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A preliminary estimation of the accuracy of the inner planet's co-ordinates

Published online by Cambridge University Press:  14 August 2015

D. K. Kulikov

Abstract

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In the construction of analytical theories of planetary motion, the effect is considered of errors in the adopted values of masses, orbital elements and ephemeris time upon the accuracy of computed co-ordinates of the inner planets in accordance with Newcomb's expansions and constants (with Ross's elements for Mars). These are accurate to five decimal places. The errors in the orbital elements are the principal source of inaccuracy in the positions of the planets. The precision of the ephemerides can be considerably improved by introducing appropriate corrections.

Résumé. — L'auteur étudie successivement les effets d'erreurs dans les développements analytiques des théories des planètes, ou dans les valeurs adoptées pour les masses, pour les éléments et pour le temps des éphémérides, sur la précision des coordonnées des planètes inférieures calculées à partir des développements et des constantes de Newcomb (éléments de Ross pour Mars). La précision est de cinq décimales. La source principale d'erreurs sur les positions des planètes est l'imprécision des éléments. On pourrait améliorer considérablement les éphémérides en introduisant des corrections appropriées.

Zusammenfassung. — Der Einfluss von Fehlern bei der Aufstellung analytischer Theorien der Planetenbewegung und in den angenommenen Werten für die Massen, die Bahnelemente und die Ephemeridenzeit auf die Genauigkeit der berechneten Koordinaten der inneren Planeten nach den Ausdrücken und mit den Konstanten von Newcomb (mit den Marselementen von Ross) wird untersucht. Die Genauigkeit beträgt fünf Dezimalen. Die Fehler in den Bahnelementen sind die hauptsächliche Ursache für die Ungenauigkeit der Planetenörter. Die Genauigkeit der Ephemeriden kann beträchtlich gesteigert werden, wenn man geeignete Korrektionen einführt.

Резюме. — Автор последовательно изучает эффекты погрешностей в аналитических разложениях в теориях планет, или в принятых значениях масс и элементов, или еще в эфемеридном времени, на точность координат внутренних планет, вычисленных пользуясь разложениями и постоянными Ньюкомба (для Марса, элементы Росса). Они точны до пяти десятичных знаков. Погрешности в орбитальных элементах являются главной причиной неточности положений планет. Эфемериды могут быть значительно уточнены, применяя надлежащие поправки.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 21: The System of Astronomical Constants , 1965 , pp. 139 - 151
Copyright
Copyright © CNRS 1965 

References

[1] Astron. Papers , vol. 6, Parts I–IV, 1895–1898; vol. 9, Part II, 1917.Google Scholar
[2] Newcomb, S., Elements of the four Inner Planets and Astronomical Constants , Washington, 1896.Google Scholar
[3] Kulikov, D. K., Integration of the equations of motion in Celestial Mechanics on electronic computers by Cowell's method with an automatic choice of the step (Bull. Inst. Astron. théor. Leningrad, vol. 7, No. 10, 1960.)Google Scholar
[4] Kulikov, D. K., Integration of equations of celestial mechanics by Cowell's method with variable intervals (I.U.T.A.M. Symposium, Paris, 1962, p. 123).Google Scholar
[5] Clemence, G. M., First-order Theory of Mars (Astron. Papers , vol. 11, Part II, 1949).Google Scholar
[6] Clemence, G. M., Theory of Mars. Completion (Astron. Papers , vol. 16, Part II, 1961).Google Scholar
[7] Duncombe, R. L. and Clemence, G. M., Provisional Ephemeris of Mars 1950–2000. United States Naval Obs. Circular No. 90, 1960.Google Scholar
[8] Clemence, G. M., Relativity Effects in Planetary Motion (Proc. Amer. Phil. Soc., vol. 93, No. 7, 1949).Google ScholarPubMed
[9] Rabe, E., Derivation of Fundamental Astronomical Constants from the Observations of Eros during 1926–1945 ( Astron. J. , vol. 55, No. 1184, 1950).Google Scholar
[10] Brouwer, D., Comments on the masses of the Inner Planets (Bull. Astron., 1. 15, fasc. III, 1950).Google Scholar
[11] Brouwer, D. and Clemence, G. M., Orbits and Masses of Planets and Satellites ( The Solar system , edited by Kuiper, H. and Middlehurst, B., vol. 3, 1961).Google Scholar
[12] Duncombe, R. L., Motion of Venus 1750–1949 (Astron. Papers, vol. 16, Part I, 1958).Google Scholar
[13] Makover, S. G. and Bochan, N. A., The motion of the comet Encke-Backlund for the years 1898–1911 and a new determination of the mass of Mercury (Dokl. Acad. Sc. U.R.S.S., vol. 134, No. 3, 1960).Google Scholar
[14] Fotheringham, J. K., Note on the mass of Venus (Month. Not., vol. 86, 1926, p. 296).CrossRefGoogle Scholar
[15] Jones, Spencer, Discussion of the Greenwich Observations of the Sun 1836–1923 ( Month. Not. , vol. 86, 1926, p. 426).CrossRefGoogle Scholar
[16] Fotheringham, J. K., The mass of Venus and the obliquity of the ecliptic (Astron. Nachr., vol. 256, No. 6121, 1935).Google Scholar
[17] Morgan, H. R. and Scott, F. P., Observations of the Sun 1900–1937 compared with Newcomb's Tables (Astron. J., vol. 47, No. 1100, 1939).Google Scholar
[18] Clemence, G. M., The motion of Mercury 1765–1937 (Astron. Papers, vol. 11, Part I, 1943).Google Scholar
[19] Noteboom, E., Beiträge zur Theorie der Bewegung des Planeten 433 Eros (Astron. Nachr., vol. 214, No. 5122–23, 1921).Google Scholar
[20] Bosch, C. A., De Massa's van de Groote Planeten , Baarn, 1927.Google Scholar
[21] Witt, G., Barycentrische Ephemeride des Planeten 433 Eros für die Perihelopposition 1930–1931 (Astr. Abhand. zu A. N., vol. 9, 1935).Google Scholar
[22] Rabe, E., Additional Note on the Solar Parallax from Eros (Astron. J., vol. 59, No. 1222, 1954).Google Scholar
[23] Sky and Telescope , vol. 20, No. 6, 1960.Google Scholar
[24] Kotelnikov, V. A. et al., Radar observations of Venus (Dokl. Acad. Sc. U. R. S. S., vol. 145, No. 5, 1962).Google Scholar
[25] Astron. J. , vol. 67, No. 1299, 1962.Google Scholar
[26] de Sitter, W., On the system of Astronomical Constants (Bull. Astr. Inst. Netherl., vol. 8, No. 307, 1938).Google Scholar
[27] Urey, H. C., The Planets (New Haven, 1952).Google Scholar
[28] Newcomb, S., On the mass of Jupiter and the orbit of Polyhymnia (Astron. Papers, vol. 5, 1895).Google Scholar
[29] Hill, , Tables of Saturn (Astron. Papers, vol. 7, 1898).Google Scholar
[30] Cookson, , Determination of the mass of Jupiter and Orbits of the Satellites (Ann. Cape Obs., vol. 12, Part II, 1906).Google Scholar
[31] Samter, H., Die Bewegungen des Planeten (13) Egeria (Astr. Abhand. zu A. N., vol. 3, No. 17, 1910).Google Scholar
[32] Osten, H., 447 Valentine und Jupitermasse (Astron. Nachr., vol. 232, No. 557, 1928).CrossRefGoogle Scholar
[33] Kulikov, D. K., Numerical methods in Celestial Mechanics and their application to the motion of the VIIIth satellite of Jupiter- (Bull. Inst. Astron. théor. Leningrad, vol. 4, No. 7, 1950).Google Scholar
[34] Hill, , Tables of Jupiter (Astron. Papers, vol. 7, 1898).Google Scholar
[35] Gaillot, M. A., Tables rectifiées du mouvement de Jupiter (Ann. Obs. de Paris, 1913).Google Scholar
[36] Hertz, H. G., The mass of Saturn and the motion of Jupiter 1884–1948 (Astron. Papers, vol. 15, Part II, 1953).Google Scholar
[37] Jeffreys, H., Second-order Terms in the Figure of Saturn (Month. Not. , vol. 114, No. 4, 1954).Google Scholar
[38] Glemence, G. M., Motion of Jupiter and mass of Saturn (Astron. J., vol. 65, No. 1276, 1960).Google Scholar
[39] Kulikov, D. K. and Subbotina, N. S., On the precision of the Ephemerides of Inner planets published in Astronomical Ephemerides (Transactions of the conference on general and applied problems of theoretical astronomy , Moscow, 1963).Google Scholar
[40] Morgan, H. R., The Earth's Perihelion Motion (Astron. J.). Google Scholar
[41] Kulikov, D. K., Ephemerides of the outer planets and problems of astrometry (Proceedings of the 15th Conference on astrometry , Leningrad, 1963).Google Scholar