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As an example of why I personally find Interactive Physics so useful,
allow me to share my experience of the last two or three days:
A few days ago Alex Burr posted a short note about his IP site. One of
the items there is a simple simulation of the L4 or L5 Lagrange point.
Although I had previously put together what I thought was a pretty nice
Lagrange point simulation using "Gravitation, Ltd.," I had not thought to
do so with IP. Alex's demo inspired me to create a more fully featured
simulation that allows the user to adjust the mass ratio of the primary
bodies and their orbital eccentricity as well as to perturb the orbital
velocity of a particle placed at the Lagrange point and then to observe
the motion from either a fixed or corotating frame. The results surprised
me for they suggest that the stability of the point (which attains for
mass ratios larger than about 25) is substantial for mass ratios like that
of the Jupiter-Sun system. While I knew about the Trojan asteroids, I had
always assumed that they were highly concentrated near the Lagrange
points, and perhaps they are. However, the simulation shows that, for the
parameters of the Jupiter-Sun system (mass ratio ~1000, eccentricity
~.05), a particle will stably orbit in a region that extends over a
remarkably large distance from the Lagrange point. I have attached a
thumbnail gif that shows the extent of one such orbit relative to the Sun
and Jupiter in the corotating frame.
John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
Professor of Physics mailto:ajmallinckro@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223