The semi-analytic planetary theory VSOP (French: Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) was developed and is maintained (updating it with the results of the latest and most accurate measurements) by the scientists at the Bureau des Longitudes in Paris, France. The first version, VSOP82, computed only the orbital elements at any moment.

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  • Die Variations Séculaires des Orbites Planétaires (VSOP, deutsch „Säkulare Variation der Planetenorbits“) ist eine Planetentheorie, eine Methode zur Berechnung der Bahnen für die Planeten des Sonnensystems mit sehr hoher Genauigkeit. VSOP87 etwa erreicht für die inneren Planeten eine maximale Winkelabweichung von einer Bogensekunde über den Zeitraum von 2000 vor Christus bis 6000 nach Christus.Sie wurde im Jahre 1982 von Pierre Bretagnon, einem Mitglied des Bureau des Longitudes in Paris, veröffentlicht (VSOP82), und seither weiterentwickelt: VSOP87, VSOP2000 und VSOP2002. Sie gilt – mit den Erweiterungen – noch heute (2006) als Referenz für die numerische Modellierung der Dynamik des Sonnensystems.
  • The semi-analytic planetary theory VSOP (French: Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) was developed and is maintained (updating it with the results of the latest and most accurate measurements) by the scientists at the Bureau des Longitudes in Paris, France. The first version, VSOP82, computed only the orbital elements at any moment. An updated version, VSOP87, besides providing improved accuracy, computed the positions of the planets directly, as well as their orbital elements, at any moment.The secular variations of the planetary orbits is a concept describing long-term changes (secular variation) in the orbits of the planets Mercury to Neptune. If one ignores the gravitational attraction between the planets and only models the attraction between the Sun and the planets, then with some further idealisations, the resulting orbits would be Keplerian ellipses. In this idealised model the shape and orientation of these ellipses would be constant in time. In reality, while the planets are at all times roughly in Keplerian orbits, the shape and orientation of these ellipses does change slowly over time. Over the centuries increasingly complex models have been made of the deviations from simple Keplerian orbits. In addition to the models, efficient and accurate numerical approximation methods have also been developed.At present the difference between computational predictions and observations is sufficiently small that the observations do not support the hypothesis that the models are missing some fundamental physics.[citation needed] Such hypothetical deviations are often referred to as post-Keplerian effects.[citation needed]
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  • The semi-analytic planetary theory VSOP (French: Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) was developed and is maintained (updating it with the results of the latest and most accurate measurements) by the scientists at the Bureau des Longitudes in Paris, France. The first version, VSOP82, computed only the orbital elements at any moment.
  • Die Variations Séculaires des Orbites Planétaires (VSOP, deutsch „Säkulare Variation der Planetenorbits“) ist eine Planetentheorie, eine Methode zur Berechnung der Bahnen für die Planeten des Sonnensystems mit sehr hoher Genauigkeit.
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  • VSOP (planets)
  • Variations Séculaires des Orbites Planétaires
  • Variations séculaires des orbites planétaires
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