Analytical Solutions for J3, J4, J5 and Third Body Perturbations for Orbit Propagation

This dataset accompanies the paper "Extended Analytical Formulae for the Perturbed Keplerian Motion Under Low-Thrust Acceleration and Orbital Perturbations", submitted to Celestial Mechanics and Dynamical Astronomy. It contains formulas used to obtain the osculating and averaged variations of the equinoctial elements for a spacecraft under the effect of J3, J4, J5 and third body perturbations. The J3, J4, and J5 integrals are contained in the Matlab files in "IntegralsJ3J4J5.zip" Their names indicate which perturbation and element is considered. The third body calculations are contained in "ThirdBody.zip" The Matlab code is contained in file "thirdbody_gauss.m" The sane formulas are also contained in two notebook files, which show their derivations: -"integrals.nb" contains the integrals mentioned in the paper -"Thirdbody_Legendre_coefficients.nb" contains the coefficients for the acceleration vector and for the VoP equations. Besides these files, two packages containing definitions for some of these formulas are also included, to save running time: -"integrals.wl" contains full formulas for the integrals -"split_integrals.wl" has the same integrals split into secular and short-periodic forms. Secular terms were modified to not require complex algebra, and the short-periodic were modified to eliminate singularities.