Abstract
FOR some years past, Prof. G. H. Darwin has been engaged on the numerical solution of a particular case of the problem of three bodies, and at different times he has given some account of the progress he has made. He has now collected his very extensive material, relating to both the mathematical methods employed and the discussion of the numerical results, into one compact summary under the title of “Periodic Orbits,” which appears in Acta Mathematica, vol. xxi. The special case treated by Prof. Darwin refers to one of three classes into which M. Poincaré has divided the periodic solutions of this problem. In this class, the motion is entirely in two dimensions, and the excentricity of the planet's orbit is very small; but Prof. Darwin further supposes the perturbed body to have infinitely small mass, and the planet's orbit to be absolutely circular. The discussion of even this one class has had to be restricted in the course of the work, on account of the heavy arithmetical labour which the method of tracing the orbits by mechanical quadratures involved. Retrograde orbits have not been considered, and the motion of superior planets is still engaging Prof. Darwin's attention. Some thirty examples of periodic orbits have, however, been examined; and though the author may speak of his results very modestly, there is no doubt but that his conclusions will be welcomed as a most interesting contribution to the study of celestial mechanics.
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Periodic Orbits. Nature 57, 394 (1898). https://doi.org/10.1038/057394a0
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DOI: https://doi.org/10.1038/057394a0