Second-order theory for the two-body problem with varying mass including periastron effect

The model of varying mass function, including periastron effect, in terms of Delaunay variables will be expanded. The Hamiltonian of the problem is developed in the extended phase space by introducing a new canonical pair of variable ( q 4 , Q 4 ). The first “ q 4 ” is defined as explicit function of time and the initial mass of the system. The conjugate momenta “ Q 4 ” is assigned as the momenta raises from the varying mass. The short-period analytical solution through a second-order canonical transformation using “Hori’s” method developed by “Kamel” is obtained. The variation equations for the orbital elements are obtained too. The results of the effect of the varying mass and the periastron effect in the case n = 2 are analyzed.