Integration of the equations of general planetary theory in rectangular coordinates

1944 ◽  
Vol 51 ◽  
pp. 37 ◽  
Author(s):  
Dirk Brouwer
Keyword(s):  
Planetary Theory ◽  
Rectangular Coordinates ◽  
General Planetary Theory

Mathematical Results of the General Planetary Theory in Rectangular Coordinates

1978 ◽  
Vol 41 ◽  
pp. 33-48
Author(s):  
V.A. Brumberg ◽  
L.S. Evdokimova ◽  
V.I. Skripnichenko
Keyword(s):  
Planetary Theory ◽  
Orbital Elements ◽  
Exponential Series ◽  
Poisson Series ◽  
Rectangular Coordinates ◽  
The Mean ◽  
General Planetary Theory ◽  
Mathematical Construction

AbstractMathematical construction of the general planetary theory has led to the series of two forms for the coordinates of eight major planets (excluding Pluto). The series of the first form are Poisson series where all orbital elements except the semi-major axes occur in literal shape. The series of the second form are polynomial-exponential series with respect to the time and serve to calculate the ephemerides. The arbitrary constants of the theory are related to the Keplerian elements. The terms of the zero and first degree in eccentricities and inclinations have been found in the second approximation with, respect to the disturbing masses. Among those of particular interest are the resonant terms caused by the commensurabilities of the mean notations of triplets of planets.

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.

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
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