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6 - Celestial mechanics of the N-body problem

from Part II - Foundations of astrometry and celestial mechanics

Published online by Cambridge University Press:  05 December 2012

Sergei Klioner
Affiliation:
Technical University Dresden
William F. van Altena
Affiliation:
Yale University, Connecticut
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Summary

Introduction

The dynamics of celestial bodies is an important topic for astrometry. First, as we have seen in the previous chapter, the position and velocity of the observer with respect to the BCRS as well as the positions and velocities of Solar System objects are necessary to reduce observations for aberration, parallax, and gravitational light deflection. Second, astrometric observations represent an important source of information allowing us to model the dynamical behavior of various celestial systems: Earth satellites, interplanetary stations, major and minor planets of the Solar System, binary and multiple stars, exoplanetary systems, etc.

A modern introduction in the various techniques of celestial mechanics can be found in the books of Murray and Dermott (1999), Beutler (2005) and Roy (2005). In this chapter we give a short overview of the most important results and concentrate on the practical aspects of the N-body problem relevant to obtaining and processing high-accuracy astrometric data.

Type
Chapter
Information
Astrometry for Astrophysics
Methods, Models, and Applications
, pp. 69 - 92
Publisher: Cambridge University Press
Print publication year: 2012

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References

Aarseth, S. J. (2003). Gravitational N-body Simulations: Tools and Algorithms. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Aarseth, S. J., Tout, Chr. A., and Mardling, R. A. (2008). The Cambridge N-Body Lectures. Berlin: Springer.CrossRefGoogle Scholar
Arnold, V. I., Kozlov, V. V., and Neishtadt, A. I. (1997). Mathematical Aspects of Classical and Celestial Mechanics. Berlin: Springer.Google Scholar
Beutler, G. (2005). Methods of Celestial Mechanics. Berlin: Springer.CrossRefGoogle Scholar
Blanchet, L. (2006). Living Rev. Relativity, 9, 4, http://www.livingreviews.org/lrr-2006-4.CrossRef
Bottke, W. F. Jr., Vokrouhlický, D., Rubincam, D. P., and Nesvorný, D. (2006). Ann. Rev. Earth Planet. Sci. 34, 157.CrossRef
Bretagnon, P. and Francou, G. (1988). A&A, 202, 309.
Brouwer, D. and Clemence, G. M. (1985). Methods of Celestial Mechanics, 2nd edn. Orlando, FL: Academic Press.Google Scholar
Brumberg, V. A. (1972). Relativistic Celestial Mechanics. Moscow: Nauka (in Russian).Google Scholar
Brumberg, V. A. (1991). Essential Relativistic Celestial Mechanics. Bristol: Adam Hilger.Google Scholar
Butkevich, A. G. and Klioner, S. A. (2008). In A Giant Step: from Milli- to Microarcsecond Astrometry, eds. W. J., Jin, I., Platais and M. A. C., Perryman, Cambridge: Cambridge University Press, p. 252.Google Scholar
Chenciner, A. and Montgomery, R. (2000). Ann. Math. 152, 881.CrossRef
Damour, T. and Vockrouhlický, D. (1995). Phys. Rev.D, 52, 4455.
Damour, T., Soffel, M., and Xu, Ch. (1991). Phys. Rev.D, 43, 3273.
Everhart, E. (1985). In Dynamics of Comets: Their Origin and Evolution, eds. A., Carusi and G. B., Valsecci. Dordrecht: Reidel, Astrophysics and Space Science Library, vol. 115, p. 85.Google Scholar
Fienga, A., Manche, H., Laskar, J., and Gastineau, M. (2008). A&A, 477, 315 (see also arXiv: 0906.2860).Google Scholar
Folkner, W. M. (2010). In Relativity in Fundamental Astronomy, eds. S. A., Klioner, P. K., Seidelmann, and M. H., Soffel. Cambridge: Cambridge University Press, p. 155.Google Scholar
Fukushima, T. (1996). AJ, 112, 2858.CrossRef
Klioner, S. A. and Kopeikin, S. M. (1994). AJ, 427, 951.Google Scholar
Krasinsky, G. A., Pitjeva, E. V., Vasilyev, M. V., and Yagudina, E. I. (2002). Icarus, 158, 98.CrossRef
Krogh, F. T. (1994). Annals of Numerical Mathematics, 1, 423 (the DIVA/QIVA software is available from http://mathalacarte.com).
Kuchynka, P., Laskar, J., Fienga, A., and Manche, H. (2010). A&A, 514, A96.Google Scholar
Landau, L. D. and Lifshitz, E. M. (2007). Course of Theoretical Physics. Amsterdam: Elsevier, Butterworth-Heinemann, vol. 1.Google Scholar
Marsden, B. G., Sekanina, Z., and Yeomans, D. K. (1973). AJ, 78, 211.CrossRef
Montenbruck, O. and Gill, E. (2000). Satellite Orbits: Models, Methods and Applications. Berlin: Springer.CrossRefGoogle Scholar
Moisson, X. and Bretagnon, P. (2001). Cel. Mech. Dyn. Astron., 80, 205.CrossRef
Morbidelli, A. (2002). Modern Celestial Mechanics: Aspects of Solar System Dynamics. London: Taylor & Francis.Google Scholar
Moyer, T. D. (2003). Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation. Hoboken: Wiley-Interscience.CrossRefGoogle Scholar
Murray, C. D. and Dermott, S. F. (1999). Solar System Dynamics. Cambridge: Cambridge University Press.Google Scholar
Newhall, X. X. (1989). Cel. Mech., 45, 305.CrossRef
Pitjeva, E. V. (2005). Solar Syst. Res., 39, 176.CrossRef
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge: Cambridge University Press.Google Scholar
Roy, A. E. (2005). Orbital Motion, 4th edn. Bristol: IoP Publishing.Google Scholar
Soffel, M. H. (1989). Relativity in Astrometry, Celestial Mechanics and Geodesy. Berlin: Springer.CrossRefGoogle Scholar
Standish, E.M. and Williams, J. G. (2012). In Explanatory Supplement to the Astronomical Almanac, 3rd edn., eds. S., Urban and K., Seidelmann, Herndon, VA, University Science Books.Google Scholar
Will, C. M. (1993). Theory and Experiment in Gravitational Physics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar

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