Third world out from the gas giant, Tethys is an ice ball, cratered but slightly smoothed from old ice melts. Like Mimas, it has an enormous crater - Odysseus - that, while it's more smoothed out and eroded than Herschel, is as big - proportionally - as Herschel is. Since Tethys is twice the size of Mimas, that makes Odysseus twice the size of
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The math is complicated, but - if you have an object orbiting another much larger object, like a moon around a planet (also works for a planet around a star), the two Lagrange points on the orbit are stable: anything put in that point in the orbit will stay there, and the point acts like a gravitational attractor.
Jupiter has a quantity of asteroids caught in its L4 and L5 points in its orbit around the sun (those asteroids are called Trojan asteroids, named for the heroes of the Trojan wars, and that naming convention is how the points came to be called Trojan points for orbits in general).
The L5 Society is an organization dedicated to putting a space colony in the Moon-Earth L5 point. But the only moons in the Solar System with natural companions in the L4 or L5 points are Tethys and Dione, both of which are moons of Saturn.
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