View Full Version : Lagrange Points

2004-Jan-12, 03:33 AM
Can some explain what exactly are and inform of the significance of Lagrange Points are? What happens when two or more Lagrange points interact?

2004-Jan-12, 03:37 AM
see : http://www.physics.montana.edu/faculty/cor...h/lagrange.html (http://www.physics.montana.edu/faculty/cornish/lagrange.html)

2004-Jan-14, 05:42 AM
Can some explain what exactly are and inform of the significance of Lagrange Points are?

The main reason Lagrange Points are so useful, is that you can place a satellite or space station in the L4 Or L5 orbit and they require very little course correction which requires "Fuel"

Man made objects in these orbits would not require "Refueling"...

...which allows the object to stay in orbit for a long period of time.

2004-Jan-15, 12:17 AM
I'm not sure what you mean when you ask about two or more Lagrange points interacting.

Lagrange points really only exist in a two body system with essentially circular orbits. Oh, there can be other bodies involved, but the gravitational field has to be controlled by two overwhelmingly large bodies - the other bodies have to be orders of magnitude smaller so that you can ignore their gravitational influence on the two large bodies and each other. So you have to consider whether you can safely ignore the other bodies in the solar system when you discuss the Lagrange points of two bodies.

There's nothing but dust at the Earth/Moon Lagrange points - because the sun's influence is overwhelming (and maybe also because the Moon's orbit is relatively eccentric). In fact, the sun attracts a particle at those points more strongly than either the Earth or the Moon.

Jupiter and the sun have meaningful lagrange points, but Jupiter probably makes Saturn's Lagrange points unstable because Jupiter is bigger than Saturn, and frequently it is closer to Saturn's L4 and L5 points (the trojan points) than Saturn is.

The Earth/sun L1 and L2 points are useful (SOHO lives at L1) because they're only about a million miles from earth, and there's nothing massive enough near enough to cause problems (although the moon might add to their instabilities, I don't know).

I guess the easy way to think of this is that the "two body problem" has precise solutions that allow long term predictions of orbital motion. The Lagrange points are special cases of those solutions.

The "three body problem" on the other hand is chaotic. Small changes in initial conditions can cause huge changes in motion in a relatively short period of time. Lagrange points range from unstable to meaningless in a three body system.

Or I'm all wet. That's another viable alternative.