[Physics] Physics Digest, Vol 14, Issue 7

[cj at mb-soft.com]

L2 is extremely unstable.   Only L4 and L5 have a meta-stability.   Earth satellites launched into L1 or L2 have to constantly have thheir orbits corrected, using up rocket fuel, so they can  never stay there long.  L4 and L5, like I mentioned, even have people thinking about building a tourist hotel there (although micro-gravity would soon kill off any guests).

I brought up L4 and L5 because the orbits of objects there are VERY weird, being in three-dimension Liissajous orbits (which mathemmatically turn out to also be meta-stable)  L4 andd L5 can also have "horseshoe orbits" which are also meta stable.  I have not done that math but associates have and they think that Lissajous orbits and Horseshoe orbits can be meta-stable fo more than a million years, although Venus figures to eventually destabilize them.  Thhe gravitation of horseshoe orbits might be most productive for your purposes.  They are REALLY interesting.

You seem destined to forever seek ANYTHING that might ever mention your "favorite number".  If you ever see a traffic sign with that number on it, you will  clearly be excited.  

The REASON I mentioned the Lissajous orbits of the L4 and L5 objects is because I have no doubt that there is "undiscovered" gravitational knowledge somewhere in there (although my guess is that it will require Riemanniann Calculus to discover.)

Lissajous and Horseshoe orbits do NOT initially seem to be compatiblew with gravitation.  The "third dimensional" aspect of the orbits apparently NEED some additionall factor in Newton's (two dimmensional) Vector equation.  I just thought that you guys might be able to sleuth it out.

Carl
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