GPS Satellites Orbits: Resonance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efeitos de torques gravitacionais na dinâmica de asteróides múltiplos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo da ocorrência de trinca por fadiga em tubos de aços soldados, devido ao transporte

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

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.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

The new Golden Legend: Patrick Nicholas's secular saints

The work of Italian-based photo-artist Patrick Nicholas is analysed to show how his re-workings of classic ‘old-master’ paintings can be seen as the art of ‘redaction,’ shedding new light on the relationship between originality and copying. I argue that redactional creativity is both highly productive of new meanings and a reinvention of the role of the medieval Golden Legend. (Lives of the Saints).

International epidemiology of prostate cancer : geographical distribution and secular trends

This review outlines current international patterns in prostate cancer incidence and mortality rates and survival, including recent trends and a discussion of the possible impact of prostate-specific antigen (PSA) testing on the observed data. Internationally, prostate cancer is the second most common cancer diagnosed among men (behind lung cancer), and is the sixth most common cause of cancer death among men. Prostate cancer is particularly prevalent in developed countries such as the United States and the Scandinavian countries, with about a six-fold difference between high-incidence and low-incidence countries. Interpretation of trends in incidence and survival are complicated by the increasing impact of PSA testing, particularly in more developed countries. As Western influences become more pronounced in less developed countries, prostate cancer incidence rates in those countries are tending to increase, even though the prevalence of PSA testing is relatively low. Larger proportions of younger men are being diagnosed with prostate cancer and living longer following diagnosis of prostate cancer, which has many implications for health systems. Decreasing mortality rates are becoming widespread among more developed countries, although it is not clear whether this is due to earlier diagnosis (PSA testing), improved treatment, or some combination of these or other factors.

Increasing stochastic perturbations enhances acquisition and learning of complex sport movements

Traditionally, the aquisition of skills and sport movement has been characterised by numerous repetitions of presumed model movement pattern to be acquired by learners. This approach has been questioned by research identifying the presence of individualised movement patterns and the low probability of occurrence of two identical movements within and between individuals. In contrast, the differential learning approach claims advantage for incurring variability in the learning process by adding stochastic perturbations during practice. These ideas are exemplified by data from a high jump experiment which compared the effectiveness of classical and a differential training approach with pre-post test design. Results showed clear advantages for the group with additional stochastic perturbation during the aquisition phase in comparison to classically trained athletes. Analogies to similar phenomenological effects in the neurobiological literature are discussed.

Secular changes in BMI and obesity risk in Japanese children: Considerations from a morphologic perspective

The increasing prevalence of childhood obesity is a global health issue. Past studies in Japan have reported an increase in both body mass index (BMI) and risk of obesity among children and adolescents. However, changes in body size and proportion in this population over time have also influenced BMI. To date, no study of secular changes in childhood obesity has considered the impact of changes in morphological factors. The current study explored the secular changes in BMI and childhood obesity risk among Japanese children from 1950 to 2000 with consideration of changes in body size and the proportions using The Statistical Report of the School Health Survey (SHS). The age of peak velocity (PV) occurred approximately two years earlier in both genders across this period. While the increments in height, sitting height and sub-ischial leg length relative to height levelled off by 1980, weight gain continued in boys. Between 1980 and 2000, the rate of the upper body weight gain in boys and girls were 0.7-1.3 kg/decade and 0.2-1.0 kg/decade, respectively. After considering body proportions, increments in body weight were small. It could be suggested that the increments in weight and BMI across the 50-year period may be due to a combination of changes including the tempo of growth and body size due to lifestyle factors.

Metabolomic analysis characterizes tissue specific indomethacin-induced metabolic perturbations of rats

In this study, the promising metabolomic approach integrating with ingenuity pathway analysis (IPA) was applied to characterize the tissue specific metabolic perturbation of rats that was induced by indomethacin. The selective pattern recognition analyses were applied to analyze global metabolic profiling of urine of rats treated by indomethacin at an acute dosage of reference that has been proven to induce tissue disorders in rats, evaluated throughout the time-course of -24-72 h. The results preliminarily revealed that modifications of amino acid metabolism, fatty acid metabolism and energetically associated metabolic pathways accounted for metabolic perturbation of the rats that was induced by indomethacin. Furthermore, IPA was applied to deeply analyze the biomarkers and their relations with the metabolic perturbations evidenced by pattern recognition analyses. Specific biochemical functions affected by indomethacin suggested that there is an important correlation of its effects in kidney and liver metabolism, based on the determined metabolites and their pathway-based analysis. The IPA correlation of the three major biomarkers, identified as creatinine, prostaglandin E2 and guanosine, suggested that the administration of indomethacin induced certain levels of toxicity in the kidneys and liver. The changes in the levels of biomarker metabolites allowed the phenotypical determination of the metabolic perturbations induced by indomethacin in a time-dependent manner.