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XXII. Researches in physical astronomy

Philosophical transactions of the Royal Society of London, 1830-12, Vol.120, p.327-357

Scanned images copyright © 2017, Royal Society ;ISSN: 0261-0523 ;EISSN: 2053-9223 ;DOI: 10.1098/rstl.1830.0024

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  • Title:
    XXII. Researches in physical astronomy
  • Author: Lubbock, John William
  • Is Part Of: Philosophical transactions of the Royal Society of London, 1830-12, Vol.120, p.327-357
  • Description: In the first volume of the Mécanique Céleste, Laplace has given expressions for the variations of the elliptic constants, which are true when the square and higher powers of the disturbing force are neglected; and he has proved, upon the supposition that the planets move in the same direction, in orbits nearly circular and little inclined one to another, that the eccentricities and inclinations vary within small limits, thereby demonstrating within these conditions the stability of the planetary system. But these conditions are not necessary to the stability of a system of bodies, subject to the law of attraction, which obtains in our system. I have given in the following investigation the expres­sions for the variations of the elliptic constants, which are rigorously true whatever power of the disturbing force be retained; and it is easy to con­clude from the form of their expressions, that however far the approximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain no term which varies with the time; their variations are all periodic, and they oscillate therefore within certain limits. This theorem is no longer true if the planet moves in a resisting medium. I have also given some equations which obtain when an angle is taken for the independent variable, which in the elliptic movement is the eccentric anomaly, which are of remarkable simplicity, and which, as far as I know, have never been noticed, and the development of the disturbing function R to the quantities involving the squares and products of the eccentricities inclusive.
  • Publisher: London: The Royal Society
  • Language: English
  • Identifier: ISSN: 0261-0523
    EISSN: 2053-9223
    DOI: 10.1098/rstl.1830.0024
  • Source: Alma/SFX Local Collection
    JSTOR Early Journal Content
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