Lagrange Points

by Jean Tate on March 22, 2010

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Lagrange Points
Think of the Earth and Sun, and imagine they are the only things in our solar system. Now add a satellite; where would the gravitation pull of the Earth and Sun balance the centripetal acceleration of the satellite, for it to keep its relative location? There are five of these points, and they are called Lagrange points, in honor of Josef Lagrange who discovered their existence.

The five Lagrange points have the stunningly memorable names L1, L2, L3, L4, and L5 (never hire a mathematician to write product advertisements!).

L1, L2, and L3 are along the line which goes through the Earth and Sun; L1 is between Earth and Sun, L3 on the opposite side of the Sun from the Earth, and L2 is on the opposite side of the Earth from L1. These three Lagrange points are unstable; if you put a satellite at any one of them, the slightest bump will make it move away, and it won’t come back.

L4 and L5 are on the Earth’s orbit, 60° behind (L4) and 60° ahead (L5), so the Sun-L4-Earth forms an equilateral triangle (as does Sun-Earth-L5). These two Lagrange points are stable.

Of course, the solar system is comprised of more than the Sun and Earth, so the Lagrange points are only approximately real. Further, as the ratio of the masses of the two objects becomes more equal, the L4 and L5 points become unstable (24.96 is the magic ratio, in case you were wondering).

Any two masses will do, in terms of Lagrange points, so there are five Earth-Moon Lagrange points too, and five Sun-Jupiter ones, and … The Lagrange points are useful for space-based observatories; for example SOHO sits at the Sun-Earth L1 point, and WMAP at its L2. And let’s not forget the Jovian Trojans, hundreds of asteroids which are found near (actually orbit around!) the Sun-Jupiter L4 and L5 points!

Want to read further? Here are some resources, covering a range of levels: Home on Lagrange (NASA), What are Lagrange Points? (ESA), and Gravity Simulations (Princeton University).

Universe Today articles on Lagrange points include Sounds Painful: Are Deadly Asteroids Stuck in Earth’s Lagrangian Points?, NASA Scientists Calculate Space Highway, and Three Trojans Found in Neptune’s Orbit.

Astronomy Cast episodes Lagrange Points and the December 20th, 2008 questions show are well worth a listen; be sure to check them out!


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