1,720,980 research outputs found
Analytical perturbation method for frozen orbits around the asteroid 433 Eros
No full textIn this paper a method for obtaining initial condition for frozen orbits around fast rotating, highly irregular bodies is presented. Such method is based on a general perturbative theory of motion, for inhomogeneous gravitational fields. Taking into account the terms of the gravitational potential up to an arbitrary order to construct a precise Hamiltonian formulation of the problem, the system is averaged both over the argument of node and the mean anomaly, to reduce its complexity (i.e. the number of degrees of freedom). An approximate system is obtained, which provides an accurate description of the dynamics of the initial system. This can be applied to every celestial body and in particular, can be exploited for constructing a method for finding initial conditions to yield frozen orbits. These orbits can then be used as reference trajectories in missions that require close inspection of asteroids. To this end applications to derive frozen orbits for Eros 433 have been provided which could be of key interest for every observational, discovery mission around this asteroid
Low thrust propulsion in a coplanar circular restricted four body problem
No full textThis paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model
Analytic perturbative theories in highly inhomogeneous gravitational fields
No full textOrbital motion about irregular bodies is highly nonlinear due to inhomogeneities in the gravitational field. Classical theories of motion close to spheroidal bodies cannot be applied as for inhomogeneous bodies the Keplerian forces do not provide a good approximation of the system dynamics. In this paper a closed form, analytical method for developing the motion of a spacecraft around small bodies is presented, for the so called fast rotating case, which generalize previous results to second order, arbitrary degree, gravitational fields. Through the application of two different Lie transformations, suitable changes of coordinates are found, which reduce the initial non integrable Hamiltonian of the system into an integrable one plus a negligible, perturbative remainder of higher degree. In addition, an explicit analytical formulation for the relegated, first and second order, arbitrary degree Hamiltonian for relatively high altitude motion in any inhomogeneous gravitational field is derived in closed-form. Applications of this algorithm include a method for determining initial conditions for frozen orbits around any irregular body by simply prescribing the desired inclination and eccentricity of the orbit. This method essentially reduces the problem of computing frozen orbits to a problem of solving a 2-D algebraic equation. Results are shown for the asteroid 433-Eros
Nonlinearly stable equilibria in the Sun-Jupiter-Trojan-Spacecraft four body problem
No full textThe Trojan asteroids have been highlighted as a main target for future discovery missions, which will enable key questions about the formation of our Solar system to be answered. Programs like the Japanese Jupiter and Trojan Asteroids Exploration Programme are already testing technology demonstrators like the IKAROS spacecraft to enable future interplanetary missions to Jupiter and the Trojans. In this paper an analytic analysis of the stability of the Low thrust Sun Jupiter Asteroid Spacecraft system, is presented, from a Hamiltonian point of view. Setting the three primaries in the stable Lagrangian equilateral triangle configuration, eight natural (i.e. with zero thrust) equilibrium points are identified, four of which are close to the asteroid, two stable and two unstable, when considering as primaries the Sun and any other two bodies of the Solar System. Artificial equilibria, which can be seen as low thrust perturbations of the natural ones, are then taken into account with the aim of identifying their linearly stable subset. The Lyapunov stability of these marginally stable points is then analysed using basic KAM (Kolmogorov Arnold Moser) theory and Arnold’s stability theorem. In order to apply such theorem an iterative procedure to reduce the Hamiltonian into Birkhoff’s Normal Form is applied up to fourth order, explicitly defining, at each step, the generating function of a symplectic transformation. Despite the complexity of this process, Normal Forms are a fundamental, necessary step for any application of KAM theory; such theory, transforming a non-integrable system into a sum of perturbed integrable ones, enables the computation of a high order analytical approximation of the system dynamics, plus an estimation of the discrepancy from the initial model. As an application of KAM theory, a proof of the nonlinear stability for the low thrust generated equilibrium points under non resonant conditions is found using Arnold’s stability theorem. Results show that Lyapunov stability is guaranteed along the linearly stable domain with the exception of a set of points with zero measure where the conditions to apply Arnold‘s theorem are not satisfied
Extension of low-thrust propulsion to the autonomous coplanar circular restricted four body problem with application to future Trojan Asteroid missions
No full textAn Autonomous Coplanar Circular Restricted Four Body Problem (CRFBP) is considered, where the massless body is a low-thrust spacecraft. 'Natural' and 'artificial' (i.e. created with the use of continuous low-thrust propulsion) equilibrium solutions are identified, that have the potential to be exploited in future science missions. Results show that, with zero thrust, there are unstable equilibrium points close to the third primary. However, artificial equilibrium points, displaced from the natural ones, can be generated with the use of constant low-thrust. Furthermore, these points are proved to be stable in certain regions about the third primary mass. This is particularly advantageous since it means that it would be possible to continuously maintain a spacecraft about these strategic observation points, close to the smaller primary, without the need for state feedback control. The Sun-Jupiter-Trojan Asteroid-Spacecraft system is considered, as a particular case of the Autonomous Coplanar CRFBP. Curves of artificial equilibrium points are then identified. Furthermore, the stability analysis of these points reveals the region where they are stable. In this region four bounded orbits close to the Asteroid are proved to exist, that can be reached and maintained with a constant low-thrust lower than 10µN
Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields : A first approach
Full text linkThis article provides a method for nding initial conditions for perturbed frozen orbits around inhomogeneous fast rotating asteroids. These orbits can be used as reference trajectories in missions that require close inspection of any rigid body. The generalized perturbative procedure followed exploits the analytical methods of relegation of the argument of node and Delaunay normalisation to arbitrary order. These analytical methods are extremely powerful but highly computational. The gravitational potential of the heterogeneous body is rstly stated, in polar-nodal coordinates, which takes into account the coecients of the spherical harmonics up to an arbitrary order. Through the relegation of the argument of node and the Delaunay normalization, a series of canonical transformations of coordinates is found, which reduces the Hamiltonian describing the system to a integrable, two degrees of freedom Hamiltonian plus a truncated reminder of higher order. Setting eccentricity, argument of pericenter and inclination of the orbit of the truncated system to be constant, initial conditions are found, which evolve into frozen orbits for the truncated system. Using the same initial conditions yields perturbed frozen orbits for the full system, whose perturbation decreases with the consideration of arbitrary homologic equations in the relegation and normalization procedures. Such procedure can be automated for the first homologic equation up to the consideration of any arbitrary number of spherical harmonics coefficients. The project has been developed in collaboration with the European Space Agency (ESA)
Analytic estimates and topological properties of the weak stability boundary
No full textThe weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3 body problem (PCR3BP), 1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; 2) a precise description of the topology of the WSB; 3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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