Poisson's theorem in heliocentric variables. Conditions for the application of this theorem concerning the invariability of the major axes of planetary orbits to second order in the masses.
Abstract
Poisson's theorem states that there is no secular inequality in the major axis of the orbits of the planets to the first and second approximation with respect to the masses. An analytical expression for the secular term of the major axes in heliocentric coordinates in the second approximation is derived, and it is shown that in heliocentric elements this term does not vanish, although it does when Jacobi variables are used. However, it is also demonstrated that the secular term will vanish in a Le Verrier type planetary theory if the product of the square of mean motion times the cube of the semimajor axis is a constant having the same value for all the planets.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 1978
 Bibcode:
 1978A&A....68..199D
 Keywords:

 Orbit Perturbation;
 Orbital Elements;
 Orbital Mechanics;
 Planetary Mass;
 Secular Variations;
 Solar Orbits;
 Approximation;
 EulerLagrange Equation;
 Kepler Laws;
 Astronomy;
 Orbits:Planets;
 Planetary Theory