On the choice of reference orbit,canonical variables,and perturbation method in satellite theory

The author's second-order artificial satellite theory (Aksnes, 1970) is reviewed and compared with that of Kozai (1962). These theories differ in that the former makes use of: (1) an intermediate orbit, being a rotating ellipse instead of a fixed ellipse, (2) Hill variables instead of Delaunay variables, and (3) Hori's perturbation method in Lie series rather than Von Zeipel's method in Taylor series.It is demonstrated that because of these differences, the former theory enjoys a greater simplicity and compactness, it is non-singular at zero eccentricity, and the process of deriving the perturbations is considerably simplified (Aksnes, 1972). For example, the number of second-order short-period terms due to the planet's oblateness (J ₂) is reduced by a factor of about three (Hori, 1970). The intermediate orbit and Hori's perturbation method contribute about equally to this reduction.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.