Context. The development of precise numerical integrations of the motion of the planets, taking into account the most recent observations, lead us to improve the two families of analytical planetary theories built in the Institut de mecanique celeste et de calcul des ephemerides (IMCCE), the Variations Seculaires des Orbites Planetaires (VSOP) and the Theory of the Outer Planets (TOP) theories. Aims. We have built the solutions VSOP2010 and TOP2010 fitted to the Jet Propulsion Laboratory (JPL) numerical integration DE405 and the solutions VSOP2013 and TOP2013 fitted to the European recent numerical integration INPOP10a. This paper specifically considers VSOP2013 and TOP2013. Methods. We have improved the construction of VSOP by analytically computing the pertubations due to the asteroids and to Pluto. We have increased the precision of the VSOP solutions of Jupiter and Saturn by using TOP solutions. We have also improved the construction of TOP by computing the perturbations due to the telluric planets from VSOP solutions. Moreover, TOP contains a solution of the motion of the Pluto-Charon barycenter. Results. From 1890 to 2000, the precision of VSOP2013 goes from a few 0:01 mas (planets except Mars and Uranus) up to 0.7 mas (Mars and Uranus). Compared to the previous solution (VSOP2000), this represents an improvement of a factor of 2 to 24, depending on the planet. From4000 to 8000, the precision is of a few 0:1 00 for the telluric planets (1:6 00 for Mars), i.e. an improvement of about a factor of 5 compared to VSOP2000. The TOP2013 solution is the best for the motion of the major planets from4000 to 8000. Its precision is of a few 0:1 00 for the four planets, i.e. a gain between 1.5 and 15, depending on the planet compared to VSOP2013. The precision of the theory of Pluto remains valid up to the time span from 0 to 4000. The VSOP2013 and TOP2013 data are available on the WEB server of the IMCCE.

/pdf/new-analytical-planetary-theories-vsop2013-and-top2013-49b4wzkntg.pdf

New analytical planetary theories VSOP2013 and TOP2013

Links between climate and Earth's orbit have been proposed for about 160 years. Two decisive advances towards an astronomical theory of palaeoclimates were Milankovitch's theory of insolation (1941) and independent findings, in 1976, of a double precession frequency peak in marine sediment data and from celestial mechanics calculations. The present chapter reviews three essential elements of any astronomical theory of climate: (1) to calculate the orbital elements, (2) to infer insolation changes from climatic precession, obliquity and eccentricity, and (3) to estimate the impact of these variations on climate. The Louvain-la-Neuve climate-ice sheet model has been an important instrument for confirming the relevance of Milankovitch's theory, but it also evidences the critical role played by greenhouse gases during periods of low eccentricity. It is recognised today that climatic interactions at the global scale were involved in the processes of glacial inception and deglaciation. Three examples are given, related to the responses of the carbon cycle, hydrological cycle, and the terrestrial biosphere, respectively. The chapter concludes on an outlook on future research directions on this topic.

The Climate Response to the Astronomical Forcing

This paper aimed to address the study of a new family of anomalies, called natural anomalies, defined as a one-parameter convex linear combination of the true and secondary anomalies, measured from the primary and the secondary focus of the ellipse, and its use in the study of analytical and numerical solutions of perturbed two-body problem. We take two approaches: first, the study of the analytical development of the basic quantities of the two-body problem to be used in the analytical theories of the planetary motion and second, the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our family for each value of the eccentricity. The use of an appropriate value of the parameter can improve the length of the developments in the analytical theories and reduce the errors in the case of the numerical integration.

https://downloads.hindawi.com/journals/aaa/2014/162060.pdf

A Study about the Integration of the Elliptical Orbital Motion Based on a Special One-Parametric Family of Anomalies

Semi-analytical integration algorithms based on the use of several kinds of anomalies as temporal variable

A formulation to obtain semi-analytical planetary theories using true anomalies as temporal variables

Les auteurs presentent un formulaire sous une forme compacte pour la construction des perturbations planetaires d'ordres eleves par rapport aux masses perturbatrices. Elles ont ete construites par un processus iteratif et donnent les variations des elements osculateurs. Il n'y a pas de singularites pour les excentricites et inclinaisons nulles dans les equations differentielles. Toutes les operations elementaires sont des manipulations de series de Fourier a coefficients numeriques, et un grand soin a ete apporte pour economiser les operations algebriques. Le formulaire est presente sous trois formes:

(a)

Une forme vectorielle, a composantes reelles qui peut etre utilisee pour l'integration numerique.




(b)

Une forme complexe, afin de mettre en evidence les symetries du systeme de variables.




(c)

Une forme scalaire qui est la plus elaboree. Cette derniere forme a ete utilisee pour la construction des perturbations du premier ordre, pour tous les couples de planetes. Deux illustrations sont donnees (Jupiter et Saturne, Venus et Terre). Par ailleurs, des remarques sont faites sur l'utilisation pratique des series de Fourier, la resolution de l'equation de Kepler sous forme complexe et la construction par iteration de l'inverse de la distance entre deux corps.

Un formulaire pour le calcul des perturbations d'ordres élevés dans les problèmes planétaires

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Un formulaire pour le calcul des perturbations d'ordres élevés dans les problèmes planétaires