arXiv subjects

Elena Fantino

Publications and source records attributed to Elena Fantino.

27 records · Page 2Linked to original sources

arXiv2021

Transfer design between neighborhoods of planetary moons in the circular restricted three-body problem

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, comprised of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. In particular, connections between the periodic orbits of such two different moons are achieved. The strategy is applicable for any type of direct transfers that satisfy the analytical constraints. Case studies are presented for the Jovian and Uranian systems. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons.

astro-ph.EP↗

arXiv2021

Review of Lambert's problem

Lambert's problem is the orbital boundary-value problem constrained by two points and elapsed time. It is one of the most extensively studied problems in celestial mechanics and astrodynamics, and, as such, it has always attracted the interest of mathematicians and engineers. Its solution lies at the base of algorithms for, e.g., orbit determination, orbit design (mission planning), space rendezvous and interception, space debris correlation, missile and spacecraft targeting. There is abundancy of literature discussing various approaches developed over the years to solve Lambert's problem. We have collected more than 70 papers and, of course, the issue is treated in most astrodynamics and celestial mechanics textbooks. From our analysis of the documents, we have been able to identify six or seven main solution methods, each associated to a number of revisions and variations, and many, so to say, secondary research lines with little or no posterior development. We have ascertained plenty of literature with proposed solutions, in many cases supplemented by performance comparisons with other methods. We have reviewed and organized the existing bibliography on Lambert's problem and we have performed a quantitative comparison among the existing methods for its solution. The analysis is based on the following issues: choice of the free parameter, number of iterations, generality of the mathematical formulation, limits of applicability (degeneracies, domain of the parameter, special cases and peculiarities), accuracy, and suitability to automatic execution. Eventually we have tested the performance of each code. The solvers that incorporate the best qualities are Bate's algorithm via universal variables with Newton-Raphson and Izzo's Householder algorithm. The former is the fastest, the latter exhibits the best ratio between speed, robustness and accuracy.

math.NA↗

arXiv2021

A Method for Accurate and Efficient Propagation of Satellite Orbits: A Case Study for a Molniya Orbit

Fast and precise propagation of satellite orbits is required for mission design, orbit determination and payload data analysis. We present a method to improve the computational performance of numerical propagators and simultaneously maintain the accuracy level required by any particular application. This is achieved by determining the positional accuracy needed and the corresponding acceptable error in acceleration on the basis of the mission requirements, removing those perturbation forces whose effect is negligible compared to the accuracy requirement, implementing an efficient and precise algorithm for the harmonic synthesis of the geopotential gradient (i.e., the gravitational acceleration) and adjusting the tolerance of the numerical propagator to achieve the prescribed accuracy level with minimum cost. In particular, to achieve the optimum balance between accuracy and computational performance, the number of geopotential spherical harmonics to retain is adjusted during the integration on the basis of the accuracy requirement. The contribution of high-order harmonics decays rapidly with altitude, so the minimum expansion degree meeting the target accuracy decreases with height. The optimum degree for each altitude is determined by making the truncation error of the harmonic synthesis equal to the admissible acceleration error. This paper presents a detailed description of the technique and test cases highlighting its accuracy and efficiency.

astro-ph.EP↗

arXiv2021

Long-Term Orbit Dynamics of Decommissioned Geostationary Satellites

In nominal mission scenarios, geostationary satellites perform end-of-life orbit maneuvers to reach suitable disposal orbits, where they do not interfere with operational satellites. This research investigates the long-term orbit evolution of decommissioned geostationary satellite under the assumption that the disposal maneuver does not occur and the orbit evolves with no control. The dynamical model accounts for all the relevant harmonics of the gravity field at the altitude of geostationary orbits, as well as solar radiation pressure and third-body perturbations caused by the Moon and the Sun. Orbit propagations are performed using two algorithms based on different equations of motion and numerical integration methods: (i) Gauss planetary equations for modified equinoctial elements with a Runge-Kutta numerical integration scheme based on 8-7th-order Dorman and Prince formulas; (ii) Cartesian state equations of motion in an Earth-fixed frame with a Runge-Kutta Fehlberg 7/8 integration scheme. The numerical results exhibit excellent agreement over integration times of decades. Some well-known phenomena emerge, such as the longitudinal drift due to the resonance between the orbital motion and Earth's rotation, attributable to the J22 term of the geopotential. In addition, the third-body perturbation due to Sun and Moon causes two major effects: (a) a precession of the orbital plane, and (b) complex longitudinal dynamics. This study proposes an analytical approach for the prediction of the precessional motion and shows its agreement with the orbit evolution obtained numerically. Moreover, long-term orbit propagations show that the above mentioned complex longitudinal dynamics persists over time scales of several decades. Frequent and unpredictable migrations toward different longitude regions occur, in contrast with the known effects due only to the J22 perturbation.

astro-ph.EP↗

arXiv2021

Feasibility Study of Aerocapture at Mars with an Innovative Deployable Heat Shield

Performing orbital insertion around Mars using aerocapture instead of a propulsive orbit insertion manoeuvre allows to save resources and/or increase the payload mass fraction. Aerocapture has never been employed to date because of the high uncertainties in the parameters from which it depends, mainly related to atmospheric density modeling and navigation errors. The purpose of this work is to investigate the feasibility of aerocapture at Mars with an innovative deployable drag device, whose aperture can be modulated in flight, and assess the effects of the main uncertainties on the success of the manoeuvre. This paper starts with the presentation of a parametric bi-dimensional analysis of the effectiveness of aerocapture, for which a wide range of uncertainty levels in the atmospheric density and the ballistic coefficient are considered. Then, an application to a real mission scenario is carried out including the error of the targeting manoeuvre performed at the limit of the sphere of influence of the planet. The analyses show the strong influence of the uncertainties in the atmospheric density and the ballistic coefficient, which significantly narrow the solution space and limit its continuity. However, viable solutions for aerocapture can still be identified even in the worst conditions.

astro-ph.EP↗

arXiv2021

Science orbits in the Saturn-Enceladus circular restricted three-body problem with oblate primaries

This contribution investigates the properties of a category of orbits around Enceladus. In a previous investigation, a set of heteroclinic connections were designed between halo orbits around the equilibrium points L1 and L2 of the circular restricted three-body problem with Saturn and Enceladus as primaries. The geometrical characteristics of those trajectories makes them good candidates as science orbits for the extended observation of the surface of Enceladus: they are highly inclined, they approach the moon and they are maneuver-free. However, the low heights above the surface and the strong perturbing effect of Saturn require a study of the influence of the polar flattening of the primaries. Therefore, those solutions are here reconsidered with a dynamical model that includes the effect of the oblateness of Saturn and Enceladus, separately and in combination. The dynamical equivalents of the halo orbits around the equilibrium points L1 and L2 and their stable and unstable hyperbolic invariant manifolds are obtained in the perturbed models, and maneuver-free heteroclinic connections are identified. A comparison with the corresponding solutions of the unperturbed problem shows that qualitative and quantitative features are not significantly altered in the perturbed model. The results confirm the scientific value of the solutions obtained in the classical circular restricted three-body problem and suggests that the simpler model can be used in a preliminary feasibility analysis.

astro-ph.EP↗

arXiv2020

Reduction of Saturn Orbit Insertion Impulse using Deep-Space Low Thrust

Orbit insertion at Saturn requires a large impulsive manoeuver due to the velocity difference between the spacecraft and the planet. This paper presents a strategy to reduce dramatically the hyperbolic excess speed at Saturn by means of deep-space electric propulsion. The interplanetary trajectory includes a gravity assist at Jupiter, combined with low-thrust maneuvers. The thrust arc from Earth to Jupiter lowers the launch energy requirement, while an ad hoc steering law applied after the Jupiter flyby reduces the hyperbolic excess speed upon arrival at Saturn. This lowers the orbit insertion impulse to the point where capture is possible even with a gravity assist with Titan. The control-law algorithm, the benefits to the mass budget and the main technological aspects are presented and discussed. The simple steering law is compared with a trajectory optimizer to evaluate the quality of the results and possibilities for improvement.

astro-ph.EP↗

arXiv2019

Minimum Orbital Intersection Distance: Asymptotic Approach

The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications. The most frequent case is that in which both objects have elliptical osculating orbits. When at least one of the two orbits has low eccentricity, the latter can be used as a small parameter in an asymptotic power series expansion. The resulting approximation can be exploited to speed up the computation with negligible cost in terms of accuracy. This contribution introduces two asymptotic procedures into the SDG-MOID method presented in a previous article, it discusses the results of performance tests and their comparisons with previous findings. The best approximate procedure yields a reduction of 40% in computing speed without degrading the accuracy of the determinations. This remarkable result suggests that large benefits can be obtained in applications involving massive distance computations, such as in the analysis of large databases, in Monte Carlo simulations for impact risk assessment or in the long-time monitoring of the minimum orbital intersection distance between two objects.

astro-ph.IM↗

arXiv2005

A new reduction of the raw Hipparcos data

We present an outline of a new reduction of the Hipparcos astrometric data, the justifications of which are described in the accompanying paper. The emphasis is on those aspects of the data analysis that are fundamentally different from the ones used for the catalogue published in 1997. The new reduction uses a dynamical modelling of the satellite's attitude. It incorporates provisions for scan-phase discontinuities and hits, most of which have now been identified. Solutions for the final along-scan attitude (the reconstruction of the satellite's scan phase), the abscissa corrections and the instrument model, originally solved simultaneously in the great-circle solution, are now de-coupled. This is made possible by starting the solution iterations with the astrometric data from the published catalogue. The de-coupling removes instabilities that affected great-circle solutions for short data sets in the published data. The modelling-noise reduction implies smaller systematic errors, which is reflected in a reduction of the abscissa-error correlations by about a factor 40. Special care is taken to ensure that measurements from both fields of view contribute significantly to the along-scan attitude solution. This improves the overall connectivity of the data and rigidity of the reconstructed sky, which is of critical importance to the reliability of the astrometric data. The changes in the reduction process and the improved understanding of the dynamics of the satellite result in considerable formal-error reductions for stars brighter than 8th magnitude.

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