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\centerline{\tit Intermediate orbit for general planetary theory}
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\centerline{\tit in elliptic functions}

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\centerline{\dh V.A.Brumberg\ \ {\rm and}\ \ S.A.Klioner}

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\centerline{\it Institute of Applied Astronomy, 8, Zhdanovskaya st., 197042, St.Petersburg, Russia}

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  We discuss practical construction of the intermediate orbit for
general planetary theory in elliptic functions along lines described
in Brumberg (1992,1994) and Klioner (1992).

  For the first-order intermediary we demonstrate that the intermediary
in the form of Fourier series with respect to elliptic anomaly defined as

$$w_{ij}={\pi \over K(k_{ij})}\,
F\left({\pi\over 2}-{1\over 2}(\lambda_i-\lambda_j),k_{ij}\right), \quad
k_{ij}^2={4 a_i a_j\over (a_i+a_j)^2},$$

\noindent
is by far more efficient than the classic Fourier series involving
anomalistic variable $\lambda_i-\lambda_j$. Here $a_i$ is the major
semi-axis and $\lambda_i$ is the mean longitude of the i-th planet, F
is the elliptic integral of the first kind and K is the complete
elliptic integral of the first kind.

  We also discuss problems which we encounter when constructing second-
and higher-order intermediary orbit. The main problem here is to
take integrals involving elliptic anomalies for two or more couples of
planets.

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\centerline{\bf References}

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V.A. Brumberg, 1992: General Planetary Theory Revisited with the Aid of
Elliptic Functions. In: H.Kinoshita, H.Nakai (eds.), Proc. of the 25th
Symposium on Celestial Mechanics, Tokyo, NAO, Japan, 156-171.

V.A. Brumberg, 1994: General Planetary Theory in Elliptic Functions.
Celetial Mechanics, 59, 1-36.

S.A. Klioner, 1992: Some Typical Algorithms of the Perturbation Theory
within Mathematica and their Analysis. In: H.Kinoshita, H.Nakai (eds.),
Proc. of the 25th Symposium on Celestial Mechanics, Tokyo, NAO, Japan,
172-182.

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