  Fast and precise propagation of satellite orbits is required for mission
design, orbit determination and payload data analysis. We present a method to
improve the computational performance of numerical propagators and
simultaneously maintain the accuracy level required by any particular
application. This is achieved by determining the positional accuracy needed and
the corresponding acceptable error in acceleration on the basis of the mission
requirements, removing those perturbation forces whose effect is negligible
compared to the accuracy requirement, implementing an efficient and precise
algorithm for the harmonic synthesis of the geopotential gradient (i.e., the
gravitational acceleration) and adjusting the tolerance of the numerical
propagator to achieve the prescribed accuracy level with minimum cost. In
particular, to achieve the optimum balance between accuracy and computational
performance, the number of geopotential spherical harmonics to retain is
adjusted during the integration on the basis of the accuracy requirement. The
contribution of high-order harmonics decays rapidly with altitude, so the
minimum expansion degree meeting the target accuracy decreases with height. The
optimum degree for each altitude is determined by making the truncation error
of the harmonic synthesis equal to the admissible acceleration error. This
paper presents a detailed description of the technique and test cases
highlighting its accuracy and efficiency.
