Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

TIME-OPTIMAL GEOMAGNETIC ATTITUDE MANEUVERS OF AN AXISYMMETRICAL SPINNING SATELLITE

A formulation used to determine the time-optimal geomagnetic attitude maneuvers subject to dynamic and geometric constraints is proposed in this paper. This was obtained by a direct search procedure based on a control function parametrization method, using linear programming to obtain numerical suboptimal solutions by linear perturbation. Due to its characteristics it can be used in small computers and to generate computer programs of general application. The dynamic modeling, the magnetic torque model and the suboptimal control procedure are presented. Simulation runs have verified the feasibility of the formulation thus derived and have shown a notable improvement in performance.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Third body perturbation using a single averaged model considering elliptic orbits for the disturbing body

In the present work, we expanded the study done by Solorzanol(1) including the eccentricity of the perturbing body. The assumptions used to develop the single-averaged analytical model are the same ones of the restricted elliptic three-body problem. The disturbing function was expanded in Legendre polynomials up to fourth-order. After that, the equations of motion are obtained from the planetary equations and we performed a set of numerical simulations. Different initial eccentricities for the perturbing and perturbed body are considered. The results obtained perform an analysis of the stability of a near-circular orbits and investigate under which conditions this orbit remain near-circular.

An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing

Satellite remote sensing of ocean colour is the only method currently available for synoptically measuring wide-area properties of ocean ecosystems, such as phytoplankton chlorophyll biomass. Recently, a variety of bio-optical and ecological methods have been established that use satellite data to identify and differentiate between either phytoplankton functional types (PFTs) or phytoplankton size classes (PSCs). In this study, several of these techniques were evaluated against in situ observations to determine their ability to detect dominant phytoplankton size classes (micro-, nano- and picoplankton). The techniques are applied to a 10-year ocean-colour data series from the SeaWiFS satellite sensor and compared with in situ data (6504 samples) from a variety of locations in the global ocean. Results show that spectral-response, ecological and abundance-based approaches can all perform with similar accuracy. Detection of microplankton and picoplankton were generally better than detection of nanoplankton. Abundance-based approaches were shown to provide better spatial retrieval of PSCs. Individual model performance varied according to PSC, input satellite data sources and in situ validation data types. Uncertainty in the comparison procedure and data sources was considered. Improved availability of in situ observations would aid ongoing research in this field. (C) 2010 Elsevier B.V. All rights reserved.

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)

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

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

NDACC/SAOZ UV-visible total ozone measurements: improved retrieval and comparison with correlative ground-based and satellite observations

Accurate long-term monitoring of total ozone is one of the most important requirements for identifying possible natural or anthropogenic changes in the composition of the stratosphere. For this purpose, the NDACC (Network for the Detection of Atmospheric Composition Change) UV-visible Working Group has made recommendations for improving and homogenizing the retrieval of total ozone columns from twilight zenith-sky visible spectrometers. These instruments, deployed all over the world in about 35 stations, allow measuring total ozone twice daily with limited sensitivity to stratospheric temperature and cloud cover. The NDACC recommendations address both the DOAS spectral parameters and the calculation of air mass factors (AMF) needed for the conversion of O-3 slant column densities into vertical column amounts. The most important improvement is the use of O-3 AMF look-up tables calculated using the TOMS V8 (TV8) O-3 profile climatology, that allows accounting for the dependence of the O-3 AMF on the seasonal and latitudinal variations of the O-3 vertical distribution. To investigate their impact on the retrieved ozone columns, the recommendations have been applied to measurements from the NDACC/SAOZ (Systeme d'Analyse par Observation Zenithale) network. The revised SAOZ ozone data from eight stations deployed at all latitudes have been compared to TOMS, GOMEGDP4, SCIAMACHY-TOSOMI, SCIAMACHY-OL3, OMI-TOMS, and OMI-DOAS satellite overpass observations, as well as to those of collocated Dobson and Brewer instruments at Observatoire de Haute Provence (44 degrees N, 5.5 degrees E) and Sodankyla (67 degrees N, 27 degrees E), respectively. A significantly better agreement is obtained between SAOZ and correlative reference ground-based measurements after applying the new O-3 AMFs. However, systematic seasonal differences between SAOZ and satellite instruments remain. These are shown to mainly originate from (i) a possible problem in the satellite retrieval algorithms in dealing with the temperature dependence of the ozone cross-sections in the UV and the solar zenith angle (SZA) dependence, (ii) zonal modulations and seasonal variations of tropospheric ozone columns not accounted for in the TV8 profile climatology, and (iii) uncertainty on the stratospheric ozone profiles at high latitude in the winter in the TV8 climatology. For those measurements mostly sensitive to stratospheric temperature like TOMS, OMI-TOMS, Dobson and Brewer, or to SZA like SCIAMACHY-TOSOMI, the application of temperature and SZA corrections results in the almost complete removal of the seasonal difference with SAOZ, improving significantly the consistency between all ground-based and satellite total ozone observations.

Influence of the resonance in a gravity-gradient stabilized satellite

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

Symplectic actions on coadjoint orbits

We present a compact expression for the field theoretical actions based on the symplectic analysis of coadjoint orbits of Lie groups. The final formula for the action density α c becomes a bilinear form 〈(S, 1/λ), (y, m y)〉, where S is a 1-cocycle of the Lie group (a schwarzian type of derivative in conformai case), λ is a coefficient of the central element of the algebra and script Y sign ≡ (y, m y) is the generalized Maurer-Cartan form. In this way the action is fully determined in terms of the basic group theoretical objects. This result is illustrated on a number of examples, including the superconformal model with N = 2. In this case the method is applied to derive the N = 2 superspace generalization of the D=2 Polyakov (super-) gravity action in a manifest (2, 0) supersymmetric form. As a byproduct we also find a natural (2, 0) superspace generalization of the Beltrami equations for the (2, 0) supersymmetric world-sheet metric describing the transition from the conformal to the chiral gauge.

Application of the GPS system for preliminary satellite orbit determination

In this paper, we discuss a method of preliminary orbit determination for an artificial satellite based on the navigation message of the GPS constellation. Orbital elements are considered as state variables and a simple dynamic model, based on the classic two-body problem, is used. The observations are formed by range and range and range-rate with respect to four visible GPS. A discrete Kalman filter with simulated data is used as filtering technique. The data are obtained through numerical propagation (Cowell's method), which considers special perturbations for the GPS satellite constellation and a user satellite. © 1997 COSPAR. Published by Elsevier Science Ltd.

Influence of Earth's shadow on the rotational motion of an artificial satellite perturbed by solar radiation torque

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite under the influence of the torque due to the solar radiation pressure and taking into account the influence of Earth's shadow. The Earth's shadow is introduced in the equations for the rotational motion as a function depending on the longitude of the Sun, on the ecliptic's obliquity and on the orbital parameters of the satellite. By mapping and computing this function, we can get the periods in which the satellite is not illuminated and the torque due to the solar radiation pressure is zero. When the satellite is illuminated, a known analytical solution is used to predict the satellite's attitude. This analytical solution is expressed in terms of Andoyer's variables and depends on the physical and geometrical properties of the satellite and on the direction of the Sun radiation flux. By simulating a hypothetical circular cylindrical type satellite, an example is exhibited and the results agree quite well when compared with a numerical integration. © 1997 COSPAR. Published by Elsevier Science Ltd.

The stability evolution of a family of simply periodic lunar orbits

The present work deals with a family of simply periodic orbits around the Moon in the rotating Earth Moon-particle system. Taking the framework of the planar, circular, restricted three-body problem, we follow the evolution of this family of periodic orbits using the numerical technique of Poincaré surface of section. The maximum amplitude of oscillation about the periodic orbits are determined and can be used as a parameter to measure the degree of stability in the phase space for such orbits. Despite the fact that the whole family of periodic orbits remain stable, there is a dichotomy in the quasi-periodic ones at the Jacobi constant Cj = 2.85. The quasi-periodic orbits with Cj < 2.85 oscillate around the periodic orbits in a different way from those with Cj > 2.85. © 1999 Elsevier Science Ltd. All rights reserved.

Perturbations to Saturn's F-ring strands at their closest approach to Prometheus

The strange morphology of the F ring of Saturn is thought to be caused by the perturbing effects of two close satellites, Prometheus and Pandora. The F ring and the satellites also experience periodic close encounters as a result of differential precession arising from Saturn's oblateness. Using the orbits of the F-ring strands derived by Murray et al. (1997, Icarus 129, 304-316) the behaviour of the ring particles at their closest approach to Prometheus is analysed using numerical simulations. The results show that a gap and a wave are formed in the ring at each encounter with the satellite. However, the gap is expected to have a short lifetime due to keplerian shear. © 2000 Elsevier Science Ltd. All rights reserved.