Subject: If a Lagrange point was occupied, would its counterpart need occupation tooDate: Mon Jun 12 23:17:29 2000
Posted by Rico Anderson
Grade level: 10-12 School: El Segundo High School
City: Gardena State/Province: CA Country: United States
Area of science: Physics
I want to know if a space colony or large sattelite was established at any Lagrange point, like L5, would another Colony or sattelite have to be placed at L4 in order for the earth's orbit to remain stable?
In a word, no. In the late 1700s, French mathematician Joseph Lagrange discovered that if you have a massive object orbiting another massive object (say, the Earth orbiting the Sun), there exist five points of equilibrium where the forces all balance. A third object, if placed there, will remain there. We call these the Lagrange points, and they are numbered 1 through 5.
There are some caveats though. Three of the five points are only metastable. That means that if you give a small push on the third object, it will drift away from the point. It's like a pencil just balanced on its tip; it will stay there unless something pushes on it. Even the smallest force will knock it over.
The other two Lagrange points, L4 and L5, are more stable. An object there will actually try to stay there, so if you push on it gently, it will drift back in position. These points are located 60 degrees ahead and behind the Earth (or whatever the second massive object is).
Another caveat is that the equations are only stable if the two objects are much more massive than the third. If you put a massive object in the L4 or L5 points, the gravity of the object affects the other two, throwing things off. So as long as the third object is low-mass compared to the other two, things are stable.
So, finally, to answer your question, as long as the object is small (and a space colony counts as small compared to the Earth) you don't have to worry about both Lagrange points being filled. Everything will work fine with just one of them occupied.
A web search on ``lagrange points equilibrium'' will yield a lot of info about this interesting quirk of gravity. The website The Three Body Problem-Lagrangian Equilibrium Points has a great diagram and explanation of this; it starts simple and progresses to the math as well. Give it a read!