\documentstyle{article}
                   
    \title{Analytical solution of the motion of the planets over several\\
                       thousands of years}
		\author{Pierre Bretagnon\\
		Bureau des Longitudes}
\date{}


\begin{document}
\maketitle

We present the connection between the general theories describing
the motion of the planets over several million years and the secular 
variation theories, the validity interval of which is restricted to a few
thousands of years. We note that the secular terms of the semi major axes
correspond to long period terms in the general theories. These long period
terms give, in the longitudes, terms with very large amplitude : 12 000''
in the longitude of Saturn (54 000 year period), 20 000'' in the longitude
of Uranus (1 000 000 year period).
    The secular variation theories reach a great accuracy and allow to build
the analytical solution of the difference TCB - TCG and the relations 
between the barycentric and geocentric space coordinates.
    The analytical theories of the motion of the Moon, the Sun and the 
planets built at the Bureau des longitudes are also useful to compute the
precession and nutation expressions. Thus, we have computed, for the rigid
Earth, the influence of the Moon, the Sun and all the planets on the 
potential of the Earth limited to $C_{j0}$ for j from 2 to 5, $C_{22}$, $S_{22}$,
and $C_{3k}$, $S_{3k}$ for k from 1 to 3.


\end{document}
