heliocentric coordinates
true value
nonlinear differential equations
mass
quasiperiodic solutions
equations
intermediate solution
variables
1970
planetary theory
power series
intermediate quasiperiodic solution
values
deviation
particular solutions
method
chapters
410-450
rectangular heliocentric coordinates
false
2021-11-01T18:52
chapter
planetary mass
https://scigraph.springernature.com/explorer/license/
https://doi.org/10.1007/978-94-010-3323-7_37
behavior
general planetary theory
longitude
curves
perturbations
system
orbital eccentricity
motion
This paper suggests an algorithm for the formal solution of the N planet problem in the rectangular heliocentric coordinates. The algorithm is based on the use of the intermediate quasiperiodic solution generalizing the variation curve of Hill. This particular solution is expressed by power series in terms of the planetary masses with quasi-periodic coefficients. It contains all the inequalities that do not depend on the orbital eccentricities and inclinations. The system of the nonlinear differential equations for the deviations of the true values of the coordinates from those corresponding to the intermediate solution has been further derived. The solution of this system is presented by the series in powers of the variables slowly changing with the time. The coefficients of these series are quasi-periodic functions dependent on the mean longitudes of the planets and developable in powers of the planetary masses. The behaviour of the slowly changing variables is described by the autonomous system of the nonlinear differential equations. This final system yields the secular perturbations in the planetary motion.
terms
eccentricity
paper
lunar method
differential equations
coefficient
solution
inequality
planets
planet problem
variation curve
time
Application of Hill’s Lunar Method in General Planetary Theory
en
function
secular perturbations
1970-01-01
Hill
use
planetary motion
inclination
final system
algorithm
quasi-periodic functions
theory
Hill’s Lunar Method
quasi-periodic coefficients
coordinates
power
formal solution
applications
problem
series
mean longitude
autonomous systems
Pure Mathematics
Brumberg
V. A.
doi
10.1007/978-94-010-3323-7_37
Mathematical Sciences
Springer Nature - SN SciGraph project
978-94-010-3325-1
Periodic Orbits, Stability and Resonances
978-94-010-3323-7
dimensions_id
pub.1005622088
Giacaglia
G. E. O.
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.
Springer Nature