Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Abstract

We propose two time elements for the orbit propagator named Dromo. One is linear and the other constant with respect to the independent variable, which coincides with the osculating true anomaly in the Keplerian motion. They are defined from a generalized Kepler's equation written for negative values of the total energy and, unlike the few existing time elements of this kind, are free of singularities. To our knowledge it is the first time that a constant time element is associated with a second-order Sundman time transformation. Numerical tests to assess the performance of the Dromo method equipped with a time element show the remarkable improvement in accuracy for the perturbed bounded motion around the Earth compared to the case in which the physical time is a state variable. Moreover, the method is competitive with and even better than other efficient sets of elements. Finally, we also derive a time element for a null and positive total energy.

Multiple scales asymptotic solution for the constant radial thrust problem

“…One fundamental aspect of the analytical procedure employed in the article is the use of a convenient orbital motion formulation to ease the analytical treatment as much as possible. The so called "Dromo" formulation initially introduced by Peláez et al (2007) and complemented by other authors [see Baù et al (2013); Baù and Bombardelli (2014)] is chosen here due to its suitability when dealing with a constant radial thrust problem. This is because it is intrinsically based on a local vertical-local horizontal orbiting frame where a purely radial acceleration component appears as a simple perturbing term in the equations of motions.…”

Regularization in Astrodynamics: applications to relative motion, low-thrust missions, and orbit propagation = Regularización en Astrodinámica: aplicaciones al movimiento relativo, misiones de bajo empuje, y propagación de órbitas

“…Dromo features a second order Sundman transformation that introduces the ideal anomaly, which behaves as the independent variable. Later studies defined a time element to improve the integration of the time transformation Baù and Bombardelli, 2014). The formulation has been progressively improved and the latest version is that by Urrutxua et al (2015b).…”

“…Numerical explorations by Fukushima (2005) yielded two important conclusions about the use of time elements (in the context of the KS regularization): first, the error growth rate is reduced from quadratic to linear; second, it removes the periodic components of the error in unperturbed problems. A detailed review on time elements can be found in the work by Baù and Bombardelli (2014), where they also attached a constant and a linear time element to the set of Dromo elements.…”

Advanced orbit propagation methods applied to asteroids and space debris

“…In unperturbed motion, the fictitious time collapses to the true anomaly measured from the departure point of the ideal frame. The method was then improved by the introduction of a perturbing potential [5] and time elements [4].…”

“…With a linear time element, the rate of growth of the global truncation error behaves linearly instead, but the local truncation error is bigger. Thus, it is advised to use the latter in long-term integrations involving several millions orbits [4,76].…”