  This paper is concerned with the comparison of semi-analytical and
non-averaged propagation methods for Earth satellite orbits. We analyse the
total integration error for semi-analytical methods and propose a novel
decomposition into dynamical, model truncation, short-periodic, and numerical
error components. The first three are attributable to distinct approximations
required by the method of averaging, which fundamentally limit the attainable
accuracy. In contrast, numerical error, the only component present in
non-averaged methods, can be significantly mitigated by employing adaptive
numerical algorithms and regularized formulations of the equations of motion.
We present a collection of non-averaged methods based on the integration of
existing regularized formulations of the equations of motion through an
adaptive solver. We implemented the collection in the orbit propagation code
THALASSA, which we make publicly available, and we compared the non-averaged
methods to the semi-analytical method implemented in the orbit propagation tool
STELA through numerical tests involving long-term propagations (on the order of
decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases
considered, regularized non-averaged methods were found to be up to two times
slower than semi-analytical for the LEO orbit, to have comparable speed for the
GTO, and to be ten times as fast for the HEO (for the same accuracy). We show
for the first time that efficient implementations of non-averaged regularized
formulations of the equations of motion, and especially of non-singular element
methods, are attractive candidates for the long-term study of high-altitude and
highly elliptical Earth satellite orbits.
