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The complete set of analytic solutions of the geodesic equation in aSchwarzschild--(anti-)de Sitter space--time is presented. The solutions arederived from the Jacobi inversion problem restricted to the set of zeros of thetheta function, called the theta divisor. In its final form the solutions canbe expressed in terms of derivatives of Kleinian sigma functions. The differenttypes of the resulting orbits are characterized in terms of the conservedenergy and angular momentum as well as the cosmological constant. Using theanalytical solution, the question whether the cosmological constant could be acause of the Pioneer Anomaly is addressed. The periastron shift and itspost--Schwarzschild limit is derived. The developed method can also be appliedto the geodesic equation in higher dimensional Schwarzschild space--times.

Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications