computed in 1848 by Roche. 
And the idea is this, we have a planet 
over here, we're trying to form a moon 
over there. 
We will say a moon can accrete and form 
provided that the tidal forces of the 
planet are not enough to blow it apart. 
So we've done enough to do this 
calculation that Roche did. 
We give this a mass and planet. 
We give this a mass and moon. 
Set them a distance D apart. 
And the question is, basically, this moon 
is held together by gravity. 
Is the moons gravity enough to hold it 
together against the tidal forces? If we 
drop a pebble on the surface of moon, 
will it be lifted by tidal forces or not? 
And so, we know how to do this. we need 
to compare the tidal acceleration due to 
the planet's tidal forces on the moon. 
We computed this in the past. 
It's 2 * G times the mass of the planet, 
times the radius of the moon divided by 
the distance cubed. 
This is the tidal acceleration with which 
the planet tries to stretch the moon as 
we have it here in the horizontal 
direction. 
And we need to compare this to the 
gravitational acceleration due to the 
moon's own mass at its surface. 
And this, of course is G times the mass 
of the moon divided by the radius of the 
moon squared. 
As D gets smaller, the tidal acceleration 
increases. 
When it overwhelms the moon's own 
gravity, the moon will simply fall apart 
as long as it's gravitationally bound. Or 
if we're trying to form a moon by 
gravitationally binding moonitesimals, 
the moon will never form. 
And we'll end up as we'll see with ring 
structures. 
So, let's write these two and set them 
together. 
This is setting the gravitational 
acceleration on the moon's surface equal 
to the tidal force generated by the 
nearby planet. 
dividing through by R and canceling the 
Gs as usual I'm going to put this down 
over here. 
And I find that I have this interesting 
expression that says, the mass of the 
moon divided by its radius cubed is equal 
to twice the mass of the planet divided 
by the distance cubed. 
Which it's interesting to write in a 
different way. 
You write the mass of the planet divided 
by the distance cubed. 
But then, you divide and multiply by the 
radius of the planet cubed. 
Now, why is this useful way to write it? 
Because the cube of the radius is a 
measure of volume. 
Remember that the volume of a ball is 
four pi over three R cubed. 
And that if I know the average density of 
an object, then its mass is the density 
times the volume. 
So, dividing the mass by R cubed up to 
irrelevant cancelling factors of four pi 
over three gives me a measure of the 
density. 
In other words what this equation tells 
me is that the density of the moon is 
twice the density of the planet times the 
ratio between the cube of the ratio 
between the radius of the planet and the 
distance between them, when that distance 
is at the Roche limit. When tidal forces 
are just enough to rip the planet apart. 
In other words, I can now solve for D in 
terms of the densities and the solution 
that I get. 
So, here's the expression written that 
way. 
Again, I I rewrite things in terms of the 
densities, and this says that the density 
of the moon is twice the density of the 
planet, times the radius of the planet 
divided by D cubed. 
Now, multiplying through by D cubed 
moving dividing by row M, I finally find 
and then taking a cubed route to get my 
answer, I find the fearsome equation on 
our splash page that says that the Roche 
limit, the dist, closest distance at 
which a moon can survive, that's D, the 
Roche distance, is given by the radius of 
the planet times the, the 1/3rd power of 
the ratio of twice the planet's density 
to the moon's density. 
to make a reasonable calculation let's 
assume for example, that we're describing 
Earth and Earth's moon. 
What is the nearest distance to Earth 
that our moon could have possibly have, 
have formed? 
Remember, it formed much nearer. 
Well, let's give the moon half of Earth's 
density. 
So twice the Earth density divided by the 
moon's density would be about four. 
four to the one third is about one sixth. 
So in the case of a planet twice as dense 
as its moon, 
you find that the minimum distance is 
about 1.6 times the radius of the planet 
if a rogue planet is twice real moon, 
which is the case for our Earth, our 
moon. 
And so, our moon could not have formed 
less than about two Earth radii from the 
center. 
In other words, about 7,000 kilometers 
away from the Earth's surface. 
nearer than that, our moon would have 
been ripped apart by Earth's tidal 
forces. 
And 
this is a very useful expression. 
Objects inside the Roche radius cannot 
possibly be gravitationally bound. 
Now, that does not mean that they are 
completely ground to dust at some point. 
In the solar system, the, the rough scale 
is about a kilometer. 
We will do a homework problem that will 
help us understand how that happens. 
At some small scale, remember the 
planetesimals, were held together 
chemically. 
Smaller things are held together by 
chemical forces. 
They at small distances are able to 
withstand gravitational 
tidal forces. But gravitationally bound 
objects will be dispersed over time. 
And so, the way that this will work is if 
you bring a moon to within the Roche 
radius which is indicated by this white 
ring, tidal forces will elongate it. 
And when it crosses the Roche radius it 
will start to fall apart. 
remember it's being extended so parts 
near to the planet will fall towards the 
planet, 
parts far from the planet will fall away 
from the planet. 
And because they're all moving, imagine 
this thing was in orbit, 
all of the planet was, the moon was 
moving with the same orbital velocity. 
the bits that are falling too close to 
the planet are now moving at a speed too 
small for their now lower orbit so they 
will fall into eliptical orbits with this 
as [UNKNOWN]. 
And the bits that are falling away from 
the planet will be moving so slow, so 
they will fall into elliptical orbits. 
And when everything settles down into 
circular orbits the guys that have, that 
fell towards the planet will have 
advanced ahead. 
The guys that fell into the planet, away 
from the planet will have been left 
behind. 
And basically, the whole structure is 
smeared out along a ring. 
We'll see this happening again and again 
when tidal forces rip something apart. 
They generate that is in orbit, they 
generate a ring structure. 
So this is where the rings could have 
come from or why the rings formed but no 
moons. But stability over the long term 
of such a ring structure, you'd expect 
collisions between ring particles, you'd 
expect that mixture. 
looking at Saturn's rings, we see that 
there are changes in composition between 
thousands and thousands of ringlets. 
it's not completely understood what 
maintains the stability of this amazing 
structure. 
for the record, Saturn's rings are about 
150,000 kilometers in width. 
but by some measures, only 400 metres in 
thickness. 
This is an extremely thin object, 
precisely on the equatorial plain and 
made up of essentially of chunks of water 
ice. But, with various additives or 
various trace amounts of other materials 
so that they have slightly different 
properties in the various ringlets. 
And 
one of the things that keep maintains 
this, helps maintain this structure is 
the existence of moons that orbit both 
within the ring system and outside it 
they produce these gaps, these gaps that 
are marked here, are gaps at which 
objects orbiting in the ring would be in 
resident orbits with the moon. 
Just as in the asteroid belt, this would 
cause them to be moved into eccentric 
objects and essentially ejected. 
So, nothing orbits in the gaps and this 
separates ringlets from each other. 
Moreover, there are moons that orbit 
inside the rings, inside the Roche limit 
where a moon cannot exist. 
Indeed, those moons are slowly being 
ripped apart and perhaps resupplying 
material to the rings 
as the material is being lost to 
collisions. And, these, these objects are 
both very beautiful and very intriguing, 
and I don't think we completely 
understand what maintains their 
structure, but they're certainly a 
generic property of accretion systems.