[Physics] Physics Digest, Vol 14, Issue 5

[cj at mb-soft.com]

I might have an idea for you guys.  About two hundred years ago, Laplace and Lagrange worked out the gravitational consequences of Newton's laws of gravitation.  It's really interesting stuff.  That was all "simple" (Euclidean) calculus, and one of the consequences that they figured out the Lagrange L4 and L5 points, both for Jupiter and for the Earth.  A company is even discussing building a HOTEL at the Earth's L4 point.

In any case, I thinnk that if you duplicate the math of Lagrange and LaPlace, your understanding of gravitation may grow.

Further, there are some more advanced gravitational effects at both L4 and at L5, where the objects there follow very peculiar Lissajous orbits (in three dimensions).  I believe that math requires Riemannian Calculus to predict the orbits.  The Jupiter Trojans also move around in Lissajous orbits around each other.

In any case, I think these objects might provide for you a more thorough math of the gravitation.  Many years ago, I duplicated much of Lagrange's Calculus (all simplly based on Newton's equations) and I think I learned a lot from that "homework".  As of yet, I have not tried to do the math regarding the Lissajous orbits.

The Jupiter Trojans include thousands of asteroids in both groups.  Their Lissajous orbits are really complex, where they rarely hit each other, even in such tight orbits.  I don't think anybody knows yet WHY they don't collide more.  The Earth Trojans are pretty rare, mostly in our L4 and I think that only a couple small objects have been found in our L5 as of yet.

Carl Johnson
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