Joseph-Louis Lagrange (1736–1813) was a professional teaching and research astronomer and mathematician who, until the advent of the space program, was most famous for developing Lagrangian Mechanics, a branch of physics that uses energy principles instead of forces to describe how the universe evolves. Lagrange’s hobby was the so-called “ There are ten integrals of the Newtonian equations for motion for an arbitrary system of In 1772, Lagrange produced his “ At each Lagrange Point, the combination of the attractions of the primary and secondary bodies provides the inwards force necessary for the orbit of the tertiary body to have the same period. ## The Earth–Moon System
L1, L2 and L3 are all saddle-shaped gravitational “valleys” in which a body displaced perpendicular to the Earth-Moon axis is drawn back toward the axis. Since displacement
Lagrange’s theories were confirmed a century later with the discovery of “Trojan” asteroids in the orbit of Jupiter in 1906, in the region where L4 and L5 would’ve been had Jupiter been the Moon and the Sun been the Earth. The discovery was so profound at the time that, to this day, astronomers call the L4 and L5 points in The theories were further refined in 1970, when A. A. Kamel published his doctoral dissertation “Perturbation Theory Based On Lie Transforms and its Application to the Stability of Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points” with Stanford professor John Bleakwell. The L4 and L5 libration points are critical to the building of orbital space habitats because they give us a place in which to build. Massive objects placed in the vicinity of the Trojan points in particular will orbit those points once every 89 days (three times the 29½-day period of the Lunar orbit) while accompanying the Earth and the Moon around the Sun, without the need to expend propellant mass and energy, which might be needed elsewhere. In addition to offering zones of stability in which a space habitat can orbit without frequent and expensive course corrections, the L4 and L5 libration points have another advantage: they occupy much the same orbit as the Moon. This puts them out of the vicinity of the Earth and its orbital collection of man-made debris, but between 9.6 and 156 hours transit time using a minimum-energy trajectory such as the classic doubly-tangent transfer orbit. They are, in effect, equidistant from the Earth in terms of both metric distance and velocity change (ΔV). Since the majority of velocity change (about 8.6 kilometers per second or two-thirds of a total 12.7 kilometers per second ΔV) is expended in reaching low Terrestrial orbit, one can travel to or between any of the colonies with equal facility.
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For more information on the orbital dynamics of the Lagrange libration points and other gravity-related topics, including a link to an English translation of Lagrange’s original essay, browse Dr. J. R. Stockton’s Web page It’s worth noting that L4 and L5 in the Earth–Moon System may ## Return to Top of Page## Back to Mobile Suit Gundam: High Frontier
## Copyright © 1999–present by Dafydd Neal Dyar |

I’m sad to tell you Dr. John Stockton’s website doesn’t seem to exist any more. See https://groups.google.com/forum/#!topic/jsmentors/FQ0ry-VnRMo Perhaps you could update your link to an archived copy of his work.

Earth Moon L2 (EML2) is an interesting location. In terms of delta V it’s close to Mars and other destinations in our solar system. Using Farquhar’s route it is closer to LEO than EML1. I did a blog post on EML2: http://hopsblog-hop.blogspot.com/2015/05/eml2.html

It took me awhile to find an archived copy of the Merlyn pages, but I’ve now updated the link.

Hopefully, the archive will not subject to academic abnegation.

https://people.cs.nctu.edu.tw/~tsaiwn/sisc/runtime_error_200_div_by_0/www.merlyn.demon.co.uk/gravity4.htm