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\centerline {\bf Theory Compactification with Elliptic Functions}
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\centerline{V.A.Brumberg}
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\centerline{Institute of Applied Astronomy, 197042 St.-Petersburg, Russia}
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\centerline{\bf Abstract}
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1. Two centuries of the development of analytical theories: achievements and disappointments. 
Place of analytical theories in contemporary celestial mechanics. Poisson series processors
renaissance. Universal CAS (MAPLE, MATHEMATICA, etc.) and construction of compact
analytical theories.

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2. Classical perturbation theory with eccentric or true anomalies. Compactness of the disturbing 
function expansion and integration complications. Introducing of elliptic functions in combination
with the partial anomaly technique. Pressure of numerical integration. Elliptic functions in integrable
problems.

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3. Elliptic function expansions as convergence accelerators of celestial mechanics series.
Theta function expansions. Landen transformation.

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4. Elliptic functions in planetary problems. Generating function. Intermediate orbit by Richardson.
Planetary perturbations by Williams, Van Flandern and Wright.
CPT (compact planetary theory) by Chapront and Simon. Combination of harmonic analysis and 
elliptic arguments. 

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5. Elliptic functions in GPT (general planetary theory). Three forms of GPT series. Compactness due to 
the difference of the mean longitudes. Elliptic quadratures. Higher-order treatment by means of time
reversion, Hansen device and integration by parts. 

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6. Elliptic functions for highly eccentric orbits. Inversion problem. Perturbation theory. Resonance problem.

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7. Elliptic functions for nearly intersecting orbits. Expansion of the disturbing function. Symbolic expansion with 
elliptic Newcomb operators. Perturbation theory. 
 
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\centerline{References}
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\noindent
Brumberg E., Brumberg V.A., Konrad Th. and Soffel M. 1995. Analytical Linear Pertur-

bation Theory for Highly Eccentric Satellite Orbits. Celes. Mech. Dynam. Astron. 

(in press)

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Brumberg V.A. 1995. Analytical Techniques of Celestial Mechanics. Springer, Heidelberg

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Chapront J. and Simon J.-L. 1988. Perturbations du premier ordre pour les couples de 

plan\`etes (unpublished)

\noindent
Nacozy P. 1977. The Intermediate Anomaly. Celes. Mech. {\bf 16}, 309

\noindent
Richardson D.L. 1982.  A Third-Order Intermediate Orbit for Planetary Theory. Celes. 

Mech. {\bf 26}, 187

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Sokolsky A.G., Vakhidov A.A. and Vasiliev N.N. 1995. Computation of Elliptic Hansen 

Coefficients and Their Derivatives. Celes. Mech. Dynam. Astron. (in press)

\noindent
Williams C.A., Van Flandern T. and Wright E.A. 1987. First Order Planetary Perturba-

tions with Elliptic Functions. Celes. Mech. {\bf 40}, 367

\noindent
Zeipel H. 1912. Entwicklung der St\"orungsfunktion. Encyklop\"adie der math. Wiss. {\bf 6}(2), 

557 
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