Today in Astronomy 111: Jupiter’s moons
 Structure and composition of
the Jovian satellites
 Tidal torques
 Orbital evolution in satellite
systems
 Orbital resonances and longlived tidal heating
• Volcanoes on Io
• Liquid water oceans on
Europa
10 November 2011
Two of Io’s volcanoes, in eruption
(Galileo/JPL/NASA)
Astronomy 111, Fall 2011
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Jupiter’s regular (Galilean) satellites
All four, posing with the
Moon (Galileo/JPL/NASA)
Io
Orbital semimajor axis (cm)
4.216 × 1010
Orbital eccentricity
0.004
Sidereal revolution period (days) 1.769138
Europa
Ganymede
Callisto
6.709 × 1010
0.0101
3.551181
1.070 × 1011
0.0015
7.154553
1.883 × 1011
0.007
16.689018
Radius (cm)
1.815 × 108
1.569 × 108
2.631 × 108
2.400 × 108
Mass (gm)
Geometric albedo
8.932 × 10 25
0.62
4.800 × 10 25
0.68
1.4819 × 10 26
0.44
1.0759 × 10 26
0.19
Moment of inertia (MR 2 )
0.37
0.347
0.311
0.358
Average density (gm cm -3 )
3.530
3.010
1.940
1.830
10 November 2011
Astronomy 111, Fall 2011
Strong loworder orbital
resonances
Icy
surfaces
Rocky
interiors
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Structure and composition of the Galilean moons
 Density and moment of
inertia indicate that all four
Galilean moons are
differentiated.
• Io, Europa and
Ganymede have
have iron cores; Callisto
does not.
• Ganymede has its own
Interior structure of the Galilean
magnetic field: liquid core. moons (Galileo/JPL/NASA).
 Trend of average density
(decreasing outward from Jupiter) matches that of fraction
of mass in the form of ice (increasing outward from
Jupiter). Most mass in the form of silicates.
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Structure and composition of the Galilean moons
(continued)
 Large albedoes indicate that all four
have icy surfaces.
• Europa is completely covered
in water ice.
• Io’s yellow color is from volcanic
SO 2 , frosting the water ice.
Flying low over Ganymede
 Surfaces are not heavily cratered.
(Voyager/JPL/NASA)
• To some extent, this is expected
from their position outside the asteroid belt.
• However, Europa has far fewer craters than the other
two, and Io has no impact craters at all. They must
have been resurfaced recently. (Think lunar maria vs
lunar highlands.)
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Structure and composition of the
Galilean moons (continued)
 In Io’s case, the
resurfacing mechanism is
clear: Io is the most
volcanic object in the Solar
system.
• It must therefore have
a particularly hot
mantle.
• Volcanism is also
responsible for the SO 2
frost, frozen from gas
released during
eruptions.
Galileo/JPL/NASA
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Structure and composition of the Galilean moons
(continued)
In Europa’s case, the resurfacing may
be related to widespread liquid water
oceans underneath its frozen surface.
 Europa’s surface looks like
terrestrial, oceanic pack ice. 
 Jupiter has a strong bar-magnetlike magnetic field.
 Rocks and ice are electrical
insulators, and they do not affect
externally-applied magnetic
fields. Most moons (like ours)
behave this way in their planet’s
field.
10 November 2011
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Galileo/JPL/NASA
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Structure and composition of the Galilean moons
(continued)
 But magnetic-field measurements made
during close flybys have shown Europa to
repel Jupiter’s magnetic field, in the way an
electrically-conducting surface would do.
 A salt-water ocean under the ice, covering
most of the moon, would have the right
electrical conductivity to repel the field as
observed.
• Magnetization measurements also
indicate that Ganymede and Callisto
might also have sub-surface oceans,
though not as extensive as Europa’s.
Insulator
Conducting shell
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The irregular satellites of Jupiter
The lesser satellites tend to be in
large, eccentric, highly inclined
orbits, many of which are
retrograde (revolution opposite to
Jupiter’s rotation).
Key:
Callisto
innermost irregular prograde
satellite, Themisto.
5 irregular satellites in the
prograde group know before
2002.
11 retrograde satellites
discovered in 2001.
14 previously known
retrograde satellites.
10 November 2011
Orbits of the irregular Jovian satellites
(as of 2002), from Scott Sheppard’s
Satellites page.
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The irregular satellites of Jupiter (continued)
Their shapes are irregular too, and they tend to be dark,
resembling asteroids.
 Thus most of us think that they are captured asteroids,
rather than leftovers from the formation of Jupiter like the
Galilean moons. (Even the ring shepherds!)
Metis, Adrastea, Amalthea, and Thebe, by Galileo (JPL/NASA)
10 November 2011
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Tides and orbital energy
Jupiter is very massive, and exerts large tidal forces on
nearby moons.
 If the orientations or strength of the tidal forces change,
then parts of the moon’s interior relax, and other parts are
stretched anew.
• Orientation changes continuously if the moon rotates
at a different angular velocity than it revolves.
• Tidal-force strength changes continuously if the moon
is in an eccentric orbit.
 Repeated stretching and relaxing creates heat, which leaks
away in the form of blackbody radiation.
 Whence comes the heat? What’s losing energy?
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Tides and orbital energy (continued)
 Only one source: the kinetic energy of orbital motion. The
heat from tidal stretching and relaxing comes from the
orbital energy of the moon relative to Jupiter.
• So, as energy is lost due to heat and subsequent
radiation, the moon’s orbit changes. It will continue to
change until it rotates synchronously with its
revolution, and revolves in a circular orbit.
 But it takes torque to change angular velocities. (That is, p
and L are conserved, too.) What is the origin of the
torques that cause these orbit changes to be made?
• From the tidal bulges raised on the planet and moon
by each other, as follows…
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Reminder (?) about torque
Linear momentum
p = mv
dp
=
F = ma
dt
L = r × p = Iω
dL
N =r × F =
= Iω
dt
sin θ nˆ r⊥ Fnˆ
= rF
=
is to Force, as
Angular momentum
is to Torque.
N
θ
r
10 November 2011
F
N is perpendicular to the
plane of r and F, in the
direction given by the righthand rule.
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Tidal torque
Tidal bulges don’t generally line up perfectly with the moon
that raised them.
 Energy is dissipated in making the tidal bulge, and the
rotation and revolution rates are different in general.
 So the bulge can lead or lag the location of the moon.
Parent
rotation
Tidal
lead
Satellite
revolution
Sizes of bulges, bodies
greatly exaggerated.
10 November 2011
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Tidal torque (continued)
Let’s calculate the torque. First, satellite-bulge distances,
using the law of cosines:
rn2 =r 2 + R 2 − 2 rR cos θ
r f2 =r 2 + R 2 − 2 rR cos (π − θ ) =r 2 + R 2 + 2 rR cos θ
R
θ
rn
r
rf
10 November 2011
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Tidal torque (continued)
 Usually the orbital radius r is a good deal larger than the
planetary radius R. So these are good approximations:
2
R R
R
1 + a   + b   + ... ≅ 1 + a  
r r
r
n

 R 
R
1 + a    ≅ 1 + na  
 r 
r

You will learn why the latter is true, in the first math
course which deals with infinite series.
 Only the torques on the bulges matter: torque cancels out
for the (mirror-symmetric) rest of the planet.
10 November 2011
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Tidal torque (continued)
The magnitude of the force on the bulge nearest the satellite:
G∆Mm
G∆Mm
Fn =
rn2
r 2 + R 2 − 2 rR cos θ
G∆Mm
r2
G∆Mm 
2R

≅
 1 + r cos θ 
2
2


r
1 − 2 ( R r ) cos θ + ( R r )
1
∆M
θ
Fn
m
∆M
10 November 2011
Ff
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Tidal torque (continued)
And similarly the magnitude of the force on the other bulge:
2R
G∆Mm G∆Mm 

Ff =
≅
 1 − r cos θ 
2
2


rf
r
∆M
θ
Fn
m
∆M
10 November 2011
Ff
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Tidal torque (continued)
Now the torque on the parent body from Fn :
r
r sin θ
sin α
sin θ=
= sin (π − α=
)
rn
r 2 + R 2 − 2 rR cos θ
≅
sin θ
1 − 2 ( R r ) cos θ
(
)
≅ 1 + ( R r ) cos θ sin θ
α
θ
10 November 2011
(using
the law
of sines)
r
rn
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Tidal torque (continued)
2R
G∆Mm 
R


Nn =
RFn sin α =
R
 1 + r cos θ  1 + r cos θ  sin θ
2



r
G∆MmR sin θ 
3R

≅
 1 + r cos θ 
2


r
Direction: into page, by right-hand rule, if 0 ≤ θ < π .
R
θ
⊗
N
α
Fn
n
10 November 2011
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Tidal torque (continued)
Similarly,
G∆MmR sin θ 
3R

Nf ≅
1
−
cos
θ


2
r


r
directed out of the page.
θ
Nf
R
α
10 November 2011

Ff
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Tidal torque (continued)
Thus the net torque exerted by the satellite on the parent is
3R
3R
G∆MmR sin θ 
ˆ
N s-p
= Nn + N f ≅ −
 1 + r cos θ − 1 + r cos θ  z
2


r
6G∆MmR 2
3G∆MmR 2
=
−
−
− N p-s .
sin θ cos θ zˆ =
sin 2θ zˆ =
3
3
r
r
Parent
rotation
θ
Satellite
revolution
by
Newton’s
third law
⊗
N s-p
10 November 2011
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Tidal torque (continued)
We have so far considered the parent to be tidally distorted
and the satellite to be a point mass. Thus, with a tidal lead
(0 ≤ θ < π 2) and the corresponding direction of torque,
 the spin of the planet decreases with time (day lengthens)
 the orbital angular momentum of the satellite, L = m GMr ,
increases (r increases).
Parent
rotation
θ
Satellite
revolution
⊗
N s-p
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Tidal torque (continued)
By the same token, the parent body raises tides on the
satellite, and if the bulge leads the parent’s revolution, the
torque exerted on the bulge will also decrease the satellites
spin, and increase the parent’s orbital angular momentum
(i.e. the orbital distance r).
′
N p-s
Parent
revolution
(in satellite’s
rest frame)
10 November 2011
Tidal
lead
Astronomy 111, Fall 2011
⊗
Satellite
rotation
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Orbital evolution of satellites
If satellites form from planetary “leftovers,” their spin
periods are generally less than their orbital periods.
 In this situation, the tidal bulges lead revolution: the faster
rotation tends to drag the bulge away from the parentsatellite line – precisely the setup we just considered.
 And thus the tidal torques decrease rotational angular
momentum (the bodies spin down) and increase orbital
angular momentum (the orbital distance increases).
 For eccentric orbits: since torques are larger, the closer the
moon is to the planet, more angular momentum is
transferred from rotation the orbit near periapse.
• So as the orbit gets larger, the eccentricity decreases
(orbit gets more circular).
10 November 2011
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Orbital evolution of satellites (continued)
But two conditions can produce a lag ( − π 2 ≤ θ < 0) :
 Satellite orbits prograde (revolution same direction as
rotation) but faster than parent rotation
 Satellite orbits retrograde (revolution opposite rotation)
and the bodies spin up and decrease their distance, eventually
merging.
Tidal
lag
10 November 2011
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Orbital evolution of the Galilean satellites
When Jupiter was formed, the Galilean moons were probably
formed from the leftovers, and probably in orbits smaller
than they have now, rotating rapidly.
 The tidal interaction between Jupiter and all four satellites
quickly slowed their rotation; all are now rotating
synchronously.
 And by the same token, they drifted away from Jupiter as
their orbital angular momentum increased
 As Io drifted outwards, it captured Europa a 2:1 meanmotion resonance.
 Likewise Europa captured Ganymede, also in a 2:1
resonance.
10 November 2011
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Orbital evolution of the Galilean satellites
(continued)
 The gravitational interaction of Io with Europa, and
Europa with Ganymede, at their orbital resonances, keep
pulling the orbits of these moons slightly out of circular
shape.
 And thus the tidal force from Jupiter’s gravity changes
through the orbit, permitting a never ending cycle of
stretching and relaxing: tidal heating, again.
 And this has probably been the case since very early in the
Solar system’s history: the moons have been heated like
this for about 4.5 Gyr.
 The tidal heating on Io is most severe. Thus, as Stan Peale
predicted before the Voyagers got there to discover it, Io’s
interior is molten, and the moon is quite volcanic.
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Europa, water, and life.
 Next on the tidal heating scale is Europa, for which the
heating is probably enough to keep the interior warm.
• Not warm enough for the rocks currently to be molten,
but enough for the lower parts of the 140 km thick
water crust to be liquid.
 This is consistent with the pack-ice appearance and rarity
of impact craters on Europa’s surface, and with the
magnetic-field measurements which indicate salt-water
oceans beneath the ice.
 Thus the conditions under the ice pack on Europa may
resemble those in the Earth’s Arctic Ocean, and have been
that way for billions of years…
 …making Europa the extraterrestrial solar-system site
most likely to support life.
10 November 2011
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Art by Michael Carroll
Coming soon to a Solar system near you: the
Europa Jupiter System Mission (EJSM)
10 November 2011
Two satellites, with 21
complementary
instruments between them,
will be deployed by NASA
and ESA on a mission
of detailed
exploration of the
Jovian system,
especially Europa
and Ganymede.
Look for launches in
2020, arrival in late 2025
and early 2026.
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