Relativistic Celestial Mechanics on the verge of its 100 year anniversary View Full Text


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Article Info

DATE

2010-03

AUTHORS

V. A. Brumberg

ABSTRACT

As we are now approaching 2015, both the General Relativity Theory (GRT) and the relativistic Celestial Mechanics based on it will soon arrive at their 100 year anniversaries. There is no border between Newtonian and relativistic Celestial Mechanics. The five-decade period of intensive development of Celestial Mechanics in the second half of the 20th century left many interesting techniques and problems uncompleted. This lecture reviews some problems of Newtonian and relativistic Celestial Mechanics worthy of further investigation. Concerning Newtonian mechanics, these problems include general solution of the three-body problem by means of the series of polynomials, construction of the short-term and long-term theories of motion using the fast converging elliptic function expansions, and representation of the rotation of the planets in the form compatible with the General Planetary Theory reducing the problem to the combined secular system for translatory motion and rotation. Relativistic problems considered here include the determination of the main relativistic effects in the motion of a satellite, e.g. the Moon, and in the rotation of the primary planet using the Newtonian theories of motion and rotation combined with the relativistic transformation of the reference systems, the use of the linearized weak-field GRT metric as a basis of relativistic Celestial Mechanics in the post-Newtonian approximation, and the motion of the Solar System bodies at the cosmological background in the framework of the basic cosmological models. The exposition of the chosen relativistic problems is preceded by reminding the basic features of relativistic Celestial Mechanics with discussing some present tendencies concerning the Parametrized Post-Newtonian formalism, International Astronomical Union resolutions, and standardization of the GRT routines. More... »

PAGES

209-234

References to SciGraph publications

  • 2001-07. Elliptic Anomaly in Constructing Long-Term and Short-Term Dynamical Theories in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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  • 2008-08. Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006 in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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  • 2007-11. On derivation of EIH (Einstein–Infeld–Hoffman) equations of motion from the linearized metric of general relativity theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1996-03. Large scale chaos and marginal stability in the solar system in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-11. Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: Fitting to VLBI data in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2007-03. Precession/nutation solution consistent with the general planetary theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1913-12. Mémoire sur le problème des trois corps in ACTA MATHEMATICA
  • 2000-11. The Construction of the Theory of Motion for Solar-System Bodies Based on a Universal Method for the Perturbative Function Calculation in SOLAR SYSTEM RESEARCH
  • 2004-02. On Relativistic Equations of Motion of an Earth Satellite in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971-09. Automated, closed form integration of formulas in elliptic motion in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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