J/A+A/628/A84ivo://CDS.VizieR/J/A+A/628/A84doi:10.26093/cds/vizier.36280084CDSFu Y.N.Laskar J.2019-11-22T14:25:40Z2019-08-13T07:51:51ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frsolar-systemsolar-system-planetsephemeridesastronomical-modelsOver short time-intervals, planetary ephemerides have traditionally been represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. This representation is not well adapted for the evolution of planetary orbits in the solar system over million of years which present drifts in their main frequencies as a result of the chaotic nature of their dynamics. We aim to develop a numerical algorithm for slowly diffusing solutions of a perturbed integrable Hamiltonian system that will apply for the representation of chaotic planetary motions with varying frequencies. By simple analytical considerations, we first argue that it is possible to exactly recover a single varying frequency. Then, a function basis involving time-dependent fundamental frequencies is formulated in a semi-analytical way. Finally, starting from a numerical solution, a recursive algorithm is used to numerically decompose the solution into the significant elements of the function basis. Simple examples show that this algorithm can be used to give compact representations of different types of slowly diffusing solutions. As a test example, we show that this algorithm can be successfully applied to obtain a very compact approximation of the La2004 solution of the orbital motion of the Earth over 40Myr ([-35Myr,5Myr]). This example was chosen because this solution is widely used in the reconstruction of the past climates.2019A&A...628A..84Fhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/628/A84CatalogResearchIsServedByTAP VizieR generic servicehttps://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/628/A84https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/628/A84http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/628/A84https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/628/A84https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/628/A84http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/628/A84GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/A+A/628/A84/tablea3100 coefficients of the decomposition of z_3_ (Eq.31) (z3R100.dat)NoIndex of the termmeta.idints7Integer coefficients of s_7_ (Eq. 30)stat.fit.paramintrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintg1Integer coefficients of g_1_ (Eq. 30)stat.fit.paramintg2Integer coefficients of g_2_ (Eq. 30)stat.fit.paramintg3Integer coefficients of g_3_ (Eq. 30)stat.fit.paramintg4Integer coefficients of g_4_ (Eq. 30)stat.fit.paramintg5Integer coefficients of g_5_ (Eq. 30)stat.fit.paramintg6Integer coefficients of g_6_ (Eq. 30)stat.fit.paramintg7Integer coefficients of g_7_ (Eq. 30)stat.fit.paramintg8Integer coefficients of g_8_ (Eq. 30)stat.fit.paramints1Integer coefficients of s_1_ (Eq. 30)stat.fit.paramints2Integer coefficients of s_2_ (Eq. 30)stat.fit.paramints3Integer coefficients of s_3_ (Eq. 30)stat.fit.paramints4Integer coefficients of s_4_ (Eq. 30)stat.fit.paramints5Integer coefficients of s_5_ (Eq. 30)stat.fit.paramints6Integer coefficients of s_6_ (Eq. 30)stat.fit.paramints8Integer coefficients of s_8_ (Eq. 30)stat.fit.paramintr1Integer coefficients of r_1_ (Eq. 30)stat.fit.paramintr2Integer coefficients of r_2_ (Eq. 30)stat.fit.paramintAbsakAmplitude of a_k(j)_ for z_3_stat.fit.paramdoubleArgakdPhase of a_k(j)_ for z_3_degtime.phasedoubleJ/A+A/628/A84/tablea4100 coefficients of the decomposition of {zeta}_3_ (Eq.31) (zeta3R100.dat)g6Integer coefficients of g_6_ (Eq. 30)stat.fit.paramintg7Integer coefficients of g_7_ (Eq. 30)stat.fit.paramintrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintNoIndex of the termmeta.idintg1Integer coefficients of g_1_ (Eq. 30)stat.fit.paramintg2Integer coefficients of g_2_ (Eq. 30)stat.fit.paramintg3Integer coefficients of g_3_ (Eq. 30)stat.fit.paramintg4Integer coefficients of g_4_ (Eq. 30)stat.fit.paramintg5Integer coefficients of g_5_ (Eq. 30)stat.fit.paramintg8Integer coefficients of g_8_ (Eq. 30)stat.fit.paramints1Integer coefficients of s_1_ (Eq. 30)stat.fit.paramints2Integer coefficients of s_2_ (Eq. 30)stat.fit.paramints3Integer coefficients of s_3_ (Eq. 30)stat.fit.paramints4Integer coefficients of s_4_ (Eq. 30)stat.fit.paramints5Integer coefficients of s_5_ (Eq. 30)stat.fit.paramints6Integer coefficients of s_6_ (Eq. 30)stat.fit.paramints7Integer coefficients of s_7_ (Eq. 30)stat.fit.paramints8Integer coefficients of s_8_ (Eq. 30)stat.fit.paramintr1Integer coefficients of r_1_ (Eq. 30)stat.fit.paramintr2Integer coefficients of r_2_ (Eq. 30)stat.fit.paramintAbsakAmplitude of b_k(j)_ for {zeta}_3_stat.fit.paramdoubleArgakdPhase of b_k(j)_ for for {zeta}_3_degtime.phasedouble