[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: Lagrangian Points

I have been slowly reading "Physics and Chemistry of the Solar System"
by John Lewis, 1997, a difficult and challenging book, when today
I hit upon the Lagrange asteroid discussion in the section on the 
Trojan asteroids of Jupiter.

Some background first. The L points come about from a classical 
analysis of the 3-body problem in the special case of m1 >> m2 >> m3.
This is typical of planetary system and here m1 is the mass of the sun,
m2 that of Jupiter, and m3 a small asteroid.

It is clear from reading that that L1, L2, and L3 are unstable and
probably not possible for matter to stay in those spots for long even
in ideal settings.

L4 and L5 in this case lie in Jupiter's orbit at equilateral triangle
vertices, with Jupiter and the sun at two vertices. 

These points seem to be dynamically stable. If an object already there
were perturbed from the spot, the following happens:

Suppose it were forced to slow down. It would then fall towards 
the sun a little and assume a new orbit, revolving a bit faster than Jupiter.
As it approached Jupiter, it would be pulled closer and slowed down.
Apparently, the object would tend to stay near the L4 or L5 point.

The argument for speeding up applies similarly, but in reverse. The object
would assume a farther orbit, revolve more slowly about the sun, and
be eventually pulled towards Jupiter again when Jupiter caught up,
with similar results.

I'm not clear how this leads to an object residing at the Lagrange point,
but it is clear that the orbit is stable. I would expect the object to assume an
orbit that periodically slows down and speeds up, but perhaps there is some small
damping force when one analyzes it more closely. Or maybe I misunderstand
the nature of the Trojan asteroids - perhaps they are in these orbits and not
fixed at the L4, L5 points, does anyone know that for certain? I had always thought
they were locked at these 60 degree points in a small cluster.

Not addressed is how an object originally comes into the L-point - probably it's just a 
chance encounter.

----------
Archives located at:
http://www.meteoritecentral.com/list_best.html

For help, FAQ's and sub. info. visit:
http://www.meteoritecentral.com/mailing_list.html
----------