Hodei Urrutxua

Constant, Radial Low-Thrust Problem Including First-Order Effects of J2

Tsien studied continuous low-thrust trajectories for Earth escape from circular orbit, and in particular, he provided analytic solutions to the constant radial thrust problem, thereafter also known as the Tsien problem [2]. A comprehensive analysis of the problem was presented by Battin [3], Boltz [4], and latter work by other authors [5, 6, 7, 8] has provided further insight to the problem. The Tsien problem is integrable and admits closed-form solutions in terms of standard elliptic integrals: the radial time evolution depends on the incomplete elliptic integrals of the first and second kinds, and the orbit evolution is known to depend on the incomplete elliptic integral of the third kind [6]. Many alternative analytical solutions have been proposed, both exact [9, 10, 11] and approximate [12], as well as many interesting and innovative applications that build on radial thrust configurations [13, 14]. However, the integrability of the problem does not hold when the Earth’s oblateness perturbation is included in the dynamics. Since the dynamics of the J2 problem are non-integrable (except for equatorial motion), the only possible closed-form solutions are obtained by approximating or averaging the full J2 gravitational potential [15]. Among the many possibilities to approximate the J2 problem, the concept of intermediary orbits is particularly useful. The aim of the intermediary is to capture in an integrable model the main effects of the dynamics of the original problem. If, besides, integrability is found after an infinitesimal contact transformation, the solution improves by incorporating the short-period dynamics into the intermediary. Among these intermediaries, Deprit’s radial intermediary [16] was found particularly ∗Preliminary results were presented at the 26th AAS/AIAA Space Flight Mechanics Meetings in Napa, CA (Paper AAS 16-382) [1]. †New Frontiers Research Fellow, Dpt. of Aeronautics, Astronautics and Computer Engineering, University of Southampton, Highfield. ‡Researcher, ETSI Aeronáuticos, Pz. Cardenal Cisneros 3. Associate Fellow AIAA.

Gravitational Actions upon Tethers in Nonuniform Gravity Fields with Revolution Symmetry

General closed-form expressions for the mutual gravitational potential, resultant, and torque acting upon a rigid tethered system are derived when moving in a nonuniform gravity field produced by an attracting body with revolution symmetry, such that an arbitrary number of zonal harmonics is considered. The final expressions are series expansions in two small parameters related to the reference radius of the primary and the length of the tether, respectively, each of which are scaled by the mutual distance between their centers of mass. A few numerical experiments are performed to study the convergence behavior of the final expressions and conclude that, for high-precision applications, it might be necessary to take into account additional perturbation terms, which come from the mutual two-body interaction.

A New Regularization Method for Fast and Accurate Propagation of Roto-Translationally Coupled Asteroids

There is a well-distinguished group of asteroids for which the roto-translational coupling is known to have a non-negligible effect in the long-term. The study of such asteroids suggests the use of specialized propagation techniques, where perturbation methods make their best. The techniques from which the special regularization method DROMO is derived, have now been extended to the attitude dynamics, with equally remarkable results in terms of speed and accuracy, thus making the combination of these algorithms specially well-suited to deal with the propagation of bodies with strong attitude coupling.

An Asymptotic Solution for the Main Problem

In this paper, an analytical solution of the main problem, a satellite only perturbed by the J2 harmonic, is derived with the aid of perturbation theory and by using DROMO variables. The solution, which is valid for circular and elliptic orbits with generic eccentricity and inclination, describes the instantaneous time variation of all orbital elements, that is, the actual values of the osculating elements.