The General Planetary Theory

1995 ◽  
pp. 171-206
Author(s):  
Victor A. Brumberg
Keyword(s):  
Planetary Theory ◽  
General Planetary Theory

scholarly journals An Iterative Method of General Planetary Theory

1974 ◽  
Vol 62 ◽  
pp. 139-155
Author(s):  
V. A. Brumberg
Keyword(s):  
Power Series ◽  
Equations Of Motion ◽  
Slight Modification ◽  
Planetary Motion ◽  
Planetary Theory ◽  
Exponential Series ◽  
Numerical Series ◽  
Satellites Of Jupiter ◽  
General Planetary Theory ◽  
The Right

This paper deals with an iterative version of the general planetary theory. Just as in Airy's Lunar method the series in powers of planetary masses are replaced here by the iterations to achieve improved approximations for the coefficients of planetary inequalities. The right-hand members of the equations of motion are calculated in closed formulas, and no expansion in powers of small corrections to the planetary coordinates is needed. For the N-planet case this method requires the performance of the analytical operations on a computer with power series of 4N polynomial variables, the coefficients being the exponential series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoff's normalization or the Taylor series in powers of time. A slight modification of the method in the resonant case makes it valid for the treatment of the main problem of the Galilean satellites of Jupiter.

Application of Hori technique in general planetary theory

1989 ◽  
Vol 44 (3) ◽  
pp. 275-289 ◽  
Author(s):  
Osman M. Kamel
Keyword(s):  
Planetary Theory ◽  
General Planetary Theory

Secular perturbations in general planetary theory

1975 ◽  
Vol 11 (1) ◽  
pp. 131-138 ◽  
Author(s):  
V. A. Brumberg ◽  
L. S. Evdokimova ◽  
V. I. Skripnichenko
Keyword(s):  
Planetary Theory ◽  
Secular Perturbations ◽  
General Planetary Theory

scholarly journals Numerical efficiency of the elliptic function expansions of the first-order intermediary for general planetary theory

1996 ◽  
Vol 172 ◽  
pp. 101-104 ◽  
Author(s):  
Victor A. Brumberg ◽  
Sergei A. Klioner
Keyword(s):  
Elliptic Function ◽  
Elliptic Functions ◽  
Compact Form ◽  
Planetary Theory ◽  
Numerical Efficiency ◽  
First Order ◽  
Intermediate Orbit ◽  
General Planetary Theory

We compare numerical efficiency of the two kinds of series for the first-order intermediate orbit for general planetary theory: (1) the classical expansion involving mean longitudes of the planets; (2) an expansion resulting from the theory of elliptic functions. We conclude that mutual perturbations of close couples of planets (the ratio of major semi-axes ∼ 1) can be represented in more compact form with the aid of the second kind of series.

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