Numerical integration of the equations of motion of celestial mechanics

Title:              Numerical integration of the equations of motion of
                    celestial mechanics
Authors:            FOX, K.
Affiliation:        AA(Queen Mary College, London, England)
Journal:            Celestial Mechanics (ISSN 0008-8714), vol. 33, June
                    1984, p. 127-142.
Publication Date:   06/1984
Origin:             STI
Category:           Astronomy
NASA/STI Keywords:  CELESTIAL MECHANICS, EQUATIONS OF MOTION, NUMERICAL
                    INTEGRATION, SOLAR SYSTEM, CIRCULAR ORBITS, COMPUTER
                    PROGRAMS, ECCENTRIC ORBITS, GRAVITATIONAL EFFECTS,
                    RUNGE-KUTTA METHOD
Bibliographic Code: 1984CeMec..33..127F

Abstract

Some new techniques for numerical solutions to the differential equations governing the motion of bodies in the solar system moving under their mutual gravitational forces are presented. The methods are tested against each other and against conventional methods. The methods evaluated include: the Gauss-Jackson method; the Gauss-Jackson-Merson method; the Runge-Kutta-Butcher method; the Runge-Kutta Dormand method; the Runge-Kutta method; the Adams method; the Taylor series method; and the Bulirsch and Stoer extrapolation. The techniques are judged for speed, accuracy and ease of use in computing a two body test problem. The conclusions of the comparison are discussed in detail, and no single technique was found to be superior to all others.

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