Theory compression with elliptic functions

Abstract

Abstract. Introduction of Jacobi elliptic functions in planetary, satellite and cometary problems of celestial mechanics is a transformation of variables to present the analytical theories of motion in the more compact form as compared with the traditional series in multiples of mean longitudes or mean anomalies.

Numerical efficiency of the elliptic function expansions of the first-order intermediary for general planetary theory

“…Recently the interest in constructing analytical planetary theories has been revived by the idea to use an elliptic function of time (instead of time itself) as independent variable in order to make the resulting series more compact (see, Brumberg (1996) and references therein). Our aim is to compare the numerical efficiency of the classical series involving mean longitudes of planets and the series resulting from the application of elliptic functions for the particular case of the first-order intermediate orbit for general planetary theory (Brumberg, 1994 for s = -2,0,2 and a = ±2m t j defined as…”