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The application of computer algebra system Piranha to the investigation ofthe planetary problem is described in this work. Piranha is an echelonedPoisson series processor authored by F. Biscani from Max Planck Institute forAstronomy in Heidelberg. Using Piranha the averaged semi-analytical motiontheory of four-planetary system is constructed up to the second degree ofplanetary masses. In this work we use the algorithm of the Hamiltonianexpansion into the Poisson series in only orbital elements without othervariables. The motion equations are obtained analytically in time-averagedelements by Hori-Deprit method. Piranha showed high-performance of analyticalmanipulations. Different properties of obtained series are discussed. Thenumerical integration of the motion equations is performed by Everhart methodfor the Solar system's giant-planets and some exoplanetary systems.

The construction of averaged planetary motion theory by means of computer algebra system Piranha