J/AJ/165/147ivo://CDS.VizieR/J/AJ/165/147doi:10.26093/cds/vizier.51650147CDSLi B.-S.Hou X.-Y.2023-10-18T12:33:05Z2023-09-08T06:05:58ZCDS support team

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

cds-question@unistra.frastronomical-modelssolar-systemasteroidsA novel algorithm based on the Lindstedt-Poincare method is proposed to construct an analytical solution of the lunar orbit. Based on the analytical solution, a numerical fitting algorithm is proposed to improve the coefficients of the analytical solution so that its accuracy can reach the level of a few kilometers within 20yr. By fitting our solution to the long-term JPL ephemerides, we are able to recover the receding speed of the Moon from the Earth due to tidal effects. The proposed algorithm also provides a general way to treat the third-body perturbation in rectangular coordinates.2023AJ....165..147Lhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/AJ/165/147CatalogResearchIsServedByTAP VizieR generic servicerelated-toVI/97 : Solar and Lunar Eclipses; 1996-2020 (Espenak, 1997)VI/140 : Catalogue of Lunar Eclipse Crater Timings (Herald+ 2014)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/AJ/165/147https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/AJ/165/147http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/AJ/165/147https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/AJ/165/147https://vizier.iucaa.in/viz-bin/votable?-source=J/AJ/165/147http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/AJ/165/147GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/AJ/165/147/table3*Main terms of the fitting solutioncy[-0.9/0.75] Coefficient cy (2)stat.fit.paramdoublesy[-0.72/0.91] Coefficient sy (2)stat.fit.paramdoublecz[-0.39/0.33] Coefficient cz (2)stat.fit.paramdoublen[-3/3] Coefficient n (1)stat.fit.paramintp[-7/5] Coefficient p (1)stat.fit.paramintq[-4/4] Coefficient q (1)stat.fit.paramintsz[-0.32/0.4] Coefficient sz (2)stat.fit.paramdoublerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintStart[2000/2080] Julian Epoch, Startyrtime.startintStop[2020/2100] Julian Epoch, Stopyrtime.endintm[0/4] Coefficient m (1)stat.fit.paramintcx[-0.79/0.99] Coefficient cx (2)stat.fit.paramdoublesx[-0.82/0.98] Coefficient sx (2)stat.fit.paramdouble