On the application of Von Zeipel's theorem to the Asteroid Valentine

Abstract

In Bulletin of the A.A.A. N° 7 I have shown some previous results obtained in the application of Von Zeipel’s method to the asteroid Valentine. At present I have completed the elimination of the short period terms according to Brouwer’s precepts. Solutions for the six elements L ,G ,H ,l ,g, h include terms up to the third degree in the eccentricities of Jupiter and Valentine and the mutual inclination of the r orbits. Some selected fourth-degree terms are to be added on account of the inequality 7n — 3n. The Hamiltonian for this approximation can be easily obtained from the well known results in the theory of secular perturbations. Numerical results are being obtained by computing values of the coefficients of the analytical solutions. A program for the 1620 IBM has been developed for this purpose. The slow convergence of the solution is due to the rather large value of the relationship between semi-major axes of Jupiter and Valentine. More values for the Laplacian constants are needed to complete the numerical solution of the approximation. I hope to get final numerical results in 1970.