Lecture 19 - Saturn Lecture Notes

Chapter 12: Saturn

12.1: Orbital and Physical Properties

Saturn is the 6th planet from the Sun and the outermost planet known to ancient astronomers.
The period of Saturn’s orbit is $P = 29.4$ Earth years.
Saturn orbits at an average distance of 9.5 AU from the Sun, about twice as far as Jupiter’s orbit.
Calculating Saturn's semimajor axis $a$ using Kepler's Third Law:
- $P^2 \text{ (in Earth years)} = a^3 \text{ (in AU)}$
- $a \text{ (in AU)} = P^{2/3} \text{ (in Earth years)}$
- $a = (29.4)^{2/3} \text{ AU} = 9.5 \text{ AU}$
Saturn’s orbit has an eccentricity $e = 0.054$ . The distance from Saturn to the Sun varies by about 10% during its orbit.
- Perihelion: 9.01 AU
- Aphelion: 10.08 AU
Saturn is easiest to observe during a favorable opposition when the Earth-Saturn distance is only about 8 AU.
Saturn is the second-largest planet in the Solar System.
- Radius: 60,000 km = 9.5 $R_{\bigoplus}$
- Mass: $5.7 × 10^{26}$ kg = 95 $M_{\bigoplus}$
- Density: 700 kg/ $m^3$ (less than water!)
- Moons: 82 (as of 2021)
- Very prominent rings: over 200,000 km diameter, less than 20 m thick
The rings are tilted at 27° with respect to Saturn’s orbit.
View of rings from Earth changes as Saturn orbits the Sun.

Spacecraft Exploration of Saturn

Voyager 1 and 2 flew by Saturn.
- Voyager 1 flew by Saturn and its largest moon, Titan.
- Voyager 2 continued toward Uranus and Neptune.
- Both studied Saturn’s atmosphere and rings.
Cassini spacecraft arrived at Saturn in 2004 and its mission ended in 2017.
- Studied its rings and moons.
- Sent a lander (Huygens) to Titan.
- Returned many spectacular images.

12.2: Saturn’s Atmosphere

Saturn’s atmosphere shows zone and belt structure, but the color is much more subdued than Jupiter’s.
Like Jupiter, Saturn exhibits differential rotation; different bands of clouds rotate at different rates.
Saturn’s rotation (spin) period is determined by measuring the rotation period of its magnetic field.
Radio waves emitted from the strong magnetic field indicate the rotation period of the core is 10 hours 46 minutes.
Rapid rotation leads to oblateness.
- Saturn’s atmosphere is less dense than Jupiter’s, so it is more oblate.
- Equatorial diameter = 60,300 km
- Polar diameter = 54,400 km
- Saturn is the flattest planet in the Solar System.
Calculations show that Saturn would be more oblate than observed if it were only composed of gas, suggesting it has a small, dense, rocky core of about 15 Earth masses.
Composition of atmosphere:
- Hydrogen (H2): 92.4 %
- Helium (He): 7.4 %
- Trace amounts of methane (CH4), ammonia (NH3), and water vapor (H2O)
Like Jupiter, Saturn is over 99 % Hydrogen and Helium. Its strong gravity prevents these light gases from escaping.
Saturn has much less Helium in its atmosphere than Jupiter does.
- Jupiter’s atmosphere: H2: 86.1 %, He: 13.8 %
- Saturn’s atmosphere: H2: 92.4 %, He: 7.4 %
Saturn's atmosphere is similar to Jupiter's, except the pressure is lower.
Saturn has 3 cloud layers, like Jupiter’s:
- Ammonia
- Ammonium hydrosulfide
- Water ice
Cloud layers are thicker than Jupiter’s because of Saturn’s lower gravity (200 km compared to 80 km for Jupiter).
Thicker clouds mean optical telescopes can only see the top layer, explaining the more uniform tan-colored appearance than Jupiter.
Wind patterns on Saturn are similar to those on Jupiter, with zonal flow. Visible bands are associated with variations in wind speed.
- Fewer east-west alternations.
- Much faster wind speeds, up to 1500 km/h!
Storms are present, but not as large or powerful as Jupiter’s Great Red Spot. Jupiter-style “spots” can turn into large storms on Saturn, then dissipate relatively quickly.
Giant vortices exist at both poles of Saturn, apparently due to jet streams circling the planet.

12.3: Saturn’s Interior and Magnetosphere

Saturn’s internal structure, deduced from Voyager observations and computer modeling, is similar to Jupiter’s. Saturn’s lower mass means lower pressure, temperature, and density in its core than in Jupiter’s.
Atmosphere: radius of 60,000 km, thickness of about 200 km, mostly molecular hydrogen gas, H2
Shell of metallic hydrogen under high pressure; exists below a radius of 30,000 km
Icy, rocky core with a radius of about 15,000 km
The temperature at the cloud tops on Saturn is 97 K. The predicted equilibrium temperature at Saturn’s distance from the Sun is 73 K.
Saturn radiates about 3 times more energy than it receives from the Sun.
Unlike Jupiter, Saturn is too small to have retained its heat of formation.
Saturn is still experiencing internal differentiation as dense material sinks towards the center.
Saturn’s atmosphere is so cold that helium can condense and “rain” down into the deep interior (Jupiter is too warm for this to happen).
The ongoing differentiation causes the interior to heat up. The heating occurs when kinetic energy is converted into thermal energy. The helium droplets fall with high speed into the interior. When they bump into other droplets, energy is converted to heat.
The helium rain phenomenon explains:
- The extra heat produced by Saturn.
- The observed depletion of helium in Saturn’s atmosphere (relative to Jupiter’s).
  - Saturn’s atmosphere: H2: 92.4 %, He: 7.4 %
  - Jupiter’s atmosphere: H2: 86.1 %, He: 13.8 %
Saturn also has a strong magnetic field, due to its rapidly spinning metallic hydrogen interior, but it's only 5% as strong as Jupiter’s.
No large moons orbit completely within the magnetosphere, and therefore there is no equivalent to Jupiter’s plasma torus along Io’s orbit.
Saturn's magnetic field creates aurorae.

12.4: Saturn’s Spectacular Ring System

Saturn has a large and complex ring system, visible even to the first telescopes.
- First observed by Galileo.
- First resolved as rings by Christian Huygens.
From the outside in, the main structures are the A ring, B ring, and C ring.
Rings extend about 130,000 km above Saturn’s cloud tops.
Giovanni Cassini discovered a gap in the rings in 1675 (The Cassini Division).
In 1857, James Clerk Maxwell showed that the rings must be made of many particles or “moonlets,” each orbiting independently.
In 1895, Doppler shift observations of sunlight reflected from the ring particles confirmed Maxwell’s idea.
Properties of Saturn’s rings:
- Highly reflective – reflect 80% of sunlight
- Largely made of water ice – similar to snowballs
- Thin – only less than 20 meters thick!
- Ring particles range in size from fractions of a millimeter to tens of meters
- Rings are kept thin and in circular orbits through particle-particle collisions and gravitational interactions with Saturn’s moons
Inside the Roche limit, the tidal force of Saturn overwhelms the self-gravity of a moon, ripping it apart.
The rings may exist due to the breakup of one or more small moons that passed inside Saturn’s Roche limit.
Roche limit = about 2.4 times the radius of the parent planet = 144,000 km for Saturn.
Jovian ring systems are almost all inside the Roche limit.
The Voyager probes showed Saturn’s rings to be much more complex than originally thought.
The Cassini probe studied the rings in much more detail.
The main ring is composed of thousands of narrow ringlets.
Rings contain alternating regions of high and low density of material (“density waves”).
Ringlets are the high-density regions from the gravitational influence of the material in the rings and Saturn’s moons.
Smaller gaps are kept clear by embedded moonlets that deflect material.
Large gaps are the result of orbital resonances with Saturn’s Moons.
- Cassini division: orbit at 117,000 km, period = 0.47 days
- Mimas: orbit at 186,000 km, period = 0.94 days
- Cassini division is due to a 2:1 resonance with Mimas: ring particles at this location orbit twice for every orbit of Mimas.
- Mimas tugs on them at the same location along their orbit, which changes their orbit, clearing a gap.
- Ring particles at non-resonant orbits receive tugs spread out along the orbit, so no preferential clearing of a gap.
Orbital resonances are common in Saturn’s ring system.
- The Cassini division is in a 2:1 resonance with Mimas.
- The outer edge of the A ring is in a 3:2 resonance with Mimas.
- The Encke gap is in a 5:3 resonance with Mimas.
Voyager also found radial “spokes” that formed and then dissipated; this probably happens frequently. The spokes are caused by small particles suspended just above the ring plane.
Cassini has also seen spokes, although not as prominent as those seen by Voyager.
The backlit view taken by Cassini while in Saturn’s shadow shows the fainter F, G, and E rings. The moon Enceladus orbits within the E ring, and its eruptions likely give rise to the ring’s icy particles.
The strangest ring is the F ring, which appears to have braids and kinks.
The thinness of the F Ring is caused by two shepherd satellites (Prometheus and Pandora) that orbit near the ring.
- One orbits a few hundred kilometers inside the ring, and the other orbits a similar distance outside it.
- If a particle strays from the ring, the combined gravitational pulls from both shepherd satellites confine it back to the ring.
Details of formation of the rings are unknown.
- Probably too active to have lasted since Saturn’s formation, and not all rings may be the same age.
- Either continually replenished or the result of a catastrophic event.
- Rings are thought to be the result of a catastrophic event, either a moon torn apart or a massive collision, and may be only 50 million years old.

12.5: The Moons of Saturn

Saturn has 82 moons (as of 2021).
Saturn’s moons appear to be made of water ice, most with an average density of about 1000 kg/ $m^3$ .
- 75 small moons (irregular shapes, less than 400 km across).
- 6 medium-sized moons (spherical: 400 to 1500 km diameter): Mimas, Enceladus, Tethys, Dione, Rhea, Iapetus
- 1 large moon: Titan (5150 km diameter), which is larger than Mercury and almost as large as Jupiter’s Ganymede, and it has an atmosphere!
Titan has been known for many years to have an atmosphere.
- Voyager 1 passed by in 1980.
- Detailed observations by Cassini Mission, and the Huygens probe landed on the surface!
- Titan’s atmosphere is 60% thicker and denser than Earth’s, making the surface impossible to see with optical telescopes.
Surface temperature = 94 K
Titan's Atmosphere:
- Nitrogen (90%), Argon (7 %)
- Trace amounts of hydrocarbons: Methane (CH4), Ethane (C2H6), Propane (C3H8)
- Weak gravity means the atmosphere extends 400 km above the surface
- Haze layers, similar to smog around major cities
- Methane clouds
- Methane snow or rain
Reasons why Titan has a thick atmosphere, unlike other moons:
- Titan is much farther from the Sun and colder, so it is able to retain its methane and ammonia.
- During formation, Titan’s interior absorbed more methane and ammonia that outgassed from geological activity, then froze.
- Radioactivity warmed the ices to form an atmosphere.
- Sunlight split the ammonia (NH3) into hydrogen (which escaped into space) and nitrogen (which remained).
- Methane remained to form the dense atmosphere we see today.
Some surface features on Titan visible in Cassini infrared image (2004):
- Impact basin
- Mountain ranges caused by ancient tectonic activity
- Icy volcano, suggesting geological activity
The Huygens spacecraft landed on Titan and returned images directly from the surface, providing strong evidence for liquid surface features, such as:
- Rivers draining from uplifted terrain into darker, low-lying regions?
- Dark channels reminiscent of streams?
Radar aboard Cassini detected smooth regions on Titan thought to be lakes of liquid ethane and methane, and perhaps larger bodies of thicker, hydrocarbon sludge.
The Dragonfly (NASA) mission will launch in 2026 and arrive in 2034. It has 8 rotors and flies like a large drone and will fly to dozens of promising locations on Titan to look for prebiotic chemical processes common to Titan and Earth.
The Interior of Titan is modeled based on measurements of Titan’s gravitational field made by Cassini and Huygens. It is largely a rock–ice mixture, with a subsurface layer of liquid water a few tens of km below the surface, similar to that hypothesized on Jupiter’s Europa and Ganymede.
Saturn’s 6 medium-sized satellites as seen by the Cassini spacecraft and compared to Earth’s Moon, all to scale, are all heavily cratered and play an important role in the ring system.
Mimas, Enceladus, Tethys, Dione, and Rhea all orbit between 3 and 9 planetary radii from Saturn and are all tidally locked, meaning they have “leading” and “trailing” surfaces. The leading surfaces are more heavily cratered as the moons collide with smaller objects in their path.
Iapetus orbits 59 planetary radii away and is also tidally locked.
Enceladus:
- Saltwater ocean below the ice near the south pole.
- The long blue streaks are fractures in the ice through which gas escapes to form a thin atmosphere.
- Geysers release plumes of mostly water ice particles; hydrocarbons and organic compounds are also found, suggesting the possibility for life.
- The Southern hemisphere is younger than the northern hemisphere, possibly due to differences in the thickness of the lithosphere.
- The South pole is warmer, as high as 150 K.
- Heat source: tidal heating, but not as great as Io.
- Ash of icy particles makes the surface highly reflective. Geyser eruption replenishes the material in Saturn’s E-ring.
Masses of small moons not well known.
Two of them (Janus and Epimetheus) share a single orbit (co-orbital moons) and trade orbits, playing tag as they lap each other.
Two more moons (Telesto and Calypso) are at the Lagrangian points of a larger moon (Tethys). The combined gravitational pulls of Saturn and Tethys keep the small moons exactly 60° ahead and behind the larger moon at all times. All three moons share an orbit and never change their relative positions.

Next Lecture

Chapter 13: Uranus and Neptune
- 13.1: The Discoveries of Uranus and Neptune
- 13.2: Orbital and Physical Properties
- 13.3: The Atmospheres of Uranus and Neptune
- 13.4: Magnetospheres and Internal Structure
- 13.5: The Moon Systems of Uranus and Neptune
- 13.6: The Rings of the Outermost Jovian Planets