An Iterative Method of General Planetary Theory [chapter]

V. A. Brumberg
1974 The Stability of the Solar System and of Small Stellar Systems  
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 Af-planet case this method requires the performance
more » ... res the performance of the analytical operations on a computer with power series of AN polynomial variables, the coefficients being the exponen tial series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoffs 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.
doi:10.1007/978-94-010-9877-9_23 fatcat:m53kpj46yzcylncdo5wkscsszi