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  • 1
    Electronic Resource
    Electronic Resource
    Considerations concerning the non-rigid Earth nutation theory (1998)
    Springer
    Celestial mechanics and dynamical astronomy 72 (1998), S. 245-309 
    Details
    ISSN: 1572-9478
    Keywords: earth's rotation ; precession ; nutation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earth's density and theological properties) for the calculation of the Earth's transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earth's transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earth's nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5. Each level is discussed at the state of the art of the developments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008364926215
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  • 2
    Electronic Resource
    Electronic Resource
    Un formulaire pour le calcul des perturbations d'ordres élevés dans les problèmes planétaires (1975)
    Springer
    Celestial mechanics and dynamical astronomy 11 (1975), S. 379-399 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Abstract The authors present formulas in compact form for constructing high order planetary perturbations with respect to the disturbing masses. They have been built by an iterative process and give the variations of osculating elements. Singularities due to vanishing eccentricities and inclinations are not present in the differential equations. All elementary operations are manipulations of Fourier series with numerical coefficients, and great care has been taken to economize algebraic operations. Results are presented in three forms: (a) vectorial form, with real components which may be useful in numerical integrations; (b) complex form, to put in evidence the symmetries of the system of variables; (c) scalar form, which is the most elaborate. This last form has been used for constructing the first order perturbations for any pair of planets. Two illustrations are given (Jupiter and Saturn, Venus and Earth). Further remarks are made about the practical manipulation of Fourier series, resolution of Kepler's equation in complex form and construction by iteration of the inverse of the distance between two bodies.
    Notes: Résumé Les auteurs présentent un formulaire sous une forme compacte pour la construction des perturbations planétaires d'ordres élevés par rapport aux masses perturbatrices. Elles ont été construites par un processus itératif et donnent les variations des éléments osculateurs. Il n'y a pas de singularités pour les excentricités et inclinaisons nulles dans les équations différentielles. Toutes les opérations élémentaires sont des manipulations de séries de Fourier à coefficients numériques, et un grand soin a été apporté pour économiser les opérations algébriques. Le formulaire est présenté sous trois formes: (a) Une forme vectorielle, à composantes réelles qui peut être utilisée pour l'intégration numérique. (b) Une forme complexe, afin de mettre en évidence les symétries du système de variables. (c) Une forme scalaire qui est la plus élaborée. Cette dernière forme a été utilisée pour la construction des perturbations du premier ordre, pour tous les couples de planètes. Deux illustrations sont données (Jupiter et Saturne, Vénus et Terre). Par ailleurs, des remarques sont faites sur l'utilisation pratique des séries de Fourier, la résolution de l'équation de Kepler sous forme complexe et la construction par itération de l'inverse de la distance entre deux corps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228813
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  • 3
    Electronic Resource
    Electronic Resource
    Construction of a planetary solution with the help of anN-body program, and analytical complements (1986)
    Springer
    Celestial mechanics and dynamical astronomy 38 (1986), S. 181-190 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Up to now we have been dealing with the construction of entirely analytical planetary theories such as VSOP82 (Bretagnon, 1982) and TOP82 (Simon, 1983). These theories take into account the whole of the Newtonian perturbations of nine point masses: the Sun, the Earth-Moon barycentre, the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune. They also take into account perturbations due to some minor planets, to the action of the Moon and the relativistic effects. The perturbations of these last three types are in a very simple way under analytical form but they considerably increase the computations when introduced in the numerical integration programs. In the present paper we thus study a solution in which the Newtonian perturbations for the ten point masses are treated through numerical integration, the other perturbations being analytically added.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230430
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  • 4
    Electronic Resource
    Electronic Resource
    Theorie des planetes inferieures (1982)
    Springer
    Celestial mechanics and dynamical astronomy 26 (1982), S. 161-167 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Resumé La construction de théories planétaires a été entreprise au Bureau des Longitudes pour l'ensemble du système solaire. Il s'agit de théories semi-analytiques à variations séculaires ce qui signifie que les termes à longues périodes (périodes des périhélies et des noeuds comprises entre 50 000 ans et 2 000 000 d'années) ont été développés par rapport au temps. Ce sont donc des théories du type de celles de Le Verrier ou de Newcomb. Les théories de Le Verrier et de Newcomb ont une précision interne d'environ 0″,1 pour les planètes inférieures. La théorie de Le Verrier-Gaillot a une précision interne de quelques secondes pour les grosses planètes. Mais les constantes d'intégration de, ces théories, la dégradation des éléments moyens due à l'imprécision des termes séculaires calculés font que la précision réelle est comprise entre quelques 0″,1 et plusieurs secondes. La précision de la théorie du soleil de Newcomb, par exemple, est de l'ordre de 0″,8. Les objectifs que nous nous sommes fixés sont d'atteindre en précision; pour les planètes inférieures 0″,001 sur plusieurs siècles; pour les grosses planètes 0″,01 sur un siècle, 0″,1 sur 1000 ans. Cela implique de déterminer les perturbations au moins jusqu'a l'ordre 3 des masses pour les planètes inférieures et jusqu'à l'ordre 6 pour les grosses planètes.
    Notes: Abstract In the contruction of planetary theories for the whole of the solar system undertaken at the Bureau des Longitudes, the aim is to obtain the precision of: for the inner planets 0″.001 over several centuries; for the outer planets 0″.01 over one century, 0″.1 over 1000 years. To get these precisions one must compute the perturbations at least to the 3rd order of the masses for the inner planets and to the 6th order of the masses for the outer planets. We have used an iterative method which has given the perturbations up to the 6th order of the masses for the outer planets and a method working order after order with respect to the masses. Through the latter, we have built the perturbations up to the 3rd order with respect to the masses for all the planets. In the mean longitudes the precision now obtained is of 0″.0005 for Mercury, 0″.0030 for Venus and the Earth and 0″.0047 for Mars. For Mercury, the obtained precision is about 130 meters. One has therefore to introduce besides the advance of the perihelium due to relativity, the periodic relativistic corrections, whose amplitude is over 3000 meters for that planet. We have completed our theory of the Earth-Moon barycenter by the relativistic effects, as well as by the perturbations due to the Moon. As a whole, our solution is about 100 times better than that of Newcomb. Our solution for the variablesq andp of the Earth shows that the equinox is moved by a periodic motion of 0″.04 amplitude and with a period of 883 year-a thing not considered generally. the precision of our solution for the mean longitude of Mars is 0″.0047, which means a real progress over the theory of Clemence. We have indeed noticed many arguments missing in that theory we last mentioned. For the years to come we intend to replace to theories of Le Verrier by these solutions in the ephemerides published by the Bureau des Longitudes. Beforehand we are going to improve the constants of integration by a comparison to numerical integrations or directly to observation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230879
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  • 5
    Electronic Resource
    Electronic Resource
    Amelioration des theories planetaires analytiques (1984)
    Springer
    Celestial mechanics and dynamical astronomy 34 (1984), S. 193-201 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The VSOP82 and TOP82 theories intend to represent the motion of planets, with a satisfactory accuracy, over an interval of 1000 years from and after J2000.0. The precision of the newtonian part of the solutions for the system of the sun and eight point masses is given in table 1. We present the construction of complements in order to keep this accuracy over one thousand years for the real motion: the relativistic perturbations, the perturbations by the minor planets, the perturbations by the Moon. Besides, we have undertaken the improvement of the solutions through lengthening the interval of validity up to six thousand years from and after J2000.0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01235801
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  • 6
    Electronic Resource
    Electronic Resource
    On the use of analytical theories in the calculation of precession-nutation (1996)
    Springer
    Celestial mechanics and dynamical astronomy 65 (1996), S. 95-106 
    Details
    ISSN: 1572-9478
    Keywords: precession ; nutation ; analytical theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present the use of the analytical solutions of the planets and of the Moon's motion in the determination of the quantities which relate the barycentric and the geocentric coordinate systems and of the expressions of precession-nutation. The computation of the precession and nutation quantities are built with the analytical theories of the motion of the Moon, the Sun and the planets of the Bureau des longitudes. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth limited to C j,0 for j from 2 to 5, C 2,2, S 2,2, C 3,κ S 3, κ, for κ from 1 to 3 and C 4,1, S 4,1. We determine the 3 Euler angles ψ, ω, and π2 calculating the components of the torque of the external forces with respect to the geocenrer in the case of the rigid Earth. The equations are solved by iterations and so are taken into account the nutations-on-the-nutations effects. We have determined the analytical variations of the angles ψ and w fixing the equator with respect to the ecliptic J2000. We find, in w, a secular term of −26.5026 mas per century. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900–2050. The differences do not exceed 16 µas for ψ and 12 µas for ω.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00048441
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  • 7
    Electronic Resource
    Electronic Resource
    Astronomical frequencies for climate research at the decadal to century time scale (1992)
    Springer
    Climate dynamics 7 (1992), S. 181-194 
    Details
    ISSN: 1432-0894
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Short-term variations of the elements representing the Earth's motion around the Sun and its rotation have been analyzed over the last 6000 years using 1-year steps. Their low-frequency part is compared first to the values obtained from a secular theory of the planetary long-term motion showing that they can be considered reliable enough to represent adequately the motion of the Earth over the last 5000 years. Spectral analysis of these values shows that the main periodicities are 2.67, 3.98, 5.26, 5.93, 7.9, 9.8, 11.9, 14.7, 15.8, 29, 42, 61, 122, 165 and 250 years for the eccentricity as well as for the climatic precession, with an additional component at around 930 years for the eccentricity and around 840 years for the climatic precession. Periodicities at 2.67, 3.8, 5.9, 8.0, 9.3, 11.9, 14.7, 18.6, 29, 135, 250 and 840 yr are also shown for the obliquity. Spectral analyses of the daily July mid-month insolation at 65°N show essentially the same periodicities as the climatic precession and the obliquity, i.e. 2.67, 3.98, 5.92, 8.1, 11.9, 15.7, 18.6, 29, 40, 61 and around 900 years. Finally a wider analysis of the insolation pattern was performed related to the large periodicity band of the insolation time series for the solstices and the equinoxes for 7 different latitudes. In equatorial latitudes the insolation variance is largely explained by precession. But precession dominates everywhere with the obliquity signal being stronger at polar latitudes at the solstices. The amplitudes of the insolation change at these frequencies is of the order of 0.2 Wm−2 at the maximum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00206860
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  • 8
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    Considerations Concerning the Non-Rigid Earth Nutation Theory (1998)
    In:  Celestial Mechanics and Dynamical Astronomy
    Details
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
    Type: info:eu-repo/semantics/article
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