Saturn, I have to admit, is a bit of an easy target for this sort of thing, given that it has something like 60 or so moons. With that many satellites, it’s pretty much inevitable that you’ll find some interesting oddballs. Dione is another such moon of Saturn.
Credit: Cassini/NASA, via Wikipedia
Dione was first observed in 1684 by Giovanni Cassini, who also discovered three others of Saturn’s satellites. Dione wasn’t actually formally named until 1847; Cassini called his discoveries the ‘Sidera Lodoicea’ (‘Stars of Louis’) after his patron, the French king Louis XIV. (This sort of fawning was entirely normal at that point in history … luckily, it’s one practise we seem to have left behind!)
At 1,122 Km in diameter, Dione is reasonably large; it ranks as the 15th biggest moon in the Solar System. It’s also more massive than all of the smaller ones combined – although in fairness, that’s less impressive than it sounds, given that many of the smaller ones are barely more than pebbles. Dione’s average density appears to be somewhat more than that of ice, suggesting that it probably does have some kind of rocky core deep inside it. Some estimates say it might contain about 46% rocky material to 54% ice. It’s also very, very shiny indeed, with a surface that reflects about 98% of all incoming light. (Again, this is consistent with a primarily icy outer surface.)
The moon’s surface is a mixture of heavily- and lightly-cratered plains, along with tectonic features such as scarps and fractures. However, it’s biggest claim to oddness is probably not its surface, but the other moons it exists in an orbital relationship with.
You see, Dione doesn’t orbit Saturn alone. Rather, it shares its orbit with two other objects, called Helene and Polydeuces. These two bodies are located respectively at the L4 and L5 points of Dione. The L- or ‘Lagrangian’ points are a series of five locations, associated with any two-body orbit, where a much less massive third body could, essentially, ‘sit still’ relative to the other two. In any system, there will be five L-points, numbered from 1-5. Numbers 1-3 are literally just points, and as such are of limited use – any body that is even minutely off-centre will quickly ‘slide away’ from these points. L4 and L5, however, function as small ‘regions’. As such, it’s possible for things to ‘pool’ inside them.
This is exactly what’s happened with Polydeuces and Helene. The two moons drift along, 60 degrees behind and 60 degrees ahead of Dione, respectively, forever shadowing it as it orbits Saturn. Of the two, Polydeuces is the smallest, being about 2 miles across. Helene is somewhat more respectable, at roughly 40 Km in average diameter.
The Dione-Saturn system is not the only place where this remarkable arrangement is seen. Tethys, another Saturnian moon, acts as the ‘parent’ to a pair of rocks called Telesto and Calypso. The planet Jupiter has accumulated for itself two enormous pools of asteroids on its L4 and L5 points; these are known as the Trojans. Mars too has accumulated a handful of Trojan rocks as well.
In addition, a recent discovery has been 2010 TK7, which turns out to be in a Trojan relationship with our own planet (it’s sat on the Earth’s L4 point). Sadly for us, 2010 TK7 is even less impressive than Polydeuces, being a mere 300 metres in diameter. (If it hit us – which it can’t – it would struggle to take out even a tiny banana republic. Which is utterly pathetic!) This minute diameter is mainly why TK7 was only spotted very recently.
One interesting possibility for the future is that of Trojan exoplanets. It is possible that a relatively-close Jupiter-analogue might have smaller, terrestrial-mass planets associated with it in a Lagrangian relationship. It’s also possible that a particularly-big Jovian-type might also have Uranus/Neptune-mass gas giants Trojaning with it. In this case, the Dione system could end up being a scaled-down prototype for a category of much bigger systems.
Time will tell…
 In addition, in 1672, Cassini and a colleague called Jean Richer were also the first people to measure the distance from Earth to Mars, via a rather cunning bit of trigonometry.
 The reason for the existence of Lagrangian points involves maths … as best I understand it, the L-points come from the play-off between gravitational and centripetal accelerations. I shan’t dig deeper into that here, though. There’s a discussion on Wikipedia, however.
 One awkward issue of L-points is that bodies occupying them have to be ‘small’ relative to the masses of the other two, otherwise the third body has enough gravity to complicate things.