On the radial intermediaries and the time transformation in satellite theory

Taking advantage of the radial intermediaries and the regularization and linearization methods, the zonal Earth satellite theory is studied in the polar nodal canonical set of variables (, , ,R, ¡,N).The variable is eliminated in the first order of the Hamiltonian by applying Deprit's method. Then, the elimination of the perigee is carried out by another canonical transformation. As a consequence, a new radial intermediary, which contains all theJ _2n(n1) harmonics, is given. A comparison with the previous radial intermediaries of Cid and Lahulla, Deprit and Alfriend and Coffey is made.Finally, a regularizing transformation which allows us to linearize part of the radial intermediary is proposed, and an analytical study of this process is presented.