A Special Perturbation Method in Orbital Dynamics

Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained nu- merically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators —both in runtime and precisión that constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of sin- gularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions

Saturn power generation with electrodynamic tethers in polar orbit

A power generation scheme based on bare electrodynamic tethers (EDT), working in passive mode is investigated for the purpose of supplying power to scientific missions at Saturn. The system employs a spinning EDT on a lowaltitude polar orbit which permits to efficiently convert plasmasphere energy into useful power. After optimizing the tether design for power generation we compute the supplied power along the orbit and the impact of the Lorentz force on the orbital elements as function of the tether and orbit characteristics. Although uncertainties in the current ionosphere density modeling strongly affect the performance of the system the peak power density of the EDT appears be greater than conventional power systems.

A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations.

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