An Ocean, A Moon And A Giant

Tethys on this blog has mostly been used to refer to the ancient ocean which used to run between the southern and northern continental blocks of Gondwanaland and Laurasia, which finally closed when the Mediterranean formed, all that’s left of it today really, and North and South America collided. Up until that point, an ocean had run right round the world, a little like the Southern Ocean today but near the tropics, which therefore had a powerful circular current and perhaps also strong winds. It would’ve allowed sail boats to navigate and travel quite easily around the planet, so in a way it’s a shame it ceased to be while we were still living in the trees, but maybe not.

The reason it was called Tethys stems from the fact that today’s Atlantic Ocean was named after the titan Atlas. Tethys the titan married her brother Okeanos, who was a vast river encircling the world. Tethys herself, although a mythical figure, has hardly any mythology attached to her. She’s more like Britannia, a mere symbol, in this case for the sea, and there is a further ancient ocean named after her brother Iapetus. She’s also the mother of the sea nymphs, the Oceanids, and numerous river deities. It’s a shame she didn’t do anything really.

The moons of Saturn are of course often named after titans, apart from the one which is actually called Titan, which is a bit weird really, but then most people call Cynthia (Selene, Diana, Artemis) “the Moon”, so Earth’s not much better. Tethys the moon is the innermost large moon of Saturn with a diameter of 1 050 kilometres, and is the second brightest moon per unit area after Enceladus. It’s also practically a twin of the next moon out, Dione, in terms of size. Both moons are in similar orbital resonance relationships with Mimas and Enceladus respectively, which needs some explaining because Mimas is quiet and cold inside whereas Iapetus is quite active and heated, apparently by tidal forces from Dione. Tethys is accompanied in its orbit by two trojan moons each forming the points of an equilateral triangle with it and Saturn, called Telesto and Calypso, Telesto being the leading member of the pair. Calypso is slightly larger but both are roughly the size of the Isle of Wight. Remarkably, even though both were discovered in 1980, it wasn’t the Voyager probes what did it, but telescopes on Earth. They were originally known as Tethys B and C. I didn’t know about them at the time, although I did know about Dione B, which is another story.

As befits a moon in orbital resonance with Mimas, Tethys too has a proportionately enormous impact basin. Since it’s more than twice the diameter of the inner moon, Odysseus, the crater, is itself four hundred kilometres in diameter, which is larger than the whole of Mimas and forty percent of the diameter of Tethys, making it proportionately the biggest crater that actually still looks like one on any moon. Unlike Herschel on Mimas, the floor of the crater does conform to the spheroidal shape of the moon, meaning that it has little influence on the distance to the horizon. The floor is three kilometres below the mean radius and the rim five kilometres above it, making the edge of the crater almost as high as Mount Everest above sea level, except that in the case of the mountain it rises from a plateau and would therefore not appear to be anything like as high. Nepal is on average already three kilometres above sea level. Moreover, this is a ring around 1 260 kilometres in circumference. In the centre of the crater is a plateau called Scheria Montes around three kilometres high with a basin in its own centre. There are faults around the rim, of which the largest is called Ogygia Chasma.

Even though the proportions of the craters to the moons are similar in both cases, it’s not Tethys but Mimas which has been called the Death Star Moon. This is because Herschel on the latter is relatively speaking a deeper dent than Odysseus. When I first came across Tethys, I’d just been impressed by Herschel’s size, so I was amazed that this second crater was bigger than the whole of Mimas and it is initially puzzling that it’s Mimas which gets all the kudos, but the reason is that Odysseus is smoother and flatter. However, Herschel is centred on the Mimantean equator whereas Odysseus is centred at around 35° north, so it’s actually off-centre in the same way as the Death Star’s depression is. It’s thought that when the crater originally formed, it was deeper but the relative softness of the surface and the higher gravity led to it being smoothed out as the millennia went by. The surface gravity on Mimas is 0.6% of Earth’s, whereas that of Tethys is more than twice that at 1.4%.

Although the gravity is greater, it was formerly thought that the crack across the middle of Tethys was a sign that the entire moon had been shattered by the impact and had fallen back together again. This is known as Ithaca Chasma, and at this point readers of the Iliad and Odyssey will have detected a theme to the names of the features: others include Polyphemus, Ajax, Circe and Penelope. Ithaca probably looks something like this:

Ithaca stretches three-quarters of the way around the world at 2 000 kilometres and is situated at a great circle centred on Odysseus and crossing both poles, interrupted by the crater Telemachus, so it might be thought that it’s connected to the giant crater, but remarkably it’s been found to be coincidental. The relative ages of features on many bodies with little to no atmosphere can be estimated by how cratered they are, and by this method Odysseus has been established to be younger than Ithaca. It was there already. I find this quite a remarkable coincidence, but a crater of that size seems to stand quite a good chance of being aligned with such a feature due to its large size. It’s 20° from the centre of the circle outlined by the chasm, and allowing for that on the surface means it would either be in the hemisphere on one side or the other of the moon from it, which doubles the probability, and allowing for 20° means the area which could be seen as the centre of the circle actually covers sixty degrees of 180, raising the probability to more than one in ten, and there are more than ten round moons orbiting Saturn so it becomes a lot less noteworthy that way. It’s an interesting demonstration of how misleading intuition regarding probability can be.

The chasm is about three kilometres deep and up to a hundred wide, though it varies a lot down to just a few kilometres. It seems to have been caused by the expansion of ice on freezing when the internal ocean froze early in the history of the moon, although it might have resulted from early tidal heating from Dione, which is in 3:2 orbital resonance with it.

The fourth-largest crater is called Penelope, and is just north of the equator about a third of the way across the globe from Odysseus, and has a diameter of two hundred kilometres. It was the second largest known crater before the whole of Tethys was mapped. It’s named after the wife of Odysseus. Away from these two craters, the terrain is quite heavily cratered with an alignment parallel to Ithaca.

It’s Enceladus which makes Tethys so bright. Ice from the geysers on the other moon hit the surface, covering it in very bright material, particularly on the leading side, which is around 12% brighter. The darker hemisphere is about the same colour as the darker of Saturn’s moons and may be high in iron. There are likely to be other constituents than water ice on or near the surface but these are hidden by the ice and so it’s difficult to tell what else is there. The regolith, i.e. the “soil”, actually ice, on Tethys, is unusual in that it’s 95% empty, kind of like polystyrene foam, a situation I imagine is helped by the low gravity and caused by the steady deposition of small particles of ice gently resting on each other over millions of years.

The moon is slightly redder and brighter near the centre of the leading hemisphere, bluer around Ithaca and somewhat darker red on the other side.

That’s about all I have to say about Tethys, which is incidentally about the same size as Ceres but otherwise quite different, being much icier. Next time, Dione.

The Death Star Moon

Mimas is special. In fact, I hope all worlds described in this series are special, but to me, Mimas is special. I’m no fan of ‘Star Wars’, so I note in passing that it looks a bit like the Death Star but may not go too much further in commenting on that. Or I might.

The Death Star is 160 kilometres in diameter, and apparently (I know little of the franchise) was replaced by another one 200 kilometres across. If that’s so, the scale on the above picture is approximately correct because Mimas has a diameter of 396 kilometres. That’s slightly smaller than mainland Scotland, although obviously its surface area is greater.

Do I need to say it’s a moon of Saturn?

Mimas is a kind of landmark in the Solar System, and in fact in terms of size generally. It’s the smallest body which has achieved approximately spherical shape by means of hydrostatic equilibrium. Most or all bodies smaller than Mimas are far from being round, and most or all bodies bigger than it are round. However, this isn’t inevitable, for two reasons. One is that objects smaller than Mimas can still just happen to be round, and considering the huge number of smaller objects there are, I wouldn’t be surprised if some of them just happened to turn out to be round by chance. It’s also possible that a larger body than Mimas could turn out to be irregular in shape due either to having lower density or being made of stronger materials. Vesta, for instance, is larger than Mimas but isn’t anywhere near as round. Taking this the other way, there can also be smaller but denser or weaker bodies which are round for that reason. An extreme example would be a neutron star, which would be only ten kilometres in diameter but would be so perfectly round it would act as a mirror. Another factor which might or might not come into consideration is surface tension. If an object made of liquid water were able to hold together in a vacuum, the chances are it could be a tiny fraction of the size of Mimas and still be spheroidal. Hence I can ask a question I don’t know the answer to: is the surface tension of molten lava sufficient to make a body spherical at a much smaller size than Mimas?

A few bits of maths can be done with this moon before actually considering anything else about it other than its rough shape and size. It has a surface area of 493 650 km², slightly smaller than Spain, although the climate is somewhat cooler and there’s no rain at all, on the plain or otherwise. Its volume is 32.6 million cubic kilometres, which makes it less than a five hundredth the volume of Cynthia or five times the volume of all the water on this planet. And it is in fact substantially made of water ice, at a cold enough temperature that it will have contracted from the volume it would’ve been at freezing point.

Before the Voyager probes, nobody had any idea that Mimas looked like the Death Star, and since they got there in 1980 CE and ‘Star Wars’ started in 1977, there couldn’t have been any conscious inspiration, but it does make me wonder if these things sometimes happen in other ways, but I imagine this is not the kind of thing which comes up much in astronomy. Pioneer 11, with its poor camera, had approached the 400 km satellite to within 104 263 kilometres, too distant to pick out any details, even the absolutely bloody massive one of the enormous crater Herschel which is the first thing anyone notices about it. However, Voyager 1 didn’t get much closer than Pioneer 11 at 88 400 kilometres, and I don’t know about now but at the time only about half the moon was seen.

Herschel is a third the diameter of Mimas itself, with walls five kilometres high and a central peak six kilometres in height and twenty by thirty kilometres across. To scale on Earth, it would be wider than Canada. It’s centred on the equator, which makes me wonder if that’s significant. None of the other craters on the surface are more than fifty kilometres across. There’s also a distinctive distribution of craters, where more than an entire hemisphere only has small craters less than twenty kilometres in diameter and the other hemisphere, which of course includes Herschel, has larger craters. There are also valleys.

The name can be pronounced either “My mass”, which is what I say or “Me mass”, which is closer to the classical pronunciation. The way I pronounce the names of astronomical bodies reflects a time before I knew much about the way Greek and Latin were spoken and therefore I often say them as if they were English words. The adjective, a little surprisingly, is “Mimantean”, like “Atlas” and “Atlantean.” Mimas the mythological figure was the son of Gaia and born from the blood of Uranus’s castration. I’m not quite sure how they could be both.

Herschel is of course mainly flat, meaning that the horizon from anywhere on its surface is further away than the horizon at eye level on Earth. From the central peak it would be even further. This probably means that of any spheroidal body in the system, the central peak of Mimas is the record-breaking location for seeing the maximum portion of any world at something like a twentieth of the moon’s surface. From the rim, it’s possible to see all the way across the crater, a distance of up to thirty kilometres, but also, because the rim is raised five kilometres above the “geoid”, it’s possible to see the rim from more than twenty kilometres away. To some extent it’s mysterious that the moon managed to hold together at all from the impact which formed the crater. Although there are much larger impact basins elsewhere, only the one on Mimas has a practically flat surface because of the small size and low gravity of the moon.

The way Mimas moves suggests that it contains a liquid ocean, but some scientists consider this unlikely because the moon is so small one would normally expect it to be frozen solid, so it isn’t known for sure if this is so. It’s more likely that the reason is either that the core is not spherical, not at the centre, or that HersUnlike many other places, Mimas has no ray craters. These are craters whose rims have lines radiating out from them such as Tycho, as can be seen clearly on Cynthia. This is thought to be due to the extreme brightness of the surface, which reflects 96% of the light falling upon it, thought to be due to it being covered in the kind of frost found on Earth. However, there are chasms around ten kilometres wide, around one to two kilometres deep and up to ninety kilometres long. I would imagine these are cracks caused by the impact, and on another Saturnian moon, which I will cover in future, it’s thought that an impact broke the entire moon apart and it fell back together again. I would expect the same to have happened to Mimas, although its lower gravity might have stopped this from happening.

Mimas is at least sixty percent water ice. What isn’t is probably due to impact by non-icy meteorites becoming embedded and gradually sinking into the interior.

It has exactly half the orbital period of the more distant moon Tethys and orbits twice for every three orbits of the moon Pandora, which is a shepherd moon. It’s also responsible for the Cassini Division.

The only other thing I can think of is that the map of the moon’s surface temperature looks like Pacman.

Because I just spent two posts not talking about the Solar System, for reasons I hope make sense, tomorrow’s post will be about one of the most interesting moons of all: Enceladus.

The Saturnian System

(this is effectively a poster, if you want to download it, but it uses a lot of black ink).

Saturn and its moons are the second example of a mini-solar system within the big one. For thousands of years, Saturn was thought to be the outer limit of the Solar System, and has its own associations because of that, but for today I want to concentrate on the whole system of Saturn, with moons, rings and magnetosphere all included, rather than the planet itself.

Saturn has a prodigious number of moons, the count sometimes exceeding Jupiter’s. This is because of the Titius-Bode series. As you go further out, the orbits of the planets get more widely separated, meaning that a planet of the same mass has a longer gravitational reach over its surroundings. Saturn is of course considerably less massive than Jupiter, but its Hill Sphere, the region where its gravity is dominant, is bigger than Jupiter’s, at 1025 radii compared to Jupiter’s 687. Working this out in kilometres, Jupiter’s has a diameter of 96 million kilometres and Saturn’s is 119 million. Against this is the fact that the system is less cluttered out by Saturn than it is near Jupiter, with the asteroid belt being near the larger planet. Saturn has eighty-three moons not including the ones which form part of the rings, compared to Jupiter’s eighty. There was a point when Saturn’s moon count far exceeded Jupiter’s, but this seems to be over. The Hill Spheres are nowhere near each other and there is no competition between the two in this way. Unlike the magnetospheres.

When Voyager 2 was on its way to Saturn, it encountered Jupiter’s magnetotail in February 1981, which may indicate that the tail is forked. It did so again in May that year by which time it was nine-tenths of the way there, or around eighty million kilometres from Saturn. Saturn can even be within Jupiter’s magnetotail at times. As far as Saturn’s magnetosphere is concerned, all its moons out to Titan orbit entirely within it. Titan itself is very close to the edge and passes in and out of it, spending about a fifth of its time within. It’s surrounded by a doughnut of hydrogen extending inwards to Rhea, which is the second-largest moon. The bow shock is somewhat further out and extends north and south of the planet for at least thirty radii. Sunward it extends for almost two million kilometres. This means that of the large moons, only Iapetus and Phoebe orbit outside it entirely. As well as the neutral hydrogen torus around the orbit of Titan, there’s an inner torus of rarefied plasma of ionised hydrogen and oxygen, which effectively means protons and oxygen ions, whose outer diameter is about 400 000 kilometres. At the edge of this torus the temperature is over 400 million degrees C, but it should be born in mind that Earth’s thermosphere is 2 500°C and the Sun’s atmosphere is over a million Kelvin, which is hot but didn’t destroy the probe recently sent there. Temperature really represents the average kinetic energy of the particles and not heat. In a sauna, the air temperature can be over 100°C but the effect on the human body is nowhere near as harsh as boiling water for this reason.

Titan comprises 96% of the mass of all Saturn’s moons put together. This seems actually to be more typical than Jupiter with its four large moons, as similar mass distributions are found among the moons of Uranus and Neptune. The whole system has a kind of quietness and serenity to it, at least from afar. Some of the moons are active, but there’s nothing like the hot volcanism found on Io. All the moons are substantially icy. Saturn’s moons are unique in that some of them have trojans – moons which share their orbits but are sixty degrees behind or ahead of the larger moons. Saturn in general has quite a cluttered and ice-strewn neighbourhood in connection with its rings, and this seems to be part of this aspect of it. This means that the exact number of moons can never be determined because the size of bodies orbiting it goes all the way down, fairly evenly, to miscroscopic grains of ice and dust. In a way, all that can be said is that Titan is the biggest by far, being about the same size as Ganymede.

The five large inner moons, Mimas, Enceladus, Tethys, Dione and Rhea, all participate in the magnetosphere, absorbing protons, as do the particles making up the very sparse E ring. I’ll talk about the rings in detail when I get to Saturn itself, but another unique feature of Saturn’s system is the interaction between the particularly substantial rings and the magnetosphere. The other giant planets have much less substantial rings and therefore less significant interactions. Electrons are absorbed by the main rings, and below the main rings towards Saturn is the least radioactive region of the entire Solar System outside of large bodies and their atmospheres because the rings act as a radiation shield. There is, however, nothing as strong as the plasma tunnels and torus around Io, which influences radio transmissions from Jupiter.

Radio signals from Saturn are weaker than the ones from Jupiter in a broad range from twenty kilohertz to one megahertz, so listening to long or medium wave radio stations there would be right out. Like Jupiter’s System III, which is the common rotation of the interior of the planet with its magnetosphere, Saturn has its own System III, lasting ten hours, 34 minutes and two dozen seconds. There is nothing as strong as Io’s influence, but there is a relatively mild variation corresponding to the time taken for Dione to orbit, 2.7 days. This could be coincidence. When Saturn passes close to Jupiter’s magnetotail, the radio transmissions become undetectable but it isn’t clear whether they cease because of it or are just overwhelmed by Jovian radio noise.

The moons have fairly regularly spaced orbits out to Rhea, although there are some smaller moons which either share orbits with larger moons or regularly swap over. Titan, though, is over twice as far from Saturn as Rhea, then Hyperion is relatively close to Titan, Iapetus over twice as far from Saturn as Hyperion, and finally Phœbe is much further out and orbits backwards compared to the others and the majority of other worlds in the Solar System. This suggests that Phœbe is a captured asteroid. Surprisingly, although it was discovered in 1898, no moons further out were found until the twenty-first century despite the fact that the planet was visited several times by spacecraft. However, almost four dozen moons have now been found which orbit backwards. More than two dozen moons have yet to receive names because there are just so many of them. Even the most distant moon is well within Saturn’s Hill sphere, so it’s still possible that there are more. There’s also a cluster of moons, including shepherd moons and coörbitals, near the rings and possibly even within them, but it should be borne in mind that there’s a judgement call here regarding how big a ring particle is before it counts as a moon or moonlet.

Saturn, and therefore its system to some extent, is tilted 27° with respect to its orbit. This also tilts some of the moons but others are already at odd angles and it’s fairly meaningless to regard them as influenced by this tilt. For Dermott’s Law, mentioned in connection with the Galileans a couple of days ago, T=0.462 days and C=1.59.

I’m going to end on a personal note. I don’t remember Kepler’s third law of planetary motion very clearly, so I always use Saturn to work it out. Saturn is about ten AU from the Sun, i.e. ten times Earth’s distance. The cube of this is a thousand, and that’s square root is thirty. Saturn takes thirty years to orbit the Sun once, hence the Saturn Return of astrology, meaning that the cube of the semimajor axis (average distance from the Sun) of a planet is directly proportional to the square of its sidereal period (“year”).

Next time I’ll be looking at Saturn itself, including its rings, the famous hexagon and the unexpected connection with a certain comedian.