The Safest Satellite

Calista Flockhart sticks in my mind. She used to play Ally McBeal, and most remarkably she’s the absolute double of a friend of mine who lived in Yorkshire when it was on. I used to commute to Leeds at the time and stay over at her house. But there are three other reasons Ms Flockhart has come to my attention intermittently. She was the “single female lawyer” of Futurama fame, impersonated by Turanga Leela with a stick-on googly eye. She was rather thin, and that used to worry me although I suppose I mustn’t “skinny-shame”. And finally, her name was similar to that of Jupiter’s outermost large moon, Callisto, illustrated above.

I’m sure the actor wasn’t named after the moon, but ultimately the Greek nymph. Once again, Kallisto, or more correctly Καλλιστώ, was one of Zeus’s “conquests”. I can’t help but think that some kind of “me too” moment should’ve come to pass in Olympus at some point, and I’m not really joking. Being a religious figure, Zeus was I imagine seen as a rôle model by many a Greek male, and seems to have spent most of his time raping and sexually harrassing people. Then again, maybe this was around anyway and merely served as an expression of that behaviour. However, just as Ganymede was Zeus’s homosexual lover, so was Kallisto, even though she was female. Zeus transformed himself into the likeness of Artemis to seduce her, meaning that they were lesbian lovers. So we have the two hetero moons and the two gay moons, which in a way is neat. Kallisto’s other claim to fame is that while pregnant she was thrown into the sky to escape the anger of the real Artemis, which stretched her tail and changed her into Ursa Major. ‘Αρκας, their son, became Ursa Minor.

Kallisto means “most beautiful”. When I learnt this, I suddenly realised that the Greek ending for the superlative, -ιστος, was cognate with its English and Germanic equivalent “-est”, although I don’t think you can do much with καλλος in that way. Anyway, I thought it was neat.

Callisto the moon is beautiful if you like that sort of thing. It’s somewhat similar to Ganymede but has an older surface, is a little smaller and is somewhat apart from the other Galileans, taking more than sixteen days to orbit, and therefore having a day more than two weeks long. Due to its separation, it doesn’t undergo the tidal stresses and strains of the others and therefore hasn’t had its surface remodelled at all since it formed. It’s both the most heavily cratered known body in the system and, at least when the Voyager probes visited, the least dense. It continues the trend of reducing density found among the Galileans. It’s also unique among them in orbiting outside the radiation belts, although it’s still within a fairly strong magnetic field. This is what makes it the “safest satellite”. Unlike the others, if humans ever went there landing on Callisto would be basically the same job as the Apollo astronauts did, and if anything there’d be less radiation because it’s five times as far from the Sun, although perhaps Jovian cosmic rays would still be a hazard.

It’s slightly smaller than Mercury, by about twenty kilometres, but still larger than Cynthia and Pluto. By mass, it’s the twelfth largest world in the system, being somewhat more massive than Cynthia and Io. It has the lowest gravity of the Galileans at around an eighth of Earth’s. There are so many craters that it’s hard for any more to fit on. Any new craters would probably overlap with old ones. This has happened because the surface froze before the Late Heavy Bombardment, so it retains a record of how violent the early Solar System was. Extremely, it seems. This also suggests strongly that Jupiter was almost like a second Sun at the time, although by Callisto’s distance, 1 882 700 kilometres away, it was well-frozen. However, an important influence on the inner moons is the tidal tugs on each other, which don’t affect Callisto, so that heating effect is absent. Nonetheless, Io’s density and complete absence of water does seem to indicate it was pretty hot that close.

The place nowadays all seems to be all about peace and serenity, which considering the onslaught it clearly received thousands of millions of years ago and the scars it still bears is pretty ironic. All the other moons have got something going on, Io most of all but the others show signs of activity fairly recently. Callisto doesn’t. It lacks anything like the regiones and sulci of Ganymede or the smooth surface of Europa, which implies that the latter underwent some melting after most of its meteorites hit. Of the four therefore, Callisto has the oldest surface. Nothing ever happens there, at least on the surface.

However, that doesn’t mean it’s boring! There are two gigantic impact basins, Valhalla and Asgard, the former of which is three hundred and sixty kilometres across at the centre and is surrounded, like Asgard, with rings, in this case up to eighteen hundred kilometres from the centre. It is in fact the largest impact basin in the system, comparable in appearance to Mare Orientale on Cynthia and Caloris Basin on Mercury. If the centre of Valhalla was in Glasgow, the outermost ring would cross Lithuania, southern Spain and Kalaalit Nunaat (Greenland), and this is on a moon with less than a seventh our planet’s diameter. On the moon itself it stretches across almost a quarter of the way round its world. The central crater is a palimpsest, a type of crater also common on Ganymede which has been partly eroded over time in one way or another. I personally imagine the cause in this case is that the impactor melted the surface, considering it’s mainly made of ice, but I don’t know what the experts think. The ringed area around it has outward facing slopes with steep escarpments, and although those sound like waves emanating from the impact they’re probably grabens – downward fractured areas like the equatorial rings on Vesta. Further out still, at the edge of the area, the rings are more vaguely defined and consist of troughs.

The other impact basin, Asgard, is a “mere” sixteen hundred kilometres in diameter, making it the size of Greenland/Kalaalit Nunaat. The centres of the two basins are about nine thousand kilometres apart. At its centre is the crater Doh, which has a large raised area at the centre. A third ringed structure is superimposed on it, called Utgard, which is slightly smaller than Adlinda, the third largest. There are also faculæ, which are frosty-looking spots dotted about, of which only one, Kol, seems to be named. The features on Callisto are named after mythological beings and items in Nordic and Inuit folklore.

The presence of the ringed basins on Callisto would be expected to lead to distinctive features on their antipodes, because the shape of the moon would focus the shockwaves on the other side as they travelled across the surface, but I haven’t heard that this is so, even though there are good-quality images of that side.

Considering the number of craters on Callisto, it’s unsurprising that there are also catenæ. These are chains of craters caused by objects breaking up before they reach the surface, which happens due to their size and also when they’re rubble piles, which many small objects are. There are at least eight of these. They occur elsewhere in the system, but are bound to be more common on this moon due to the extreme nature of the cratering. I first learnt the word “catena”, meaning chain, from this context, and eventually noticed the Castilian word «cadena». It may be worth answering the question at this point of why craters tend to be circular. After all, don’t they strike the surface of a body at various angles? If a hard projectile is thrown at a soft surface, it would only produce a round dent if it was perpendicular. The reason craters are circular is that it isn’t the mechanical impact of the object that causes the dent, but the heat and explosion of the energy release, so craters of this kind are more like bomb craters than the kind induced by a pebble hitting some mud. The catena above, Gomul, is actually within the rings of Valhalla.

Ganymede may have a complex interior consisting of alternating shells of ice of various kinds separated by water, and the similarity between the two moons might lead one to expect Callisto to have the same, but this doesn’t appear to be so. Instead, it probably looks like this:

As mentioned in the post about Ganymede, hexagonal ice is the kind we’re likely to encounter on Earth’s surface. The ocean is hundred and fifty to two hundred kilometres deep and since the moon is not geologically active, it has no thermal vents supplying it with energy. In any case, the ice is so thick there’s no chance of penetration. The rock portion at the centre is also even proportionately much smaller than Ganymede’s and there seems to be no magnetic field either. The interior also differs from Ganymede’s in containing a layer of ice VII. Surprisingly, ice VII is actually present on Earth inside diamonds. It can only form with a combination of high pressure and low temperature, so it proved to be a surprise that it was present on Earth, but on Callisto it’s to be expected. It’s fifty percent denser than our own ice and has a cubic crystal habit. This doesn’t mean it has cube-shaped crystals, but that the axes of symmetry are equal and at right angles to each other. Diamonds also have cubic symmetry, so in a way ice VII is like diamond, and it’s also extremely hard, being about as tough as quartz. Its melting point is always at least 82°C and can be above 400, so in many ways this is not like the ice we’re familiar with at all. The moon also gets steadily rockier towards the centre. The lack of activity means there is no magnetic field, which would be generated by currents in metallic liquid. This also means that unlike Ganymede there is no aurora, but there probably wouldn’t be anyway because it’s too far from the radiation belt.

There is an atmosphere, although it’s unsurprisingly extremely thin. It consists of carbon dioxide, and it’s a little surprising even that’s there because left alone it would leave the moon within a hundred hours due to its low escape velocity. It’s thought that there is dry ice slowly subliming from the surface, which also contributes to the smoothing out of the features seen, for instance, in the lower and gentler crater peaks. Ther’s also atomic hydrogen, which stretches higher up from the leading hemisphere.

The question arises here of whether Callisto is actually just a moon, unlike the other Galileans. The recent rival definition of planet requires it to be geologically active, and this is certainly true of Io in particular but also Europa and Ganymede. Callisto, however, is only active in that carbon dioxide seems to be gradually evaporating from its surface and it lacks any apparent internal or surface activity. Nothing much seems to have happened on its ancient surface for over four æons apart from the occasional meteor or comet strike: most of the craters are very old. Therefore, although I doubt anyone has ever considered the question, the body isn’t really a planet, but just a moon. In fact it may even be the largest moon that isn’t also a planet.

Out of all the bodies in the system, strangely Callisto may be one of the most hospitable to humans for exploration and settlement. The level of radiation on the surface is not only relatively low compared to the other Galileans, but actually lower than most of the inner planets and bodies in the asteroid belt except for Earth. This is because it’s over five times further out. It’s also more accessible than more distant moons, and is also fairly large. It’s larger than Cynthia and almost the same size as Mercury. Consequently, it has been considered as a potential target for astronaut visitation. As just mentioned, it’s extremely geologically stable, and there’s an ample source of water on the moon. It could also serve as a base for activities on the other Galileans and Jupiter, which is a good source of fuel for interstellar travel. In fact the moon itself provides this in the form of water ice, which could also be used as a source of oxygen for breathing. The interior, having water in liquid form, is also likely to be warm enough for habitation at some level. NASA carried out an investigation into the possibility in 2003 called HOPE – the Human Outer Planets Exploration – and suggested that it would be possible to reach Callisto by 2040. Of course this won’t happen but it’s nice to dream. I remember noticing that Nigel Calder included Callisto as a major power base in a simulation of Solar System power politics in his 1978 TV series ‘Spaceships Of The Mind’, although I’m surprised enough was known about it that far back to suggest such a situation.

Callisto doesn’t seem to crop up much in science fiction, possibly because not much happens there, but an exception is Asimov’s ‘The Callistan Menace’. This is a story about the mystery of astronauts attempting to visit the moon but never returning. I’m not going to spoil it, but its depiction of the place is quite inaccurate as it’s given a substantial atmosphere even though the author knew it couldn’t have one even back then. It’s also a bit unusual in referring to it as Callisto at a time when usual practice was to number the moons – Callisto is “Jupiter IV”.

Right, that’s it for Callisto. I’m not sure what to do next because Jupiter has something like eighty more moons but the Jovian system has already been covered. I might talk about the Galileans as a group, or I might move on to Saturn.

The Jovian System

I started this series of posts with a survey of our Solar System itself and I’m going to do the same with Jupiter and its moons. When Steve suggested this project, he also suggested working outward from the Sun. The problems with doing this become very evident once one gets to Jupiter, although they were already there with the asteroid belt.

Just with the asteroid belt, I mentioned that although the average distances from the Sun can be organised into bands according to their ratio to Jupiter’s “year” (the official name is “sidereal period”), this isn’t evident at any one moment because many of their orbits are markèdly elliptical and an asteroid in, say, the Hilda group near the outer edge of the belt may well approach the Sun at its closest at the average distance of a Flora asteroid near the inner. Vesta and Ceres seem to approach each other to within four million kilometres, and this will sometimes happen, but lines drawn between each closest approach (perihelion) and the Sun are different lines and the tilt of their orbits also differs, so it isn’t like the system is a flat surface with all the orbits in a plane with their ellipses lined up precisely, or even approximately.

When it comes to Jupiter, a separate problem begins to become evident. All four of the gas giants have extensive satellite systems, and these moons orbit at various distances from the planets, and therefore from the Sun. A moon which is closest to the Sun at one time will be the furthest from it at another, and some of them even regularly swap orbits. It’s actually worth considering this in detail because of what it illustrates about the nature of the systems in general. It’s not much of an exaggeration to say that each of the four planets and their moons is like a mini-solar system in its own right. Perhaps unexpectedly, the system with the most moons is Saturn’s, not Jupiter’s, even though Jupiter is larger, more massive and closer to the asteroid belt. However, for today I’ll mainly be considering the Jovian system rather than the others.

Just before I get going on that, there are “rogue planets”, which in a sense are technically not planets at all, wandering through interstellar space independently of specific stars. These may well have their own satellite systems, and are in a sense “failed stars” because they’re too small to shine, but may even so be several times Jupiter’s mass. Jupiter is therefore in a sense almost our second local “solar” system. Incidentally, there seems to be a gap between the largest planets and the smallest stars, in that the former are much less massive than the other, and there’s also a gap in the sizes of the two types of body because planets tend not to get much bigger than Jupiter in diameter. Above that point, the gravity increases and compresses the substance of the planet more, although there are also examples of planets so close to their suns and therefore hot that they become “puffy planets” which are far larger but also much less dense than Jupiter.

I’ll start with Sinope. Sinope is the most distant moon of Jupiter, and has a surprisingly long astronomical history. It was discovered in 1914 and although it’s quite small, no moon has since been discovered which orbits further out, in spite of today’s space telescopes, the several space missions sent to and through the Jovian system and the discovery of other moons which have turned out to be much smaller, so it was quite an achievement to do that over a century ago. Sinope orbits an average of 24 371 650 kilometres from Jupiter, which is a figure more precisely known today than before. Its eccentricity is, however, considerable, at 0.3366550, meaning that its maximum distance from Jupiter is around 32 576 000 kilometres, which is only a sixth greater than the gap between the orbits of Venus and Mercury at its own aphelion (greatest distance from the Sun). The diameter of that orbit is therefore almost 49 million kilometres, which is comparable to the distances between the orbits of all the inner planets.

Sinope is important because it can be thought of as marking some kind of outer limit to the Jovian system. If we could see that orbit in the night sky it would look larger than the Sun to us. Since it’s further away from us, this means the Jovian system is also literally much larger than the Sun. Sinope takes over two years to orbit Jupiter. There is a large asteroid in the belt named Hilda, whose diameter is 170 kilometres and has an aphelion of 678 million kilometres. Sinope, assuming it to be orbiting in the same plane, takes on average 24 371 650 kilometres off Jupiter’s distance from the Sun, meaning it will be somewhere around 38 million kilometres from Hilda, perhaps less (or perhaps more). Hence Jupiter’s outer moons are actually not that far from the outer asteroid belt. On the other side, Sinope adds the same distance to Jupiter’s orbit and Saturn’s outermost known moon can be taken into consideration, taking it out to 841 million kilometres from the Sun, and Saturn’s apparent counterpart, the as-yet unnamed S2004 S26, approaches the Sun to within 1326 million kilometres, leaving a gap of just under 485 million kilometres. The gap between the two systems is quite small.

Incidentally, another moon, Pasiphaë, is slightly further in but also more eccentric than Sinope, so it can sometimes get even further out.

The magnetosphere also needs to be taken into consideration. Jupiter has a strong magnetic field which starts to interact with the Sun far in front of the position of the planet itself, and also trails behind it in a tail longer than the sunward side. This amounts to eighty radii of the planet to the bow shock, which is the surface where the speed of the solar wind suddenly drops in response to Jupiter’s magnetic field, and is named after the wave in front of the bow of a ship. The bow shock also extends “above” and “below” Jupiter’s orbit by about the same distance, making it the biggest “bump” in the system. The shock is located about six million miles inward of the planet, which is within the satellite system. However, the magnetotail is another matter. The bow shock is actually compressed by the solar wind, so the magnetotail is much, much larger. The entire magnetosphere is somewhat similar to a teardrop shape viewed in cross section perpendicular to the orbit, and the magnetotail is a gradually tapering part away from the Sun. Magnetotails generally are much larger than the magnetic objects associated with them and in Jupiter’s is around 489 million kilometres long, which is almost as far as Saturn and also means that the outermost moons of that planet actually pass through Jupiter’s magnetotail at times, and that the magnetospheres probably touch sometimes. Strictly speaking, magnetic fields have infinite range but after a while it gets silly.

Like Earth’s Van Allen belts of Apollo mission fame, further in towards the planet Jupiter traps charged particles, which are unfortunately where three of the four largest moons orbit. There is also a plasma tunnel, but this will be made clearer on a later date.

Jupiter has eighty moons. Sixty are less than ten kilometres across. I tend to think of both Jupiter and Saturn as like archipelagos of islands with a few large islands and multitudes of smaller ones. In Jupiter’s case, the moons are grouped into orbital zones with large gaps between them. I’ve already talked about Amalthea, one of the inner moons, and I’m not planning to plod through a massive long list of mostly tiny, boring and very similar moons, but they’re collectively of interest and the way they’re grouped is also significant.

The Galileans are the “big four”. Each of them is practically a planet in its own right, and they were also the first moons to be discovered orbiting another planet, by Galileo in 1609. Another astronomer, Marius, found them just one day later and he’s responsible for the names. These are also the first celestial bodies to be given names in written history. However, the Chinese astronomer 甘德 discovered either Ganymede or Callisto in 364 BCE, because they are bright enough to be visible to the naked eye of someone with good vision. All of them are brighter than Vega from here. The Galileans form an important rung on the ladder of establishing the scale of the system and Kepler’s laws of planetary motion. When they’re relatively nearby, that is, when Earth and Jupiter are on the same side of the Sun, it’s fairly easy to look through a telescope and time their movements, as in, the points when they’re furthest from Jupiter, when they pass behind and in front of the planet and emerge on the other sides, a total of two dozen events. Their relative distances can be measured using this observation because of their maximum visual distance from Jupiter, and this enables it to be observed that, like the planets with the Sun, the cube of their average distance is directly proportional to the square of the time taken to orbit, Kepler’s third law of planetary motion. Then, when Jupiter is on the other side of the Sun from us, there’s a delay in these observations of up to almost exactly a thousand seconds, which enables the width of our orbit to be calculated if one knows the speed of light. This in turn enables the scale of the orbits all observable planets in the Solar System to be calculated, and the difference between the periods of Jupiter’s Galilean moons and a hypothetical planet orbiting an object the mass of the Sun enables the mass of Jupiter compared to the Sun to be worked out as well. Working out the speed of light itself is a somewhat different problem. I’ve tried to do this but was stymied by fog. You need a clear day, a hill, a cogwheel, a mirror and a distant telescope.

The moons are organised into six groups. There are the inner moons, which include Amalthea, the Galileans Io, Europa, Ganymede and Callisto, and the Himalia, Ananke, Carme and Pasiphaë groups. These occur in bunches of orbits, but before I get to that I want to point out something else which is rarely mentioned: they changed the names of many of the moons in 1975. When I was a small child, before Pioneer 10 and 11 had been sent there, the names of the moons were completely different. This would’ve been in about 1972. By the early 1980s, the names of the outer moons had completely changed. The previous names were as follows:

  • VI – Hestia
  • X – Demeter
  • VII – Hera
  • XII – Adrastea
  • XI – Pan
  • VIII – Poseidon
  • IX – Hades

The corresponding names now, in order, are: Himalia, Lysithea, Elara, Ananke, Carme, Pasiphaë and Sinope. Many more moons have been discovered since then. It’s all the more confusing because one of the inner moons is now named Adrastea. The scheme I was familiar with was apparently the 1955 proposal, which was used after a phase during which they were simply referred to by their Roman numerals, listed in order of discovery. There were also proposals in 1962 and 1973, and once again Adrastea is used, this time to refer to Himalia. The current names are the 1975 IAU version, and there is also Carl Sagan’s 1976 version. Nowadays, the moon names ending in E are retrograde – they orbit in the opposite direction from the majority of bodies in the Solar System – and prograde moons have names ending in A. There was also a tendency to choose names from the lovers of Zeus or Jupiter in Greek or Roman mythology, of which there are a very large number, so the supply was clearly considered almost inexhaustible. The view was also taken that irregular moons shouldn’t be named at all but just left with Roman numerals. Now that eighty moons are known, I suspect they’ve finally run out of lovers. The question arises in my mind of why there are no homosexual lovers since homophobia didn’t exist in the Greco-Roman world before the arrival of Christianity, but I think this is because one of the reasons Jupiter and Zeus had so many is so they could serve as the origin story for various beings seen as a mixture of the qualities of the two parents. There’s also an inconsistent tendency for the moons to be given names across the systems which start with the same letter, such as Hestia and Himalia, and Poseidon, Persephone and Pasiphaë. Up until the 1970s, there seemed little point in naming them since at that time they were simply rocks spinning round Jupiter without much being known about them, although Isaac Asimov does refer to them in his ‘Lucky Starr And The Moons Of Jupiter’, though by the numerals rather than the name.

The inner satellites are all small, but Amalthea is the biggest satellite after the Galileans. Himalia is only slightly smaller although it isn’t an inner satellite. I’ve never really got used to using the newer names by the way. There are four small inner moons. Metis is actually technically too close to hold together, which is appropriate since it’s named after a titaness who turned herself into a fly and was eaten by Zeus. Incidentally, if I’d written the sequel to ‘Replicas’ it would’ve included a planet called Metis as an important plot point, but sadly it was not to be. The real Metis is on the brink of being devoured by Jupiter and is also only ten kilometres across. The three other moons were discovered via the Voyager probes in 1979 and not named for quite some time after. The spacing of their orbits is similar in scale to that of the Galileans. Amalthea may have associated moonlets but they’re not confirmed, the “flashes” only having been detected once.

After the Galileans there’s a big gap, and to some extent Jupiter’s system reflects the shape of the Solar System here in that there are four smaller inner moons like the four smaller inner planets followed by four much larger moons like the gas giants, but unlike the Solar System Ganymede, the largest moon of all, and in fact the largest moon in the entire Solar System, is the third large body rather than the first, and there doesn’t seem to be anything corresponding to the asteroid belt. The pattern of distribution of moon sizes may be a guide to how other star systems form and the Galilean orbits are in harmony with each other. Callisto is somewhat separated from the others, making it easier to spot and reflecting something like the Bode-Titius Series with the spacing of the planets. However, after Callisto comes a big gap. There is one small moon, Themisto, discovered in 1975, orbiting about halfway across that gap, but wasn’t observed for long enough for its orbit to be established. It was lost for a quarter of a century, and none of the probes investigated it. It’s fairly common for small Solar System bodies to be lost and later found again.

The next bunch, of seven moons, includes the incredible Leda, which is absolutely tiny for a moon discovered and confirmed from Earth observations in the 1970s. It’s turned out to be somewhat bigger than originally thought, and was discovered by the extremely prolific “discoverer” Charles Kowal who also observed Themisto, in 1974. Kowal also discovered the centaur Chiron. This set of moons is tilted at 30° to the inner group and has more elliptical orbits, all of which line up with each other. These are between eleven and thirteen million kilometres from Jupiter.

There is then another gap, within which orbit Carpo and Valetudo, closer to the third group rather than orbiting in isolation like Themisto. Unlike the outer group, however, they orbit in the same direction as the inner moons. Valetudo is only one kilometre in diameter, like several other moons, making it joint smallest, although there will presumably be some differences in size. It’s also currently the smallest named moon. I don’t know if they’re going to bother naming the others of this size, but the asteroid Adonis was named and is only five hundred metres across, although it’s also a potentially hazardous asteroid so that may be why it got one.

The outermost group orbits backwards compared to the others and in fact compared to most other bodies in the Solar System, which generally orbit clockwise viewed from the South. Hence they all have names ending in E: Carme, Ananke, Pasiphaë and Sinopë, which apparently is supposed to have a diæresis over the E. Incidentally there’s a village in this county called Sinope and also a town in Turkey, probably named after the nymph in the latter case, and no longer spelt that way. By the time you get to the outermost group, the orbits are considerably perturbed by the Sun. There’s a concept called the Hill Sphere, which is the sphere within which a body’s gravitational influence is stronger than any others, generally a planet and its star. Jupiter’s is fifty-five million kilometres in diameter, so the outermost group of moons are close to its edge. The ellipses of their orbits are also lined up, but currently at close to right angles to the middle group.

Although Jupiter’s Hill Sphere is not as large as Neptune’s, which is the furthest known large planet from the Sun and so has more elbow room despite its much smaller mass, Jupiter is more likely to sweep bodies up into its. This is because it only takes a dozen years to orbit the Sun compared to Neptune’s more than a gross, and is doing so much faster and in a more crowded region of the system.

The Solar System has jokingly been described as consisting of the Sun, Jupiter and assorted débris. Jupiter, although far less massive than the Sun, has around two and a half times the mass of all the other known bodies in the system put together.

There are many more things to say about Jupiter and its moons, but these will be about the planet and the bodies themselves, so for now I’m going to knock this on the head and publish it.