Sub-Optimal Orbital Maneuvers for Artificial Satellites

The determination of a specific orbit and the procedure to calculate orbital maneuvers of artificial satellites are problems of extreme importance in the study of orbital mechanics. Therefore, the transferring problem of a spaceship from one orbit to another, and the attention due to this subject has in increased during the last years. Many applications can be found in several space activities, for example, to put a satellite in a geostationary orbit, to change the position of a spaceship, to maintain a specific satellite's orbit, in the design of an interplanetary mission, and others. The Brazilian Satellite SCD-1 (Data Collecting Satellite) will be used as example in this paper. It is the first satellite developed entirely in Brazil, and it remains in operation to this date. SCD-1 was designed, developed, built, and tested by Brazilian scientists, engineers, and technicians working at INPE (National Institute for Space Research, and in Brazilian Industries. During the lifetime, it might be necessary do some complementary maneuvers, being this one either an orbital transferring, or just to make periodical corrections. The purpose of transferring problem is to change the position, velocity and the satellite's mass to a new pre determined state. This transfer can be totally linked (in the case of "Rendezvous") or partially free (free time, free final velocity, etc). In the global case, the direction, the orientation and the magnitude of the thrust to be applied must be chosen, respecting the equipment's limit. In order to make this transferring, either sub-optimal or optimal maneuvers may be used. In the present study, only the sub-optimal will be shown. Hence, this method will simplify the direction of thrust application, to allow a fast calculation that may be used in real time, with a very fast processing. The thrust application direction to be applied will be assumed small and constant, and the purpose of this paper is to find the time interval that the thrust is applied. This paper is basically divided into three parts: during the first one the sub-optimal maneuver is explained and detailed, the second presents the Satellite SCD-1, and finally the last part shows the results using the sub-optimal maneuver applied to the Brazilian Satellite.

Orbital maneuvers using gravitational capture times

Artificial satellites around the Earth can be temporarily captured by the Moon via gravitational mechanisms., How long the capture remains depends on the phase space region where the trajectory is located. This interval of time (capture time) ranges from less than one day (a single passage), up to 500 days, or even more. Orbits of longer times might be very useful for certain types of missions. The advantage of the ballistic capture is to save fuel consumption in an orbit transference from around the Earth to around the Moon. Some of the impulse needed in the transference is saved by the use of the gravitational forces involved. However, the time needed for the transference is elongated from days to months. In the present work we have mapped a significant part of the phase space of the Earth-Moon system, determining the length of the capture times and the origin of the trajectory, if it comes from the Earth direction, or from the opposite direction. Using such map we present a set of missions considering the utilization of the long capture times. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Determination of onboard coplanar orbital maneuvers with orbits determined using GPS

In the present paper a study is made in order to find an algorithm that can calculate coplanar orbital maneuvers for an artificial satellite. The idea is to find a method that is fast enough to be combined with onboard orbit determination using GPS data collected from a receiver that is located in the satellite. After a search in the literature, three algorithms are selected to be tested. Preliminary studies show that one of them (the so called Minimum Delta-V Lambert Problem) has several advantages over the two others, both in terms of accuracy and time required for processing. So, this algorithm is implemented and tested numerically combined with the orbit determination procedure. Some adjustments are performed in this algorithm in the present paper to allow its use in real-time onboard applications. Considering the whole maneuver, first of all a simplified and compact algorithm is used to estimate in real-time and onboard the artificial satellite orbit using the GPS measurements. By using the estimated orbit as the initial one and the information of the final desired orbit (from the specification of the mission) as the final one, a coplanar bi-impulsive maneuver is calculated. This maneuver searches for the minimum fuel consumption. Two kinds of maneuvers are performed, one varying only the semi major axis and the other varying the semi major axis and the eccentricity of the orbit, simultaneously. The possibilities of restrictions in the locations to apply the impulses are included, as well as the possibility to control the relation between the processing time and the solution accuracy. Those are the two main reasons to recommend this method for use in the proposed application.

Effects of the Eccentricity of a Perturbing Third Body on the Orbital Correction Maneuvers of a Spacecraft

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An analytical and numerical study of plane change maneuvers using aerodynamic force

The goal of the present work is to analyze space missions that use the terrestrial atmosphere to accomplish orbital maneuvers that involve a plane change. A set of analytical solutions is presented for the variation of the orbital elements due to a single passage through the atmosphere, assuming that the interval the spacecraft travels through the atmosphere is not too large. The study considers both the lift influence on the spacecraft orbit as well as drag. The final equations are tested with numerical integration and can be considered in accordance with the numerical results whenever the perigee height is larger than a critical value. Next, a numerical study of the ratio between the velocity increment required to correct the semimajor axis decay due to the atmospheric passage and the velocity variation required to obtain the change in the inclination is also presented. This analysis can be used to decide if a maneuver passing through the atmosphere can decrease the fuel consumption of the mission and, in the cases where this technique can be used, if a multiple passage is more efficient than a single passage.

Multispacecraft refueling optimization considering the J2 perturbation and window constraints

The optimization of a near-circular low-Earth-orbit multispacecraft refueling problem is studied. The refueling sequence, service time, and orbital transfer time are used as design variables, whereas the mean mission completion time and mean propellant consumed by orbital maneuvers are used as design objectives. The J2 term of the Earth's nonspherical gravity perturbation and the constraints of rendezvous time windows are taken into account. A hybridencoding genetic algorithm, which uses normal fitness assignment to find the minimum mean propellant-cost solution and fitness assignment based on the concept of Pareto-optimality to find multi-objective optimal solutions, is presented. The proposed approach is demonstrated for a typical multispacecraft refueling problem. The results show that the proposed approach is effective, and that the J2 perturbation and the time-window constraints have considerable influences on the optimization results. For the problems in which the J2 perturbation is not accounted for, the optimal refueling order can be simply determined as a sequential order or as the order only based on orbitalplane differences. In contrast, for the problems that do consider the J2 perturbation, the optimal solutions obtained have a variety of refueling orders and use the drift of nodes effectively to reduce the propellant cost for eliminating orbital-plane differences. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

GPS Satellites Orbits: Resonance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alternative paths for insertion of probes into high inclination lunar orbits

The dynamics of the restricted three-body Earth-Moon-particle problem predicts the existence of direct periodic orbits around the Lagrangian equilibrium point L1. From these orbits, we derive a set of trajectories that form links between the Earth and the Moon and are capable of performing transfers between terrestrial and lunar orbits, in addition to defining an escape route from the Earth-Moon system. When we consider a more complex and realistic dynamical system - the four-body Sun-Earth-Moon-particle (probe) problem - the trajectories have an expressive gain of inclination when they penetrate in the lunar influence sphere, thus allowing the insertion of probes into low-altitude lunar orbits with high inclinations, including polar orbits. In this study, we present these links and investigate some possibilities for performing an Earth-Moon transfer based on these trajectories. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A numerical study of powered Swing-Bys around the Moon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Searching for capture and escape trajectories around Jupiter using its Galilean satellites

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Orbital propagation for Brazilian satellites using NORAD models

The performance of the NORAD models for near Earth satellites (SGP, SGP4, SGP8) using two Brazilian flying satellites, SCD-1 and SCD-2, and the Chinese-Brazilian satellite CBERS-1 is compared. The achievable accuracy of such models is compared against the predicted 2-lines elements set for the satellites. Every week an updated fresh set of 2-lines elements for these satellites is made available through the Internet. About ten years of observations of the SCD-1 satellite are available and therefore solar activity influences on the orbit can be analyzed. Data are selected considering also orbital (for CBERS-1) and attitude (for SCD-2) maneuvers - (C) 2002 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.