Sternberg State Astronomical Institute of the Moscow University, University prosp. 13, 119899 Moscow, Russia
The development of analytical theories of the Earth's artificial satellite motion is considered. A new approach to the problem is proposed which essentially depends on the structure of the disturbing body coordinate representation. A new kind of analytical theory of combined trigonometric- polynomial form was developed, in which the Moon's and Sun's coordinates were taken from the planet-Moon ephemeris DE200/LE200, in form of Chebyshev polynomial series whose arguments are linear functions of time. In this approach the disturbing body perturbations are short truncated trigonometric series whose coefficients represent Chebyshev polynomial linear functions on 4-days intervals with a time-dependent argument. The form of perturbations is more compact and less time consuming over short time intervals as compared with a previous pure trigonometric approach.
The theory takes into account the first order perturbations due to the Moon's and Sun's attractions.
The corresponding effective software was elaborated. The efficiency of the algorithm was tested by performing numerical integration for the cases of some types of satellites.