Talk:Lagrangian Point

I was about to submit the following, but Paul Drye beat me by a few seconds. I can't be bothered to try to integrate this with his work, so I leave it here, in case anyone else wants to. --Zundark, 2001 Sep 19

A Lagrangian point (or L-point, or libration point) is a position in space where the gravitational field of two bodies interact forming a stable point. Bodies at the L-point will not move relative to the parent bodies.

There are five Lagrangian points, conventionally labelled L1, L2, L3, L4 and L5. In order to describe these points, let us assume that we are talking about the Earth-Sun system. The same principles apply to other systems.

L1.

An object which orbits the Sun more closely than the Earth does would normally have a shorter orbital period than the Earth, but that ignores the effect of the Earth's own gravitational pull. If the object is directly between the Earth and the Sun, then the effect of the Earth's gravity is to weaken the force pulling the object towards the Sun, and therefore increase the orbital period of the object. The closer to Earth the object is, the greater this effect is. At a certain point, called the L1 point, the orbital period of the object becomes exactly equal to the Earth's orbital period.

L2.

A similar effect occurs on the other side of the Earth, further away from the Sun, where the orbital period of an object would normally be greater than that of the Earth. The extra pull of the Earth's gravity decreases the orbital period of the object, and at the L2 point that orbital period becomes equal to the Earth's.

L3.

A third Lagrangian point, L3, exists on the opposite side of the Sun, a little further away from the Sun than the Earth is, where the combined pull of the Earth and Sun again causes the object to orbit with the same period as the Earth. (However, the Earth's gravitational pull at that distance is less important than the gravitational pull of other planets, so the L3 point is largely theoretical.)

L4 and L5.

The L4 and L5 points lie 60 degrees ahead of and 60 degrees behind the Earth in its orbit around the Sun. Unlike the other Lagrangian points, these points are stable to perturbation, and therefore objects tend to accumulate around these points. Of particular interest are the L4 and L5 points of the Jupiter-Sun system, where a number of asteroids, collectively referred to as Trojans, are to be found.