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From: dalex@eleazar.dartmouth.edu (Dave Alexander)
Newsgroups: sci.astro,sci.space
Subject: Re: Finding Lagrange's Libration Points
Message-ID: <11854@dartvax.Dartmouth.EDU>
Date: 19 Jan 89 15:50:58 GMT
References: <1989Jan18.044744.18328@sq.uucp>
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Reply-To: dalex@eleazar.dartmouth.edu (Dave Alexander)
Organization: Dartmouth College, Hanover, NH
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In article <1989Jan18.044744.18328@sq.uucp>
                                        msb@sq.com (Mark Brader) writes:
> Lagrange found that there are exactly 5 positions that the tertiary
> can occupy with respect to the primary and secondary.  The three
> bodies can be in a straight line: position L1 has the tertiary in the
> middle, L2 the secondary, and L3 the primary.  Or they can be in an
> equilateral triangle, with the tertiary either leading or trailing the
> secondary as they move around the primary; these positions are L4 and
> L5.

...

> The L in each of these positions stands for libration, as a body near
> those positions may librate or oscillate around them, and not for
> Lagrange.

...

> This is as far as I have gotten on my own.  Now, I observe that if a
> body is placed near one of the L1, L2, L3 points but slightly off the
> straight line, then there will be a sideways force on it, so it makes
> sense that, as I have read, these are unstable equilibria.

So if L1, L2, and L3 are loci of unstable equilibrium, how can we expect
an object to librate or oscillate about any of them?


                        -- Dave Alexander

--
"Experience has proved that some people indeed know everything."
                                     -- Russell Baker