Effects of the eccentricity on the primames in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Mitigating systematic errors for single frequency GPS receivers employing a penalized least squares methodology

Among the positioning systems that compose GNSS (Global Navigation Satellite System), GPS has the capability of providing low, medium and high precision positioning data. However, GPS observables may be subject to many different types of errors. These systematic errors can degrade the accuracy of the positioning provided by GPS. These errors are mainly related to GPS satellite orbits, multipath, and atmospheric effects. In order to mitigate these errors, a semiparametric model and the penalized least squares technique were employed in this study. This is similar to changing the stochastical model, in which error functions are incorporated and the results are similar to those in which the functional model is changed instead. Using this method, it was shown that ambiguities and the estimation of station coordinates were more reliable and accurate than when employing a conventional least squares methodology.

Real time orbit determination using GPS navigation solution

This work analyses a real time orbit estimator using the raw navigation solution provided by GPS receivers. The estimation algorithm considers a Kalman filter with a rather simple orbit dynamic model and random walk modeling of the receiver clock bias and drift. Using the Topex/Poseidon satellite as test bed, characteristics of model truncation, sampling rates and degradation of the GPS receiver (Selective Availability) were analysed. Copyright © 2007 by ABCM.

Modifying the stochastic model to mitigate GPS systematic errors in relative positioning

The GPS observables are subject to several errors. Among them, the systematic ones have great impact, because they degrade the accuracy of the accomplished positioning. These errors are those related, mainly, to GPS satellites orbits, multipath and atmospheric effects. Lately, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique (PLS). In this method, the errors are modeled as functions varying smoothly in time. It is like to change the stochastic model, in which the errors functions are incorporated, the results obtained are similar to those in which the functional model is changed. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method (CLS). In general, the solution requires a shorter data interval, minimizing costs. The method performance was analyzed in two experiments, using data from single frequency receivers. The first one was accomplished with a short baseline, where the main error was the multipath. In the second experiment, a baseline of 102 km was used. In this case, the predominant errors were due to the ionosphere and troposphere refraction. In the first experiment, using 5 minutes of data collection, the largest coordinates discrepancies in relation to the ground truth reached 1.6 cm and 3.3 cm in h coordinate for PLS and the CLS, respectively, in the second one, also using 5 minutes of data, the discrepancies were 27 cm in h for the PLS and 175 cm in h for the CLS. In these tests, it was also possible to verify a considerable improvement in the ambiguities resolution using the PLS in relation to the CLS, with a reduced data collection time interval. © Springer-Verlag Berlin Heidelberg 2007.

Permanent Magnet Hall Thruster for satellite orbit raising with low power energy consumption

Electric propulsion is now a succeful method for primary propulsion of deep space long duration missions and for geosyncronous satellite attitude control. Closed Drift Thruster, so called Hall Thruster or SPT (Stationary Plasma Thruster), was primarily conceived in USSR (the ancient Soviet Union) and, since then, it has been developed by space agencies, space research institutes and industries in several countries such as France, USA, Israel, Russian Federation and Brazil. In this work we present the main features of the Permanent Magnet Hall Thruster (PMHT) developed at the Plasma Laboratory of the University of Brasilia. The idea of using an array of permanent magnets, instead of an electromagnet, to produce a radial magnetic field inside the plasma channel of the thruster is very significant. It allows the development of a Hall Thruster with power consumption low enough to be used in small and medium size satellites. Description of a new vacuum chamber used to test the second prototype of the PMHT (PHALL II) will be given. PHALL II has an aluminum plasma chamber and is smaller with 15 cm diameter and will contain rare earth magnets. We will show plasma density and temperature space profiles inside and outside the thruster channel. Ion temperature measurements based on Doppler broadening of spectral lines and ion energy measurements are also shown. Based on the measured plasma parameters we constructed an aptitude figure of the PMHT. It contains the specific impulse, total thrust, propellant flow rate and power consumption necessary for orbit raising of satellites. Based on previous studies of geosyncronous satellite orbit positioning we perform numerical simulations of satellite orbit raising from an altitude of 700 km to 36000 km using a PMHT operating in the 100 mN - 500 mN thrust range. In order to perform these calculations integration techniques were used. The main simulation paraters were orbit raising time, fuel mass, total satellite mass, thrust and exaust velocity. We conclude comparing our results with results obtainned with known space missions performed with Hall Thrusters. © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

A study of the relative velocities of small particles that are orbiting the earth

The evolution of the velocity of the particles with respect to the circular orbits of satellites that are around the Earth that the particles will cross, suggests a range of possible velocities of impact as a function of the altitude of the satellite. A study made from those results show that the maximum relative velocities occur at the semi-latus rectum, independent of the initial semi-major axis of the particle. Considering both the solar radiation pressure and the oblateness of the Earth, it is visible that a precession in the orbit occurs and there is also a variation in the eccentricity of the particle as a function of its orbital region and its size. This is important information, because the damage caused in a spacecraft depends on the impact velocity.

Swarm control designs applied to a micro-electro-mechanical gyroscope system (MEMS)

This paper analyzes the non-linear dynamics of a MEMS Gyroscope system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We demonstrated that this model has an unstable behavior. Control problems consist of attempts to stabilize a system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. We also developed a particle swarm optimization technique for reducing the oscillatory movement of the nonlinear system to a periodic orbit. © 2010 Springer-Verlag.

Optimization of satellite constellations in the moon

Nowadays, we return to live a period of lunar exploration. China, Japan and India heavily invest in missions to the moon, and then try to implement manned bases on this satellite. These bases must be installed in polar regions due to the apparent existence of water. Therefore, the study of the feasibility of satellite constellations for navigation, control and communication recovers importance. The Moon's gravitational potential and resonant movements due to the proximity to Earth as the Kozai-Lidov resonance, must be considered in addition to other perturbations of lesser magnitude. The usual satellite constellations provide, as a basic feature, continuous and global coverage of the Earth. With this goal, they are designed for the smallest number of objects possible to perform a specific task and this amount is directly related to the altitude of the orbits and visual abilities of the members of the constellation. However the problem is different when the area to be covered is reduced to a given zone. The required number of space objects can be reduced. Furthermore, depending on the mission requirements it may be not necessary to provide continuous coverage. Taking into account the possibility of setting up a constellation that covers a specific region of the Moon on a non-continuous base, in this study we seek a criterion of optimization related to the time between visits. The propagation of the orbits of objects in the constellation in conjunction with the coverage constraints, provide information on the periods of time in which points of the surface are covered by a satellite, and time intervals in which they are not. So we minimize the time between visits considering several sets of possible constellations and using genetic algorithms.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Artificial satellites: Resonance effects produced by terrestrial tide

Effects due to resonances in the orbital motion of artificial satellites disturbed by the terrestrial tide are analyzed. The nodal co-rotation resonance, apsidal co-rotation resonance and the Lidov-Kozai's mechanism are studied. The effects of the resonances are analyzed through the variations of the metric orbital elements. Libration and circulation motions for high orbits with high eccentricities are verified for the Lidov-Kozai's mechanism.

Peri-orbital bone dimensional analysis using computed tomography for placement of osseointegrated implants

Craniofacial osseointegrated implants enabled producing implant-retained facial prosthesis, namely the orbital prosthesis. Aim: To evaluate the length and width of the bone structure of the peri-orbital region and to present the method validation. Methods: Computed tomography scans of 30 dry human skulls were obtained in order to register linear length and width measurements of the periorbital region. Two examiners made the measurements twice with intervals of at least 7 days between them. Data were analyzed by descriptive statistics and the paired Student's t-test was used as inferential technique (SAS, α =0.05). Results: In most cases, the intra- and inter-examiner variations were not significant (p>0.05). Therefore, the method proposed was considered as precise and valid for the measurement of the peri-orbital region. The measured points correspond to the hours of a clock. The major lengths were observed at 1 h (18.32 mm) for the left peri-orbital bone and at 11h (19.28 mm) for the right peri-orbital bone, followed by the points situated at 2h (13.05 mm) and 12h (11.37 mm) for the left side and at 10 h (12.34 mm) and 12 h (11.56 mm) for the right side. It was verified that the three points with lowest values followed the same anatomical sequence in the supraorbital rim for the right and left orbits, showing compatibility with the insertion of the intraoral osseointegrated implants. The medial wall of both orbits did not present sufficient length to allow the insertion of intraoral or craniofacial implants. Conclusions: The largest width points were observed in the supraorbital rim and in the infralateral region of both orbits and those of smallest width were found in the supralateral region of both orbits.

Artificial satellites dynamics: Resonant effects

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J20 and J40 and the tesseral harmonics J22 and J42. Through successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, two critical angles are studied, 2201 and 4211. Numerical results show the time behavior of the semi-major axis and 2 angle.

Analytical direct planetary perturbations on the orbital motion of satellites

An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. © 2012 Springer Science+Business Media Dordrecht.

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization process we prove that hyperbolic closed poly-trajectories are limit sets of a sequence of limit cycles of smooth vector fields. In our approach the Poincaré Index for non-smooth vector fields is introduced. © 2013 Springer Science+Business Media New York.