Special perturbation theory methods in celestial mechanics. I. Principles for the construction and substantiation of the application

Abstract

The ideas and principles for the construction of methods in special perturbation theory are discussed, and their application to the solution of problems in classical celestial mechanics is substantiated. The problem of shortperiod perturbations and their effect on the numerical integration is investigated.

Special perturbation theory methods in celestial mechanics. II. Comparative analysis of numerical efficiency

“…Table 1 gives references to earlier derived formulas [1]; the column G presents designations of the corresponding integration variables for the characteristics of the numerical efficiency of methods in the figures given below; N is the number of equations to be integrated. It should be noted that in the Encke methods [1] the reference solutions were recalculated after every two turns.…”

“…Table 1 gives references to earlier derived formulas [1]; the column G presents designations of the corresponding integration variables for the characteristics of the numerical efficiency of methods in the figures given below; N is the number of equations to be integrated. It should be noted that in the Encke methods [1] the reference solutions were recalculated after every two turns. In Table 2, T , e , and i are, respectively, the period, eccentricity, and inclination of the orbit under investigation (the inclinations are given relative to the equator of the central planet for satellites and relative to the ecliptic for asteroids); J is the coefficient of the second zonal harmonic of the planet, and ν is the coefficient of influence of short-period perturbations [1].…”

“…It should be noted that in the Encke methods [1] the reference solutions were recalculated after every two turns. In Table 2, T , e , and i are, respectively, the period, eccentricity, and inclination of the orbit under investigation (the inclinations are given relative to the equator of the central planet for satellites and relative to the ecliptic for asteroids); J is the coefficient of the second zonal harmonic of the planet, and ν is the coefficient of influence of short-period perturbations [1]. For the problems under consideration the following perturbing factors were considered: the effect of nonsphericity of the central body (for satellites), J; the attraction by massive bodies (for satellites and planets), ; and the attraction by the Sun (for satellites),…”

“…In the first part of the present work [1] the basic ideas and principles for the construction of methods in special perturbation theory are proposed and their application to the solution of problems in celestial mechanics is substantiated. To give clear recommendations on using the methods, a comparative analysis of their efficiency as applied to numerical simulation of satellite, asteroid, and planetary orbits is performed.…”

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A comparative analysis of the efficiency of methods in special perturbation theory [1] is performed as applied to the numerical simulation of satellite, asteroid, and planetary orbits, and recommendations on their use are given.

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