Download Dynamics of Planets and Satellites and Theories of Their by R. L. Duncombe, P. K. Seidelmann (auth.), Victor Szebehely PDF

By R. L. Duncombe, P. K. Seidelmann (auth.), Victor Szebehely (eds.)

P. J. MESSAGE collage of Liverpool The papers which include this quantity have been offered at Colloquium No. forty-one of the foreign Astronimical Union, which was once held in Cambridge, England, from the seventeenth to the nineteenth of August, 1976, and had as its topic 'Dynamics of Planets and Satellites and Theories in their Motion'. The Colloquium used to be held simply ahead of the XVIth normal meeting of the Union (which was once held from twenty fourth August to 2d September, in Grenoble, France) to supply a chance for the presentation of study papers on a few energetic and full of life branches of Celestial Mechanics to a meeting of specialists within the box, and for the stimulus of dialogue of analysis difficulties of curiosity to contributors. a few papers testify to the development being made generally Planetary conception, the theories of movement of the minor planets, the Moon, and the satellites of Jupiter and Saturn, and to major advances in either the overall and limited gravitational difficulties of 3 our bodies. The Organizing Committee of the Colloquium used to be made out of J. Chapront, R. L. Duncombe, J. Hadjidemetriou, Y. Kozai, B. Morando, J. Schubart, V. Szebehely, and P. J. Message (Chairman). The neighborhood Organizer used to be D. C. Heggie, to whose tireless efforts the good fortune of the preparations is due. IX record OF individuals N. Abu-el-Ata, Bureau des Longitudes, seventy seven road Denfert Rochereau, 75014 Paris, France okay. Aksnes, middle for Astrophysics, 60 backyard road, Cambridge, Massachusetts 02138, U. S. A.

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Additional info for Dynamics of Planets and Satellites and Theories of Their Motion: Proceedings of the 41st Colloquium of the International Astronomical Union Held in Cambridge, England, 17–19 August 1976

Sample text

We are indebted to M. Luc Duriez for this remark. GENERAL THEORY IN RECTANGULAR COORDINATES 4S d(i,j,k,l)a j + C(i,k,j,l)~ + d(i,k,j,l)~, - (34) - f(i,j,k,O)b. + f(i,j,k,O)b. + f(i,j,k,l)b. + l -f(i,j,k,l)b- J l -- j + f(i,k,j,l)b k + f(i,k,j,l)b k · (35) Here c(i,j,k,~), d(i,j,k,~), f(i,j,k,~) (~=O, ~=1) are exponential series in two arguments: 1-1 (Ai - Aj) and 1-1 (Ai - Ak)' These series have been constructed in the range from -7 to +7 in each argument. This construction has revealed many resonance terms caused by the close commensurabilities between mean motions of some triplets of planets.

Series (9) is self-conjugate and does not contain pure exponentail terms with m = 0 (such terms in (8) yield the quasi-periodic intermediary) • Our work results mainly in actual constructing (8) and (9) for all couples of the major planets. Literal series (5), (6), (8), (9) are important for the investigation of the analytical and numerical structure of the planetary inequalities. For ephemeris computation the second form of the series of the general planetary theory is more suitable. By this form only the 36 V.

L~J 1: k=O k t, (ij) k wk t. (13) (14) and wk ~n (13) are one-argument exponential series with respect to 1-1 Ai and the terms of order m in (5) and (6) lead in these . I . •• , m- , m. Pk k two-argument exponential series with regard to 1=1 Ai and 1=1 Aj. The terms of the power order m and multiple ±a with respect to 1=1 (Ai -Aj) in (8) and (9) result in (14) to multiples 1=1 (kAi + IAj) with k and I changing in limits ±a ±m provided that the sum k+l may take only the values -m, -m+2, ••. , m-2, m.

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