VELOCITY CORRECTIONS TO KEPLER ENERGY AND LAPLACE INTEGRAL

• DOI: 10.1142/s0129183108012996
• Publication Date: 2008-10-21T07:55:48Z
• Authors: DA-ZHU MA; XIN WU; FU-YAO LIU
• Keywords: Kepler problem; Eccentricity (behavior); Integration by parts

For each celestial body of multi-planet systems, there are two slowly varying quantities or quasi-integrals, Kepler energy and Laplace integral, which closely associated with the orbital semimajor axis eccentricity, respectively. To correct numerical errors quantities, we give an extension Nacozy's approach develop a new manifold correction method, where corresponding reference values at every integration step obtained from integral invariant relations, only velocity corrections used to approximately satisfy quasi-integrals. As result, scheme does enhance quality by significantly raising accuracy elements. Especially, it is superior existing dual scaling method in improvement eccentricity general when adopted integrator provides sufficient precision eccentricity.