Note: You must be registered in order to post a reply.To register, click here. Registration is FREE!
quote:Originally posted by Jim
...many points of mass cannot perform in the same way as one point of mass does.
L1 has been calculated to be an unstable position (see, among others, Cornish's article on Lagrange points, linked to Nasa's website) but the calculation assumes a circular orbit, and negligible third mass. The presumed 1987 (not 1986) position of Frey, is roughly consistent with L4, but in the circular orbit / negligible third mass approximation, L4 also is unstable for m2 / m1 < about 25.
My own numerical simulation, like that of Cornish but in the instantaneous rotating frame for an elliptical orbit, linearized in tiny displacements from the origin at L1, shows that for negligible third mass, L1 is only slightly more unstable for e = 0.24 than for e = 0. Small displacements grow exponentially roughly 30x per radian of the binary orbit.
A few months ago I mentioned on this messageboard thread, that a well-known astrophotographer had published a photo of a mystery object near Jupiter. This might have been a temporary accumulation of material at or near Jupiter's L1. Also I recall that some modern astronomers have seen faint accumulations of dust at some of the Earth/Luna Lagrange points.
Maybe resources should be allocated differently. Tombaugh found Pluto after only a few months of intense observation. Someone like Tombaugh could have found Neptune in a few weeks, without doing any calculus. That's much less costly than requiring hundreds of astronomers to learn calculus so that LeVerrier or Adams could calculate Neptune's position. Telescopes were better in Tombaugh's time than in LeVerrier's, Tombaugh had a better geographical vantage (Arizona), and above all Tombaugh had photographic plates. However if there had been less emphasis on the abstract, and more emphasis on empirical science and industrial arts in European schools, photography might have been developed earlier.