Talk:Lagrangian point

That would be lovely, but I'm restricted to ASCII here and I'm not about to start fiddling with slashes and backslashes and capital letter O's all afternoon :P -- Paul Drye

The Earth's companion object Cruithne is in a somewhat Trojan-like orbit around the Earth, but not in the same manner as a true Trojan. It has a regular solar orbit that is bumped at times by Earth. When the asteroid approaches Earth, the asteroid takes orbital energy from Earth and moves into a larger, higher energy orbit. When the asteroid (in a larger and slower orbit) is caught up by Earth, Earth takes the energy back and so the asteroid falls into a smaller, faster orbit and eventually catches Earth to begin the cycle anew. Epimetheus and Janus, satellites of Saturn, have a similar relationship, though they are of similar masses and so actually exchange orbits periodically.

is fascinating information, but has nothing to do with Lagrangian points or Trojan objects. Whither should it be moved?

Maybe to asteroid? --AN

Which class of asteroids is Cruithne in and do we have a page for it?

Put back in the "but differing" that Xaonon took out. It's a critical part of the definition!

Are you sure? I'm fairly certain that two equal masses orbiting each other would result in libration points as well -- a binary star system, for example. -- Xaonon

Well, technically you get them, but without the mass difference you lose the fundamental quality of an L-point: stability. Unless...

• Mass A is "substantially" larger than mass B -- by about a factor of 30.
• Mass C, at the libration point, has essentially no mass in comparison to both A and B.

...the points aren't linearly stable and can't hold anything. Basically, the centre of gravity of the system must be pretty close to A or it doesn't work. See J.M.A. Danby's "Fundamentals of Celestial Mechanics" (I think) where the ratio is discussed. -- Paul Drye