Lesson7b_Jupiter and its moons
Galilean Moons of Jupiter
Jupiter formed an accretion disk
• The disk would have formed directly above
the equator of Jupiter.
• As material accumulated in the disk, it was
possible to form moons in the debris found in
the disk.
• This is like how the Galilean moons formed.
• They could not hold on to hydrogen and
helium but were able to accumulate rocky
material and water ice.
Galilean Moon Data
Moon
Orbital
Radius (km) Mass
Radius (km)
(in Earth
masses)
Density
(g/cm3)
Orbital
Period
(Earth
days)
Relative
surface age
Io
422,000
1,815
0.0145
3.53
1.77
Youngest
Europa
671,000
1,569
0.0080
3.03
3.55
Young
Ganymede
1,070,000
2,631
0.0242
1.93
7.16
Older
Callisto
1,883,000
2,400
0.0176
1.79
16.69
Oldest
Correlations with surface age
• Unlike the terrestrial planets, no correlation with
mass or radius of the moon
• There are correlations between orbital radius,
orbital period, and density.
• The sense of the correlation is:
Closer to Jupiter the younger the surface
Shorter the orbital period the younger the surface
More dense the moon, the younger the surface
• For objects orbiting another body, is there a
relationship between orbital radius and orbital
period?
• We learned earlier in this class that the bigger
the orbital radius the slower the object moves
in its orbit.
• Also the larger the radius the bigger the
circumference of the orbit (C = 2πR).
• So the bigger the orbit, the longer the time it
takes an object to orbit. (Orbital Period)
• So Orbital Period depends on the radius of the
orbit.
• We can eliminate the orbital period in our
correlation. It is the same as saying the orbital
radius is bigger.
• Now let’s consider the density of the Moons.
• What can you conclude about the reason why
Io has a much higher, mean density than
Ganymede and Callisto?
.
1. Io is smaller so it has a smaller
volume. That makes it more dense
2. Io is closer to Jupiter so it has a
different chemical composition
3. Io doesn’t have water
4. Io must have been captured by
Jupiter
0%
1
0%
2
0%
3
0%
4
• Io is more dense because it doesn’t have large
amounts of water ice covering its rocky
surface like Europa, Ganymede and Callisto
do.
• We know that Io is very geologically active. If
it was once covered with ice, the ice probably
evaporated and was lost.
• Io may have been close to the same
composition as Ganymede and Callisto
originally.
• Because of its volcanic activity, the icy surface
was evaporated. Since Io has no atmosphere,
the pressure is too low for liquid water to be
possible.
• The water vapor was lost and eventually Io
became a much denser moon on average.
How big was Io?
• If we assume it had the same average density
as Callisto, originally, then is had to have the
equivalent of 0.006 Earth masses in water in
order to drop its density to Callisto’s density.
• That would give Io a mass of 0.0145 + 0.006(in
water) = 0.0205 Earth masses.
• That’s actually bigger than the current day
Callisto.
Galilean Moon Data
Moon
Orbital
Radius (km) Mass
Radius (km)
(in Earth
masses)
Density
(g/cm3)
Orbital
Period
(Earth
days)
Relative
surface age
Io
422,000
1,815
0.0145
(0.0205)
3.53
(1.79)
1.77
Youngest
Europa
671,000
1,569
0.0080
3.03
3.55
Young
Ganymede
1,070,000
2,631
0.0242
1.93
7.16
Older
Callisto
1,883,000
2,400
0.0176
1.79
16.69
Oldest
Io may have formed this way
• The other possibility is that Io formed this
way.
• Jupiter was probably much hotter at the time
it formed. It is possible that Jupiter was hot
enough that water was in a gas phase at the
distance of Io.
• Io would have therefore formed without any
water ice on its surface.
• Today Jupiter is much cooler than in the past.
Jupiter formed an accretion disk
How active is Io?
• It is estimated that Io resurfaces its self to a
depth of about 1 cm/year.
• This rate of resurfacing is estimated using the
amount of time it takes to fill in a crater.
• On the moon there is a relation between the
size of a crater and its depth. In general the
depth to diameter ratio is 1.3:10.
• In other words, a 10 km wide crater is about
1.3 km deep.
• There are no 20 km craters on Io. A typical
depth for a crater is about 10% of the
diameter.
20 km
2 km
• There are no 20 km craters on Io. This means
that about 2 km of material had to be
deposited to fill the crater in. How can this be
used to estimate the global resurfacing rate?
20 km
2 km
• There are no 20 km craters on Io. This means
that about 2 km of magma material had to be
deposited to fill the crater in.
• By estimating how frequently a 20 km impact
crater is formed on Io, it is possible to
estimate the how long it took to fill that last
20 km crater in.
• These types of analysis give about 1 cm/yr
added to the global surface.
• This is a phenomenal rate. If this rate were
constant back to the formation of Io 4.5 billion
years ago, then Io added:
(1 cm/yr)(4.5 x 109 yrs) = 4.5 x 109 cm.
That is 450,000 km. Io only has a radius of 1815 km
(450,000 km)/(1815 km) = 248 !!
This means Io turned itself, inside out, 248 times.
Or it completely turns itself inside out every 18
million years.
Cavaets…
• Io may not have always been as active as it is
today.
• Magma from inside Io, likely comes from its
lithosphere, which is closer to the surface. So
it doesn’t actually “turn-itself inside out.”
• If the lithosphere on Io is 100 km thick, then
the lithosphere has recycled, 4500 times, or
about once every 1 million years.
Why so active???
• The correlation appears to show that the
closer a Moon is to Jupiter, the more active it
is, or the younger the surface.
• This means that the physical mechanism that
is causing all of this activity decreases as a
function of distance from Jupiter.
• Gravity does exactly that.
• But how does Jupiter’s gravity cause Io to be
active?
.
1. Since Jupiter has a large gravity it pulls
harder on the side of Io nearer to it, causing
stretching
2. Jupiter pulls on one side of Io and the other
moons pull in the opposite direction,
stretching Io.
3. Io is in an elliptical orbit and Jupiter twists it,
trying to bring it back into alignment.
0%
1
0%
2
0%
3
Here’s what we know…
• Io’s rotation is synchronously locked to Jupiter.
(It keeps the same side facing Jupiter at all
times)
• Io is in a slightly elliptical orbit.
• Io bulges in the direction of Jupiter. (These
are tidal bulges)
• The Moon’s rotational period (spin on its axis)
is always the same.
• This means that the Moon turns a little too
much when it is moving the slowest in its
orbit, and it doesn’t turn quite fast enough
when it is moving the fastest in its orbit.
• This causes the Moon to appear to wobble as
it orbits the Earth. We can actually see 59% of
the Moon’s surface instead of 50%.
• Io does the same thing. It over turns and
under turns as its orbital speed increases and
decreases.
• This causes the tidal bulge to be out of
alignment with Jupiter.
• Jupiter attempting to re-align Io causes a
torque that twists Io as it orbits.
• The result is the heating of the interior of Io
from the strong gravity of Jupiter.
• Would this happen if Io were in a circular
orbit?
• Jupiter attempting to re-align Io causes a
torque that twists Io as it orbits.
• The result is the heating of the interior of Io
from the strong gravity of Jupiter.
• Would this happen if Io were in a circular
orbit?
• No
• No, if Io were in a circular orbit, then it would
be truly synchronous, and there would be no
torque acting to bring it back in line.
Io’s orbit should be circular
• It turns out that Jupiter is large enough that Io
should have been forced into a circular orbit
very long ago.
• So Io shouldn’t have activity.
• But it obviously does. And its orbit is not
circular.
• Let’s think about why.
What do you notice about the orbital periods of
the Galilean moons?
Moon
Orbital
Radius (km) Mass
Radius (km)
(in Earth
masses)
Density
(g/cm3)
Orbital
Period
(Earth
days)
Relative
surface age
Io
422,000
1,815
0.0145
3.53
1.77
Youngest
Europa
671,000
1,569
0.0080
3.03
3.55
Young
Ganymede
1,070,000
2,631
0.0242
1.93
7.16
Older
Callisto
1,883,000
2,400
0.0176
1.79
16.69
Oldest
.
1. The close in moons have shorter
periods than the ones farther away
from Jupiter.
2. The orbital period is related to the
density of the moon
3. The moon-to-moon relation is
related by a factor of 2
0%
1
0%
2
0%
3
• From moon-to-moon the orbital period changes
by a factor of 2.
• PEuropa /PIo = 3.55/1.77 = 2
• PGanymede/PIo = 7.16/1.77 = 4
• PCallisto/Pio = 16.69/1.77 = 9.24 (not 8 but close)
• What are the chances that Io, Europa,
Ganymede should have this relationship?
.
1. It is not very likely
2. It’s 100%
3. It seems likely, there isn’t really
any reason they shouldn’t have
these orbital periods.
0%
1
0%
2
0%
3
• In a given, random system, with four moons it
would seem that such an alignment is highly
unlikely.
• Just as it is highly unlikely that most of the big
moons in the solar system are in synchronous
orbits about their planets.
• When something unlikely occurs we need to
think more deeply as to what mechanism
would cause this.
• What do you think? Why the factor of 2 in
the periods?
.
1. The pull of gravity from Jupiter drops off
like the distance squared. That makes the
moons move to a factor of two distance.
2. There are four moons so the number has
to be a multiple of four
3. The moons exchanged angular momentum
and this is the lowest energy state.
0%
1
0%
2
0%
3
Notice: Orbital radius is NOT a factor of 2.
Only the period.
Moon
Orbital
Radius (km) Mass
Radius (km)
(in Earth
masses)
Density
(g/cm3)
Orbital
Period
(Earth
days)
Relative
surface age
Io
422,000
1,815
0.0145
3.53
1.77
Youngest
Europa
671,000
1,569
0.0080
3.03
3.55
Young
Ganymede
1,070,000
2,631
0.0242
1.93
7.16
Older
Callisto
1,883,000
2,400
0.0176
1.79
16.69
Oldest
• It is caused by the exchange of orbital angular
momentum between the moons.
• Io, Europa and Ganymede pass each other
very frequently. When they do so, the faster
orbiting moon tries to pull the slower moon
ahead in its orbit, while the more slowly
moving moon tries to pull the fast one back.
• This causes an exchange of angular
momentum between the moons, until they
reach a resonance orbit.
• This takes a long time… Callisto still isn’t there
yet.
Here is why Io is in an elliptical orbit
• The moons’ gravities are very weak. They can
perturb each other only very slightly.
• If Io passed by the other moons at random
places in its orbit, the effect would average
out and Io would be in a circular orbit.
Ganymede
Io
Europa
Ganymede
Io
Europa
Ganymede
Io
Europa
• If Io just randomly passed the other moons at
various positions, the net result would be
virtually no effect on Io’s orbit.
• But the resonance orbits of the three mean
that they pass at the same location each time.
• Here is an example.
Initial orientation of the
Moons
Ganymede
Europa
Io
Io completes one orbit
Io
Ganymede
Europa
Io completes two orbits
Io
Io completes three orbits
Io
Io completes four orbits
Io
• The effect of gravity is the strongest when the
moons are close together.
• This happens at the same location all the time.
It’s like a game of knuckles
• This allows the little perturbing effects of
Europa and Ganymede to add up as time goes
by.
• The result is that Io’s orbit becomes slightly
elliptical.
• So Europa and Ganymede force Io into a
slightly elliptical orbit.
• This orbit causes Io’s tidal bulges to advance
and lag the direction to the center of Jupiter,
slightly.
• Jupiter exerts a torque, trying to bring Io back
into alignment.
• This torque heats up the interior of Io.
• Without the other moons, Io would be a dead
world today.