Precise orbit determination of LEO (Low Earth Orbiter) satellites plays an important role in satellite geodesy. In this work, a technique for a precise determination of short arcs (ca. 30 minutes) of low flying satellites is proposed. The procedure is based on the solution of Newton’s equation of motion solved as a boundary value problem. The technique allows determining kinematical orbits without any force function information as well as semi-dynamic with partial force function information or dynamic orbits with full information of the forces acting on the satellites.Furthermore, the procedure allows a computation in the space domain as well as in the spectral domain. To accelerate the convergence of the solution in the spectral domain, special polynomials (i.e. Euler-Bernoulli polynomial) have to be used to avoid Gibbs’ effects at the boundaries of the arcs. The precisely determined shortarcs can be used for regional as well as for global gravity field recovery tasks.