
\documentstyle{article}
\title{
       TWO APPROACHES TO THE DETERMINATION OF SATELLITE\\
       PERTURBATIONS DUE TO AN EXTERNAL BODY ATTRACTION}
\author{
                N.V.Emelianov, A.A.Kanter\\
           Sternberg State Astronomical Institute,\\
       Universitetskij prosp. 13, 119899 Moscow, Russia\\
                E-mail: emelia@sai.msu.su}
\date{}

\begin{document}
\maketitle





Abstract.
    The development of analytical theories of the Earth's
satellite motion is considered. Two different approaches to the
problem are developed which essentially depend on the structure of
the disturbing body coordinate representation. The corresponding
effective softwares are elaborated.  An advanced pure
trigonometric theory of satellite motion is constructed for the
case when the disturbing bodies are the Moon and the Sun. Then a
new kind of analytical theory of combined trigonometric-polynomial
form is developed, in which the Moon's and Sun's coordinates are
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 with time-dependent
argument: the latter form of perturbations is more compact and
less time consuming over short time intervals than pure
trigonometric series. Both theories take into account the first
order perturbations due to the Moon's and Sun's attractions.
The advantage of the methods results from the fact that the motion
model of the disturbing bodies can be included to the theory with
a full necessary precision. The efficiency of both approaches is
tested by performing numerical integration for the cases of some
types of satellites.
\end{document}
