Abstract
We eliminate by the method of von Zeipel the short-period terms in a first order-with respect to planetary masses—general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power.
Our variables are the Poincaré canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms.
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References
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Kamel, O. S. M.: 1970, M.Sc. Thesis, Cairo University, Egypt.
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Kamel, O.M., Bakry, A.A. The elimination of short-periodic terms in a Uranus-Neptune general planetary theory by von Zeipel's method. Astrophys Space Sci 62, 79–116 (1979). https://doi.org/10.1007/BF00643905
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DOI: https://doi.org/10.1007/BF00643905