Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L ₁ and beyond L ₂ where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s².     

Artificial frozen orbits around Mercury

Orbits around Mercury are influenced by the strong elliptic third-body perturbation, especially for high eccentricity orbits, the periapsis altitude changes dramatically. Frozen orbits whose mean eccentricity and argument of perigee remain constants are obviously a good choice for space missions, but the forming conditions are too harsh to meet practical needs. To deal with this problem, a continuous control method that combines analytical theory and parameter optimization is proposed to build an artificial frozen orbit. The artificial frozen orbits are investigated on the basis of double averaged Hamiltonian, of which the second and third zonal harmonics and the perturbation of elliptic third-body gravity are considered. In this paper, coefficients of perturbations which satisfy the conditions of frozen orbits are involved as control parameters, and the relevant artificial perturbations are compensated by the control strategy. So probes around Mercury can be kept on frozen orbit under the influence of continuous control force. Then complex method of optimization is used to search for the energy optimized artificial frozen orbits. The choosing of optimal parameters, the objective function setting and other issues are also discussed in the study. Evolution of optimal control parameters are given in large ranges of semi-major axis and eccentricity, through the variation of these curves, the fuel efficiency is discussed. The result shows that the control method proposed in this paper can effectively maintain the eccentricity and argument of perigee frozen.     

Analytical investigations of quasi-circular frozen orbits in the Martian gravity field

Frozen orbits are always important foci of orbit design because of their valuable characteristics that their eccentricity and argument of pericentre remain constant on average. This study investigates quasi-circular frozen orbits and examines their basic nature analytically using two different methods. First, an analytical method based on Lagrangian formulations is applied to obtain constraint conditions for Martian frozen orbits. Second, Lie transforms are employed to locate these orbits accurately, and draw the contours of the Hamiltonian to show evolutions of the equilibria. Both methods are verified by numerical integrations in an 80 × 80 Mars gravity field. The simulations demonstrate that these two analytical methods can provide accurate enough results. By comparison, the two methods are found well consistent with each other, and both discover four families of Martian frozen orbits: three families with small eccentricities and one family near the critical inclination. The results also show some valuable conclusions: for the majority of Martian frozen orbits, argument of pericentre is kept at 270° because J ₃ has the same sign as J ₂; while for a minority of ones with low altitude and low inclination, argument of pericentre can be kept at 90° because of the effect of the higher degree odd zonals; for the critical inclination cases, argument of pericentre can also be kept at 90°. It is worthwhile to note that there exist some special frozen orbits with extremely small eccentricity, which could provide much convenience for reconnaissance. Finally, the stability of Martian frozen orbits is estimated based on the trace of the monodromy matrix. The analytical investigations can provide good initial conditions for numerical correction methods in the more complex models.     

Multi-rendezvous low-thrust trajectory optimization using costate transforming and homotopic approach

This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient.     

Accurate Mars Express orbits to improve the determination of the mass and ephemeris of the Martian moons

The determination of the ephemeris of the Martian moons has benefited from observations of their plane-of-sky positions derived from images taken by cameras onboard spacecraft orbiting Mars. Images obtained by the Super Resolution Camera (SRC) onboard Mars Express (MEX) have been used to derive moon positions relative to Mars on the basis of a fit of a complete dynamical model of their motion around Mars. Since, these positions are computed from the relative position of the spacecraft when the images are taken, those positions need to be known as accurately as possible. An accurate MEX orbit is obtained by fitting two years of tracking data of the Mars Express Radio Science (MaRS) experiment onboard MEX. The average accuracy of the orbits has been estimated to be around 20–25 m. From these orbits, we have re-derived the positions of Phobos and Deimos at the epoch of the SRC observations and compared them with the positions derived by using the MEX orbits provided by the ESOC navigation team. After fit of the orbital model of Phobos and Deimos, the gain in precision in the Phobos position is roughly 30 m, corresponding to the estimated gain of accuracy of the MEX orbits. A new solution of the GM of the Martian moons has also been obtained from the accurate MEX orbits, which is consistent with previous solutions and, for Phobos, is more precise than the solution from the Mars Global Surveyor (MGS) and Mars Odyssey (ODY) tracking data. It will be further improved with data from MEX-Phobos closer encounters (at a distance less than 300 km). This study also demonstrates the advantage of combining observations of the moon positions from a spacecraft and from the Earth to assess the real accuracy of the spacecraft orbit. In turn, the natural satellite ephemerides can be improved and participate to a better knowledge of the origin and evolution of the Martian moons.     

Equilibria and orbits around asteroid using the polyhedral model

In the current study, we use the polyhedral model to compute the potential of the asteroid. There are five equilibrium points in the gravitational field of the asteroid 283 Emma. We concluded that the zero-velocity surfaces and the equilibrium points change with the suppositive variation of the rotational speed of the asteroid. It is found that if the rotational speed equals a half as it is in present, the number of equilibrium points is also five. However, if the rotational speed equals twice as it is in present, there are only three equilibrium points left. Four different periodic orbits are calculated using the hierarchical grid searching method. We calculated characteristic multipliers of periodic orbits to investigate the stability of these periodic orbits. The orbit near the primary's equatorial plane is more likely to be stable when the separation/ primary-radius is a large number.     

A deep search for Martian dust rings and inner moons using the Hubble Space Telescope

It has long been suspected that Mars might be encircled by two faint rings, one originating from each of its moons Phobos and Deimos. Meteoroid impacts into these moons should release clouds of dust that quickly spread out to become rings; similar dust rings have been associated with several small inner moons of the gas giants. On May 28, 2001 Mars’ hypothetical ring plane appeared edge-on to Earth within weeks of its opposition, providing the best Earth-based opportunity to detect these rings in several decades. Using the Wide Field/Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we obtained a set of deep exposures off the east and west limbs of Mars to search for these hypothetical rings. No rings were detected. This result limits normal optical depths to ∼3×10⁻⁸ for the Phobos ring and ∼10⁻⁷ for the Deimos ring. These limits fall at the low end of prior dynamical predictions and a factor of 1000 below previous observational limits. However, our limit for the Deimos ring is more tentative because of large uncertainties about this ring's expected shape, size and orientation. Our data set is also sensitive to small, previously undetected inner moons. No moons were detected down to a radius limit of 75–125 m. Longitudinal coverage of the region near and between Phobos and Deimos is 40–80% complete. We conclude by describing a promising opportunity for further Martian ring viewing in December 2007.     

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

The dynamics of the circular restricted three-body Earth-Moon-particle problem predicts the existence of the retrograde periodic orbits around the Lagrangian equilibrium point L1. Such orbits belong to the so-called family G (Broucke, Periodic orbits in the restricted three-body problem with Earth-Moon masses, JPL Technical Report 32–1168, 1968) and starting from them it is possible to define a set of trajectories that form round trip links between the Earth and the Moon. These links occur even with more complex dynamical systems as the complete Sun-Earth-Moon-particle problem. One of the most remarkable properties of these trajectories, observed for the four-body problem, is a meaningful inclination gain when they penetrate into the lunar sphere of influence and accomplish a swing-by with the Moon. This way, when one of these trajectories returns to the proximities of the Earth, it will be in a different orbital plane from its initial Earth orbit. In this work, we present studies that show the possibility of using this property mainly to accomplish transfer maneuvers between two Earth orbits with different altitudes and inclinations, with low cost, taking into account the dynamics of the four-body problem and of the swing-by as well. The results show that it is possible to design a set of nominal transfer trajectories that require ΔV _Total less than conventional methods like Hohmann, bi-elliptic and bi-parabolic transfer with plane change.     

Decomposition of mineral absorption bands using nonlinear least squares curve fitting: Application to Martian meteorites and CRISM data

This study advances curve-fitting modeling of absorption bands of reflectance spectra and applies this new model to spectra of Martian meteorites ALH 84001 and EETA 79001 and data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM). This study also details a recently introduced automated parameter initialization technique. We assess the performance of this automated procedure by comparing it to the currently available initialization method and perform a sensitivity analysis of the fit results to variation in initial guesses. We explore the issues related to the removal of the continuum, offer guidelines for continuum removal when modeling the absorptions and explore different continuum-removal techniques. We further evaluate the suitability of curve fitting techniques using Gaussians/Modified Gaussians to decompose spectra into individual end-member bands. We show that nonlinear least squares techniques such as the Levenberg–Marquardt algorithm achieve comparable results to the MGM model (Sunshine and Pieters, 1993, Sunshine et al., 1990) for meteorite spectra. Finally we use Gaussian modeling to fit CRISM spectra of pyroxene and olivine-rich terrains on Mars. Analysis of CRISM spectra of two regions show that the pyroxene-dominated rock spectra measured at Juventae Chasma were modeled well with low Ca pyroxene, while the pyroxene-rich spectra acquired at Libya Montes required both low-Ca and high-Ca pyroxene for a good fit.     

A southern hemisphere survey of meteor shower radiants and associated stream orbits using single station radar observations

The 33.2 MHz interferometric meteor radars located at Davis Station, Antarctica and Darwin, Australia typically detect around 15 000 specular underdense meteor echoes every day. While the angle of arrival of the scattered radio wave can be inferred using phase differences between receive antennae, the direction of individual meteors is not known beyond a plane of ambiguity perpendicular to the angle of arrival. Using the great circle mapping technique with a Jones & Jones type weighting function, 37 meteor shower systems were detected in data collected at both locations over 2006–2007, including nine undocumented showers. The orbital elements of the parent debris streams were then calculated for the 31 showers where sufficiently precise measurements were available.     

Stellar Spectral Classification using Principal Component Analysis and Artificial Neural Networks

A fast and robust method of classifying a library of optical stellar spectra for O to M type stars is presented. The method employs, as tools: (1) principal component analysis (PCA) for reducing the dimensionality of the data and (2) multilayer back propagation network (MBPN) based artificial neural network (ANN) scheme to automate the process of classification. We are able to reduce the dimensionality of the original spectral data to very few components by using PCA and are able to successfully reconstruct the original spectra. A number of NN architectures are used to classify the library of test spectra. Performance of ANN with this reduced dimension shows that the library can be classified to accuracies similar to those achieved by Gulati et al. but with less computational load. Furthermore, the data compression is so efficient that the NN scheme successfully classifies to the desired accuracy for a wide range of architectures. The procedure will greatly improve our capabilities in handling and analysing large spectral data bases of the future.     

A search for amino acids and nucleobases in the Martian meteorite Roberts Massif 04262 using liquid chromatography‐mass spectrometry

The investigation into whether Mars contains signatures of past or present life is of great interest to science and society. Amino acids and nucleobases are compounds that are essential for all known life on Earth and are excellent target molecules in the search for potential Martian biomarkers or prebiotic chemistry. Martian meteorites represent the only samples from Mars that can be studied directly in the laboratory on Earth. Here, we analyzed the amino acid and nucleobase content of the shergottite Roberts Massif (RBT) 04262 using liquid chromatography‐mass spectrometry. We did not detect any nucleobases above our detection limit in formic acid extracts; however, we did measure a suite of protein and nonprotein amino acids in hot‐water extracts with high relative abundances of β‐alanine and γ‐amino‐n‐butyric acid. The presence of only low (to absent) levels of several proteinogenic amino acids and a lack of nucleobases suggest that this meteorite fragment is fairly uncontaminated with respect to these common biological compounds. The distribution of straight‐chained amine‐terminal n‐ω‐amino acids in RBT 04262 resembled those previously measured in thermally altered carbonaceous meteorites (Burton et al. 2012; Chan et al. 2012). A carbon isotope ratio of ?24‰ ± 6‰ for β‐alanine in RBT 04262 is in the range of reduced organic carbon previously measured in Martian meteorites (Steele et al. 2012). The presence of n‐ω‐amino acids may be due to a high temperature Fischer‐Tropsch‐type synthesis during igneous processing on Mars or impact ejection of the meteorites from Mars, but more experimental data are needed to support these hypotheses.     

Prediction of satellite orbits contraction due to diurnally varying oblate atmosphere and altitude-dependent scale height using KS canonical elements

A new non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of uniformly regular KS canonical elements. Diurnally varying oblate atmosphere is considered with variation in density scale height dependent on altitude. The series expansion method is utilized to generate the analytical solutions and terms up to fourth-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere) are retained. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The important drag perturbed orbital parameters: semi-major axis and eccentricity are obtained up to 500 revolutions, with the present analytical theory and by numerical integration over a wide range of perigee height, eccentricity and inclination. The differences between the two are found to be very less. A comparison between the theories generated with terms up to third- and fourth-order terms in c and e shows an improvement in the computation of the orbital parameters semi-major axis and eccentricity, up to 9%. The theory can be effectively used for the re-entry of the near-Earth objects, which mainly decay due to atmospheric drag.     

Quantitative in situ XRD measurement of shock metamorphism in Martian meteorites using lattice strain and strain‐related mosaicity in olivine

All Martian meteorites have experienced shock metamorphism to some degree. We quantitatively determined shock‐related strain in olivine crystals to measure shock level and peak shock pressure experienced by five Martian meteorites. Two independent methods employing nondestructive in situ micro X‐ray diffraction (μXRD) are applied, i.e., (1) the lattice strain method, in which the lattice strain value (ε) for each olivine grain is derived from a Williamson–Hall plot using its diffraction pattern (peak width variation with diffraction angle) with reference to a best fit calibration curve of ε values obtained from experimentally shocked olivine grains; (2) the strain‐related mosaicity method, allowing shock stage to be estimated by measuring the streaking along the Debye rings of olivine grain diffraction spots to define their strain‐related mosaic spread, which can then be compared with olivine mosaicity in ordinary chondrites of known shock stage. In this study, both the calculated peak shock pressures and the estimated shock stages for Dar al Gani 476 (45.6 ± 0.6 GPa), Sayh al Uhaymir 005/8 (46.1 ± 2.2 GPa), and Nakhla (18.0 ± 0.6 GPa) compare well with literature values. Formal shock assessments for North West Africa 1068/1110 (53.9 ± 2.1 GPa) and North West Africa 6234 (44.6 ± 3.1 GPa) have not been reported within the literature; however, their calculated peak shock pressures fall within the range of peak shock pressures defining their estimated shock stages. The availability of nondestructive and quantitative μXRD methods to determine shock stage and peak shock pressure from olivine crystals provides a key tool for shock metamorphism analysis.     

Spacecraft intercept using minimum control energy and wait time

A new approach to the minimum energy impulse intercept problem for spacecraft in orbit is explored. The types of orbits investigated in this paper are not restricted to a particular one. The constrained optimization technique is formulated with the universal variable, which is used to describe orbit information with sufficient accuracy for general types of orbits. Two optimization problems are posed. First, a problem for minimum velocity change and time of flight for intercept are investigated with the constraint on the final position of two satellites. Next, the so-called wait time is also added as an additional parameter to be determined. Although a closed-form solution is not obtained, the Newton iteration technique is successfully applicable. Finally, by numerically comparing the proposed solution to the Hohmann transfer, the suggested approach is demonstrated to be a feasible technique applicable to a broad class of orbit transfer problems.     

Morphological Classification of Galaxies using Computer Vision and Artificial Neural Networks: A Computational Scheme

The morphology of galaxies is an important issue in the large scale study of the Universe. The Hubble Deep Field project has already shown that the Universe contains billions and billions of galaxies. The Sloan Digital Sky Survey is expected to map the sky for one million galaxies. One of the major challenges facing astronomers today is how to automatically identify and classify large number of galaxies that will began to show up in the hundreds of thousands of digitized images from sky surveys. Today it is possible to address this problem with the help of advances occurring in computer vision and artificial neural networks technology. This paper describes a computational scheme to develop an automatic galaxy classifier. From the scheme it is possible to visualize several different types of automatic galaxy classifiers. Two types are presented here with prototype models. The first type uses the geometric shape features as the basis for classification. The second uses the direct pixel images of galaxies and artificial neural networks to do the classification. The results show that geometric shape features are very good indicators of different types of nearby galaxies. Three test cases were presented to the prototype geometric shape classifier and it was able to successfully classify all three of them. The direct image based neural network classifier was able to learn 97% of the 171 training patterns presented to it. However when the network was presented a test set of 37 independent patterns, it was only able to classify 57% percent of the test cases. This study demonstrates that a very robust and efficient automated galaxy classifier based on shape features and artificial neural network can be develop. This revised version was published online in July 2006 with corrections to the Cover Date.     

Attitude dynamics and control of spacecraft using geomagnetic Lorentz force

Attitude stabilization of a charged rigid spacecraft in Low Earth Orbit using torques due to Lorentz force in pitch and roll directions is considered. A spacecraft that generates an electrostatic charge on its surface in the Earth's magnetic field will be subject to perturbations from the Lorentz force. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft's orientation. We assume that the spacecraft is moving in the Earth's magnetic field in an elliptical orbit under the effects of gravitational, geomagnetic and Lorentz torques. The magnetic field of the Earth is modeled as a non-tilted dipole.A model incorporating all Lorentz torques as a function of orbital elements has been developed on the basis of electric and magnetic fields. The stability of the spacecraft orientation is investigated both analytically and numerically. The existence and stability of equilibrium positions is investigated for different values of the charge to mass ratio(α*). Stable orbits are identified for various values of α*. The main parameters for stabilization of the spacecraft are α*and the difference between the components of the moment of inertia for the spacecraft.