[lbo-talk] Lagrangian point

[Les Schaffer]

Charles A. Grimes wrote:
> You find a very nice illustration. The five points labelled L1, L2,
> ... represent locations in the gravitational fields of the sun, earth
> and moon that remain `stationary' with respect to the system.
>   

the Lagrange points are not related to Lagrangian mechanics per se. They 
really represent dynamical equilibria between centrifugal  and 
gravitational potentials when a third mass orbits in the gravitational 
potential of two larger bodies, which is why its called the restricted 
three body problem. 

by the way, L1, L2, L3 are unstable equilibria. L4 and L5 are the 
interesting places to drift. notice they are the bottom of the potential 
hill in the figure here:

 http://en.wikipedia.org/wiki/Lagrangian_point#Lagrangian_point_missions

this site will explain why some observatories like orbits in the 
vicinity of the *unstable* Lagrange points:

  http://www.physics.montana.edu/faculty/cornish/lagrange.html

now for a real kick, google "horseshoe orbits", for example:

http://books.google.com/books?id=aU6vcy5L8GAC&pg=PA97&lpg=PA97&dq=horseshoe+orbits&source=web&ots=Cy9T3D0BPp&sig=Ock4YU4pwQruwqYeFg5IpEtUtck&hl=en&sa=X&oi=book_result&resnum=5&ct=result#PPA97,M1

http://en.wikipedia.org/wiki/Horseshoe_orbit

Les