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''[[Secular variations of the planetary orbits]]'' is a concept describing [[secular variation|long-term trends]] in the orbits of the [[planet]]s [[Mercury (planet)|Mercury]] to [[Neptune]]. Several attempts have from time to time been undertaken to analyze and predict such [[gravitation]]al deviations from ordinary satellite orbits. Others are often referred to as post [[Kepler's laws of planetary motion|keplerian]] effects.
''Variations Séculaires des Orbites Planétaires'' (VSOP) is a modern [[numerical]] [[model]]<ref>P. Bretagnon; [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1982A%26A...114..278B&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf "Théorie du mouvement de l'ensemble des planètes. Solution VSOP82"], (PDF 1.23MB), ''[[Astronomy & Astrophysics]]'' '''114''' (1982) 278–288.</ref>, that tries to address the problem.
[[Jet Propulsion Laboratory]] has an important role in providing scientific efemeris data. In spite of methods to deal with perturbations of numerous [[asteroids]], most of whose masses and orbits are poorly known, remains a tiny secular trend, causing the [[JPL]] to revise its published ephemerides at intervals of 20 years. Russian astronomers have taken notice of this problem. <ref>Kharin, A. S. and [[Yuri B. Kolesnik|Kolesnik, Y. B.]]; ''On the Errors of the Ephemerides Derived from Optical Observations of Planets.'' (1990), [[IAU]] SYMP.141 P.189, 1989.</ref><ref>[[Georgij A. Krasinsky]] and [[Victor A. Brumberg]], ''Secular Increase of Astronomical Unit from Analysis of the Major Planet Motions, and its Interpretation'' [http://iau-comm4.jpl.nasa.gov/GAKVAB.pdf Celestial Mechanics and Dynamical Astronomy 90: 267–288, (2004)].</ref>
Kolesnik has followed this up with an ambitious undertaking, which can be condensed in an [[empiric]] formula, that may help solving JPL's problem.<ref>[[Yuri B. Kolesnik]]; [http://adsabs.harvard.edu/abs/2002HiA....12..330K ''Analysis of the secular variations of longitudes of the Sun, Mercury and Venus from optical observations''], in Highlights of Astronomy, Vol. 12, as presented at the XXIVth General Assembly of the IAU - 2000 [Manchester, UK, 7 - 18 August 2000]. Edited by H. Rickman. San Francisco, CA: Astronomical Society of the Pacific, ISBN 1-58381-086-2, 2002, p. 330 – 333.</ref>
The net result is that the planet accelerates in its orbit, while slowly falling toward the sun. The relation for the change in angular velocity is given by
:<math>\frac{d\omega}{dt}= 3\omega{H_0}</math>
where 1/<math>{H_0}</math> is the [[Hubble's law#Units derived from the Hubble constant|Hubble time]] and '''ω''' is the increasing [[angular velocity]]. This tiny change will cause the Earth to fall roughly 22 meters closer to the Sun per year. <ref>Y. B Kolesnik;[http://adsabs.harvard.edu/full/2001ASPC..245...83K ''On the Relationship Between Dynamical Time and Atomic Time''], Astrophysical Ages and Times Scales, ASP Conference Series Vol. 245. Edited by Ted von Hippel, Chris Simpson, and Nadine Manset. San Francisco: Astronomical Society of the Pacific, ISBN: 1-58381-083-8, 2001., p.83</ref> One theoretical explanation claims that this secular acceleration is of a [[Physical cosmology|cosmological]] origin. <ref>Masreliez C. J.; [http://redshift.vif.com/JournalFiles/V11NO4PDF/V11N4MA2.pdf ''Scale Expanding Cosmos Theory II–Cosmic Drag''], [[Apeiron (tidskrift)|Apeiron]] Okt (2004)</ref>
== See also ==
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