Where the L2?

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So the European Space Agency’s Herschel and Planck telescopes are currently on their way and science teams are running around preparing for the start of observations. You may have seen various reports referring to their final destination, L2. I thought it would be a good time to write a quick bit about where this is and why it’s important.

L2 is the second Lagrange point. Lagrange is not only a reasonable rhyme for orange but is also the name of the designer of a system of mechanics that formed the basis for the only uni course I failed (the story involves a headache and a monkey). When studying gravity, finding the orbit of one body around another is fairly easy. Add a third body and the problem becomes pretty difficult. Lagrange used his new way of formulating mechanics to find a number of solutions to this three body problem. Imagine the Earth orbiting round the Sun. If you take the gravity of both into account along with the orbit of the Earth you get five special points where an object can sit without being pulled out of place (see the picture). L1, 2 and 3 lie on a line that connects the Earth and the Sun and L4 and L5 lie in the Earth’s orbit 60 degrees in-front and behind the Earth respectively. All five points stay in the same place relative to the Earth and Sun and Lagrangian points exist in all two body systems, the Sun-Earth system, the Sun-Jupiter system, planet-moon systems and even in planetary systems around other stars. In the case of the L2 point (and L1 and L3), a spacecraft can orbit around here with occasional small corrections from propulsion systems. For a space telescope this a pretty good place to be, you can orbit around L2 without using too much fuel and annoying things that get in the way like the Sun or the Earth are always in the same direction so you just need to point your telescope away from both (several telescopes that look at the Sun sit at L1 so the Earth doesn’t get in their way).

However in the L4 and L5 points are even more interesting. Not only are these points where objects can sit but nearby things are drawn towards them. Hence stuff tends to collect in these points. Saturn’s fourth largest moon Dione has two smaller moons Helene and Polydeuces sitting in in it’s L4 and L5 points respectively. Tethys, another of Saturn’s moons, also has two smaller moons in its Langrange points. In the Sun-Jupiter system there are loads of objects collected around the L4 and L5 points. These are asteroids that just seem to have wandered in there and got stuck. Those that lie at the L4 point are named after Greek characters from the Trojan war and those that lie around the L5 point are named after Trojan characters. In total there are maybe a million of these Trojans (a slightly confusing name for both the Trojan and Greek ones) over 1km in size, although I don’t think there are a million names in the Illiad so I doubt they are all named after Trojan war characters. Interestingly I read this paper a while back which came up with a way of detecting Trojans in planetary systems around other stars.