THE MOONS OF SATURN, URANUS, & NEPTUNE

THE MOONS OF SATURN, URANUS, & NEPTUNE Problem Set 8 due now Midterm #2 on Tuesday! 13 November 2018 ASTRONOMY 111 FALL 2018 1 TIDES & ORBITAL ENERGY Jupiter is very massive and exerts large tidal forces on nearby moons. If the orientations or strength of the tidal forces change, parts of the moon s interior relax while other parts are stretched. The direction of the tidal force changes continuously if the moon rotates at a different angular velocity than it revolves. The strength of the tidal force 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. From where is the heat coming? What is losing the energy? 13 November 2018 ASTRONOMY 111 FALL 2018 2 1

TIDES & ORBITAL ENERGY There is only one source: the kinetic energy of the 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. ( " and # 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. 13 November 2018 ASTRONOMY 111 FALL 2018 3 REMINDER (?) ABOUT TORQUE Linear momentum is to Force as Angular momentum is to Torque. / & q + " = $ % & = ' " '( = $ ) * = + " = -. / = + & = '* = - 0 = +& sin 4 56 '( = + 7 & 56 / is perpendicular to the plane of + and & in the direction given by the right-hand rule. 13 November 2018 ASTRONOMY 111 FALL 2018 4 2

TIDAL TORQUE Tidal bulges do not generally line up perfectly with the moon that raises them. Energy is dissipated in making the tidal bulge, and the rotation and revolution rates are different. Parent rotation Tidal lead Satellite revolution The bulge can therefore lead or lag the location of the moon. Sizes of bulges, bodies greatly exaggerated. 13 November 2018 ASTRONOMY 111 FALL 2018 5 TIDAL TORQUE Let us calculate the torque. First, satellite-bulge distances, using the law of cosines:! " # =! # + & # 2!& cos,! - # =! # + & # 2!& cos., =! # + & # + 2!& cos, R q r r n r f 13 November 2018 ASTRONOMY 111 FALL 2018 6 3

TIDAL TORQUE Usually, the orbital radius r is much larger than the planetary radius R. So, we can employ some approximations to make our lives a little more simple: ' 1 + # $ % + & $ % + 1 + # $ % * 1 + # $ % 1 + +# $ % (You will learn why the latter is true in your first math course that deals with infinite series.) Only the torques on the bulges matter: torque cancels out for the (mirror-symmetric) rest of the planet. 13 November 2018 ASTRONOMY 111 FALL 2018 7 TIDAL TORQUE The magnitude of the force on the bulge nearest the satellite is! " = $%Δ' ( " ) = $%Δ' ( ) + + ) 2(+ cos 1 = $%Δ' ( ) 1 1 2 + ( cos 1 + + ( ) DM DM F f q F n m! " $%Δ' ( ) 1 + 2+ ( cos 1 13 November 2018 ASTRONOMY 111 FALL 2018 8 4

TIDAL TORQUE Similarly, the magnitude of the force on the other bulge is! " = $%Δ' ( " ) = $%Δ' ( ) + + ) + 2(+ cos 0 = $%Δ' ( ) 1 1 + 2 + ( cos 0 + + ( ) DM DM F f q F n m! " $%Δ' ( ) 1 2+ ( cos 0 13 November 2018 ASTRONOMY 111 FALL 2018 9 TIDAL TORQUE The angle between the force and radius is sin $ = sin & $ Using the law of sines = ( sin * ( ) ( sin * = ( + + - + 2(- cos * sin * 1 2 - ( cos * q a r r n sin $ 1 + - ( cos * sin * 13 November 2018 ASTRONOMY 111 FALL 2018 10 5

TIDAL TORQUE The torque on the planet from " # is $ # = &" # sin * = & +,Δ. / 0 1 + 2& / cos 6 1 + 7 cos 6 sin 6 8? # R q Ä q F n +,& sin 6 Δ. $ # / 0 1 + 3& / cos 6 Direction: Into the page, by the right-hand rule, if 0 6 < >. 13 November 2018 ASTRONOMY 111 FALL 2018 11 TIDAL TORQUE Similarly, $%& sin * Δ,! " -. 1 3& - cos * directed out of the page.! " R q q F f 13 November 2018 ASTRONOMY 111 FALL 2018 12 6

TIDAL TORQUE Therefore, the net torque exerted by the satellite on the planet is " #$% = " ' + " ),-. sin 2 Δ4 5 6 1 + 3. 5 cos 2 1 + 3. 5 cos 2 < 6,-.6 Δ4 5 > sin 2 cos 2 < " #$% 3,-.6 Δ4 5 > sin 22 < Planet rotation q Satellite revolution " #$% = " #$% Ä @#$% By Newton s third law 13 November 2018 ASTRONOMY 111 FALL 2018 13 TIDAL TORQUE So far, we have considered the planet to be tidally distorted and the satellite to be a point mass. Thus, with a tidal lead (0 # < % ) and the corresponding & direction of torque, The spin of the planet decreases with time (day lengthens) The orbital angular momentum of the satellite (' = ) *+,) increases (r increases). Planet revolution (in satellite s rest frame) Tidal lead - /01 Ä Satellite rotation 13 November 2018 ASTRONOMY 111 FALL 2018 14 7

TIDAL TORQUE By the same token, the planet body raises tides on the satellite. If the bulge leads the planet s revolution, the torque exerted on the bulge will also decrease the satellite s spin and increase the planet s orbital angular momentum (i.e. the orbital distance r). Planet revolution (in satellite s rest frame) Tidal lead! #$% Ä Satellite rotation 13 November 2018 ASTRONOMY 111 FALL 2018 15 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 planet-satellite line precisely the setup we just considered. 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 the torques are larger, the closer the moon is to the planet, the more angular momentum is transferred from rotation in the orbit near the periapse. So, as the orbit gets larger, the eccentricity decreases (the orbit gets more circular). 13 November 2018 ASTRONOMY 111 FALL 2018 16 8

ORBITAL EVOLUTION OF SATELLITES Two conditions can produce a lag ( " # % < 0): Satellite orbits prograde (revolution in the same direction as the rotation) but faster than the planet s rotation Satellite orbits retrograde (revolution opposite rotation) And the bodies spin up and decrease their distance, eventually merging. Tidal lag 13 November 2018 ASTRONOMY 111 FALL 2018 17 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 in a 2:1 mean-motion resonance. Likewise, Europa captured Ganymede, also in a 2:1 resonance. 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. 13 November 2018 ASTRONOMY 111 FALL 2018 18 9

ORBITAL EVOLUTION OF THE GALILEAN SATELLITES Thus, the tidal force from Jupiter s gravity changes through the orbit, permitting a never-ending cycle of stretching and relaxing: tidal heating. 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. 13 November 2018 ASTRONOMY 111 FALL 2018 19 EUROPA, WATER, & 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 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 that indicate salt-water oceans beneath the ice. Thus, the conditions under the ice pack on Europa may resemble those in 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. 13 November 2018 ASTRONOMY 111 FALL 2018 20 10

THE MOONS OF SATURN, URANUS, & NEPTUNE Hyperion (Saturn VII Cassini, JPL/NASA/Space Science Institute) Names General features: structure, composition, orbits, origin Special moons Mimas Titan Enceladus Iapetus Miranda Triton 13 November 2018 ASTRONOMY 111 FALL 2018 22 GENERAL FEATURES OF THE OUTER-PLANET SATELLITES There are many of them: Saturn has 53 that we currently know of, Uranus 27, and Neptune 13, of which 8, 5, and 0 are considered Major or regular and the rest Lesser or irregular. The regular satellites are all very icy, and only the most massive are likely to be differentiated. Almost all of their densities are below those of the Galilean moons. The regular satellites are in low-eccentricity, low-inclination, prograde orbits, and they rotate synchronously with their revolution. They probably formed with the host planet. Inner, irregular satellites tend to be closely associated with the rings and tend to be similar in composition to the rings (very icy in Saturn, not quite so icy in the others). The outer, lesser satellites are all small and tend to be substantially darker (less surface ice) than the regulars or inner-lessers. 13 November 2018 ASTRONOMY 111 FALL 2018 26 11

GENERAL FEATURES OF THE OUTER-PLANET SATELLITES The outer-lessers also tend to have eccentric, highly inclined orbits, as often retrograde as prograde. They are probably captured asteroids, comets, or Kuiper-belt objects formed elsewhere, as with Jupiter. Strong mean-motion resonances among the orbits are fairly common. With one possible exception, though, none of the moons locked in orbital resonances are both large enough and close enough to their planets for tidal heating to be as important as it is for Io and Europa. 13 November 2018 ASTRONOMY 111 FALL 2018 27 Mass Radius Mean density Visual geometric albedo Semimajor axis Period Inclination [10 23 g] [10 5 cm] [g cm -3 ] [10 8 cm] [Planet radii] [days] [degrees] Mimas (SI) 0.379 208x197x191 1.15 0.6 185.52 3.0783 0.9424218 1.53 0.0202 Enceladus (SII) 1.08 257x251x248 1.61 1.0 238.02 3.9494 1.370218 0.00 0.0045 Tethys (SIII) 6.18 538x528x526 0.985 0.8 294.66 4.8892 1.887802 1.86 0.0000 Dione (SIV) 11.0 563x561x560 1.48 0.7 377.40 6.2620 2.736915 0.02 0.0022 Rhea (SV) 23.1 765x763x762 1.24 0.7 527.04 8.7449 4.517500 0.35 0.0010 Titan (SVI) 1345.5 2,575 1.88 0.22 1221.83 20.273 15.945421 0.33 0.0292 Hyperion (SVII) 0.056 180x133x103 0.550 0.3 1481.1 24.575 21.276609 0.43 0.1042 Iapetus (SVIII) 18.1 746x746x712 1.09 0.05/0.5 3561.3 59.091 79.330183 14.72 0.0283 Miranda (UV) 0.66 240x234.2x232.9 1.20 0.32 129.90 5.078 1.413479 4.34 0.0013 Ariel (UI) 12.9 581.1x577.9x577.7 1.59 0.39 199.90 7.481 2.520379 0.04 0.0012 Umbriel (UII) 12.2 584.7 1.46 0.21 266.00 10.41 4.144176 0.13 0.0039 Titania (UIII) 34.2 788.9 1.66 0.27 436.30 17.05 8.705867 0.08 0.0011 Oberon (UIV) 28.8 761.4 1.56 0.23 583.50 22.79 13.463234 0.07 0.0014 Eccentricity Triton (NI) 214 1,353.4 2.05 0.72 354.76 14.328-5.876854 157.345 0.000016 THE REGULAR SATELLITES OF SATURN, URANUS, & NEPTUNE Retrograde, so it is not really regular. Porous 13 November 2018 ASTRONOMY 111 FALL 2018 28 12

11/12/18 SATURN S SATELLITES & RINGS JPL/NASA 13 November 2018 ASTRONOMY 111 FALL 2018 29 SPECIAL MOONS: MIMAS Mimas, at the inner edge of the E ring, is involved in many important orbital resonances, most notably with the rings (e.g. the Cassini division). Its most famous feature is the gigantic crater Herschel. The impact that created Herschel must have come close to destroying the moon. (Note the central peak.) Even apart from Herschel, Mimas is much more heavily cratered than usual in the Saturnian system; similar to Iapetus and Hyperion. Why it is not heated sufficiently to be resurfaced like Io or Europa is a mystery 13 November 2018 NASA/JPL-Caltech/Space Science Institute ASTRONOMY 111 FALL 2018 30 13

SPECIAL MOONS: TITAN Titan is the second-largest satellite in the Solar System (slightly smaller than Ganymede) and was the first one discovered after the Galilean satellites (by Huygens in 1665). It is unusual in many respects: It is the only moon in the Solar System with a dense atmosphere: pressure of about 1.6 Earth atmospheres at the surface, 95% nitrogen (most of the rest is methane and ammonia), and is so heavily laden with photochemical smog that the surface cannot be seen at visible wavelengths. NASA/JPL-Caltech/Space Science Institute 13 November 2018 ASTRONOMY 111 FALL 2018 31 SPECIAL MOONS: TITAN Haze in Titan s upper atmosphere Photochemical smog below 13 November 2018 ASTRONOMY 111 FALL 2018 32 14

SPECIAL MOONS: TITAN There are few impact craters apparent (in infrared and radar images) on the surface of Titan, and there is evidence of cryovolcanism involving molten ices instead of molten rock. NASA/JPL-Caltech/Space Science Institute 13 November 2018 ASTRONOMY 111 FALL 2018 33 SPECIAL MOONS: TITAN Besides Earth, Titan is the only Solar System body to have liquids permanently resident on its surface. Hundreds of lakes are seen, especially near the poles: they change in depth over time and are fed by rivers with deltas. Near the south pole, liquid ethane (T = 90-184 K) has been positively identified in Ontario Lacus. Ontario Lacus South pole + Clouds NASA/JPL/Space Science Institute 13 November 2018 ASTRONOMY 111 FALL 2018 34 15

SPECIAL MOONS: TITAN Radar image of Ontario Lacus, taken in 2010 by Cassini. Note the rivers. River River deltas 13 November 2018 ASTRONOMY 111 FALL 2018 35 SPECIAL MOONS: TITAN Ontario Lacus (left) and Lake Ontario (right), shown on the same scale. 13 November 2018 ASTRONOMY 111 FALL 2018 36 16

SPECIAL MOONS: TITAN Titan s North-Polar Great Lake (left) and its northern lobe on the same scale as Lake Superior (right). 13 November 2018 ASTRONOMY 111 FALL 2018 37 SPECIAL MOONS: TITAN We have visited the surface of Titan: Cassini dropped a lander (named Huygens), which safely penetrated the atmosphere, landed softly, and continued to send back images for hours before it finally froze. View from Huygens after landing (ESA/ISA/NASA). The bigger rocks in the foreground are about six inches across. 13 November 2018 ASTRONOMY 111 FALL 2018 38 17

SPECIAL MOONS: ENCELADUS Enceladus has the highest albedo in the Solar System, very close to 1. So, it must be covered in clean (water) ice with a smooth surface. Indeed, the surface is smooth: not many impact craters, lots of thin cracks and fissures. At close range, it displays a pack ice -like appearance. So the surface of Enceladus is very young. This requires both heat sufficient to melt water ice and a means to distribute it over the surface. By the E-ring s structure and its position within it, Enceladus has also been identified as a major source of this ring s ice particles. Precisely how this happened was obscure until 13 November 2018 ASTRONOMY 111 FALL 2018 39 SPECIAL MOONS: ENCELADUS the close flybys by Cassini in 2005, in which the cryovolcanism that explains both the young surface and the E ring were first seen. The details are still a little obscure because, although Enceladus experiences significant tidal stretching in the Saturn system, it gets tidally stretched only about half as much as Europa. E ring Enceladus 13 November 2018 ASTRONOMY 111 FALL 2018 40 18

11/12/18 SPECIAL MOONS: IAPETUS A few of Saturn s moons have broad light or dark streaks across large fractions of their surface, probably as a result of picking up ring or outer-satellite debris, or splashes from surface impacts. Dione, Tethys, and Rhea have similar features. The most extreme of these is Iapetus, the outermost of Saturn s major satellites and the one featured in 2001: A Space Odyssey (the book; it was transplanted to Jupiter for the movie). Trailing and leading hemispheres of Iapetus (Cassini, NASA/JPL/Space Science Institute) 13 November 2018 ASTRONOMY 111 FALL 2018 41 ASTRONOMY 111 FALL 2018 42 SPECIAL MOONS: IAPETUS Giovanni Cassini discovered four of Saturn s major moons which he tried to name the Sidera Lodoicea after Louis XIV in the late 1600s, including Iapetus. He remarked that the one we now call Iapetus was only visible when on one side of Saturn, and reasoned that the moon had one dark hemisphere and one light-colored hemisphere. Cassini, NASA/JPL/Space Science Institute 13 November 2018 19

SPECIAL MOONS: IAPETUS He turned out to be correct. Iapetus s leading hemisphere has an albedo of only about 0.05; the trailing hemisphere, the usual 0.5 characteristic of ice. Infrared spectra show that the dark side is rich in carbonaceous compounds. Images taken in Cassini flybys make it clear that the leading hemisphere has a relatively thin coating of dark material that the trailing hemisphere lacks: near the edge between them, crater floors and slopes facing the dark side show up through the ice as dark patches. A thin, loose coating of asteroid-like debris swept up in orbit? Cassini, NASA/JPL/Space Science Institute 13 November 2018 ASTRONOMY 111 FALL 2018 43 SPECIAL MOONS: IAPETUS In 2009, the source of the dark material was found: the Phoebe Ring. Iapetus lies near its inner edge. The ring particles and Iapetus orbit in opposite directions. Phoebe itself is the source of the ring and is made of very dark material. Verbiscer, Skrutskie, & Hamilton (2009) 13 November 2018 ASTRONOMY 111 FALL 2018 44 20

SPECIAL MOONS: IAPETUS Iapetus rotates synchronously period of 79.3 days but, unlike all of the other regular satellites of Saturn and Jupiter, it is more oblate than can be consistent with its current rotational period (dashed curve). Oblate = bulging at the equator, flattened at the poles. It must have been spinning much faster than synchronously period of 16 hours when its lithosphere solidified. Castillo-Rogez et al. (2007) 13 November 2018 ASTRONOMY 111 FALL 2018 45 SPECIAL MOONS: IAPETUS It also has a prominent mountain ridge that runs all the way around its equator, making it look something like a walnut. In spots, this ridge has long, parallel equatorial cracks in it. Porco et al. (2005) Cassini, NASA/JPL/Space Science Institute 13 November 2018 ASTRONOMY 111 FALL 2018 46 21

SPECIAL MOONS: IAPETUS A detailed model (Castillo-Rogez et al., 2007) can explain Iapetus s shape and ridge quantitatively and precisely: 1. The moon forms in orbit around Saturn in a porous state by the accretion of smaller particles. 2. Radioactivity ( 26 Al, 60 Fe) melts ice in the interior. Porosity decreases as gravity compresses the partially-molten interior. Mismatch between new surface area and volume nicely accounted for by that of the ridge. 3. Melted ices (water with a little ammonia) have very high thermal conductivity, causing the outer layers of the moon to rapidly cool. 4. Cooling rapidly (within about 100 Myr), a thick, strong lithosphere forms, solidifying while the moon is still spinning rapidly, both freezing in the rapid-spin oblateness and comprising a particularly old surface. (This helps to explain the heavy cratering.) 5. Over a much longer time (200-900 Myr), tidal torques de-spin Iapetus to its present synchronous rotation. 13 November 2018 ASTRONOMY 111 FALL 2018 47 SPECIAL MOONS: IAPETUS What is new and interesting in this is that the successful models require that Iapetus formed in an orbit around Saturn while there were still lots of short-lived radionuclides around. Notably 26 Al, which has a half-life of only 0.7 Myr and contributes lots of heat. By lots is meant that Iapetus has to have formed within 3.5-7 26 Al half-lives of the formation of the oldest solid meteoritic particles. In turn, this requires that Saturn formed within 2-3 Myr after the Sun. It used to be thought to take much longer to form a giant planet, but this time scale is also supported by new observations of protoplanetary disks, as we will see. 13 November 2018 ASTRONOMY 111 FALL 2018 48 22

THE URANIAN SYSTEM Left: Uranus and several of its moons in the infrared at 2.17!m wavelength (E. Lellouch et al. with the ESO VLT Antu telescope) Right: The moons at closer range on a common scale (Voyager 2 JPL/NASA) 13 November 2018 ASTRONOMY 111 FALL 2018 49 THE MYSTERY OF THE URANIAN SYSTEM S OBLIQUITY Uranus s major moons orbit in the planet s equitorial plane, just like the rings. Thus, like the planet s rotation, the moons orbital axes are tilted by 98. In principle, a collision with a large body could have knocked Uranus into such an orientation, but since it is round this would not have affected the satellite orbits. Oberon Ariel Titania Umbriel 13 November 2018 ASTRONOMY 111 FALL 2018 50 23

SPECIAL MOONS: MIRANDA Discovered in 1948 by Kuiper, Miranda is neither very large nor very close to Uranus, but it has one of the most geologically-active looking surfaces in the Solar System, complete with enormous fault scarps, canyons and grabens, mountains, and plate boundaries. Miranda is locked in a 3:1 mean motion resonance with the (inner) minor satellite Desdemona. Even so, it would seem difficult to drive such violentlooking activity with tidal heating, but that is the means most often suggested for the generation of such terrain. Voyager 2, NASA/JPL 13 November 2018 ASTRONOMY 111 FALL 2018 51 SPECIAL MOONS: TRITON Triton is Neptune s only major moon: 200 times more massive than the sum of the rest, twice the mass of Pluto, and just a little smaller than Europa. It has four unusual features: 1. Retrograde orbit. It is very difficult to understand how it could have formed near Neptune in this orbit; it must have been captured. Tidal torques will cause the orbit to decay; Triton will hit the Roche limit in about 3.6 Gyr. Voyager 2, NASA/JPL 13 November 2018 ASTRONOMY 111 FALL 2018 52 24

11/12/18 SPECIAL MOONS: TRITON 2. A tenuous atmosphere (10-6 Earth atmospheric pressure), mostly composed of nitrogen, methane, and ammonia, which is probably a secondary atmosphere from 3. Cryovolcanism, visible in Voyager 2 images as a bunch of dark plumes from the vents and dark streaks on the surface from the expelled material. This is partly responsible for the fact that Triton has a 4. Very young surface: not nearly has heavily cratered as the Uranian satellites, perhaps because of filling by cryovolcanic flows and ice-plate tectonic activity. 13 November 2018 ASTRONOMY 111 FALL 2018 53 ASTRONOMY 111 FALL 2018 54 SPECIAL MOONS: TRITON Cyrovolcanoes on Triton (Voyager 2 image processed by Calvin Hamilton) 13 November 2018 25