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Elliptical shape-based model for multi-revolution planeto-centric mission scenarios Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2021-01-11 Jacopo Prinetto, Michelle Lavagna
The paper presents a novel 3-dimensional shape-based algorithm which extends the domain of analytical solutions to planeto-centric mission scenarios, which classically entail even thousands revolutions to transfer to the final orbit. Thanks to the strong physical meaning the proposed method keeps while shaping the trajectory, the method succeeds in outputting a solution close to the real optimum. The
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Attitude dynamics of a rigid body in Keplerian motion Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2021-01-10 Roshan T. Eapen, Manoranjan Majji, Kyle T. Alfriend
This paper studies the attitude dynamics of a rigid body in a Keplerian orbit. We show that the use of Classical Rodrigues Parameters for the attitude motion of the rigid body subject to gravity-gradient torques enables us to characterize the equilibria associated with the rotational motion about its mass center. A parametric study of the stability of equilibria is conducted to show that large oscillations
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Long-term evolution of orbital inclination due to third-body inclination Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2021-01-06 Tao Nie, Pini Gurfil
The effects of third-body perturbations on natural and artificial satellite orbits have been studied extensively. However, much less attention has been given to the case considering the orbital inclination of the third body. In this paper, it is shown that a perturbed orbit, even with a small initial inclination—much less than the critical Kozai inclination of 39.23 degrees—may significantly increase
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Central configurations in the spatial n -body problem for $$n=5,6$$ n = 5 , 6 with equal masses Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-12-08 Małgorzata Moczurad, Piotr Zgliczyński
We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for \(n=5\) and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for \(n=4,5,6,7\) and in the spatial case for \(n=4
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Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-27 Ioannis Gkolias, Elisa Maria Alessi, Camilla Colombo
Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun–Earth line. Resonant interactions lead to non-trivial orbital evolution
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Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-25 Vitor M. de Oliveira, Priscilla A. Sousa-Silva, Iberê L. Caldas
In this work, we investigate the Earth–Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point \(L_1\) is always open, but the orbits are bounded due to Hill stability. First,
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Impact probability under aleatory and epistemic uncertainties Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-25 Chiara Tardioli, Davide Farnocchia, Massimiliano Vasile, Steve R. Chesley
We present an approach to estimate an upper bound for the impact probability of a potentially hazardous asteroid when part of the force model depends on unknown parameters whose statistical distribution needs to be assumed. As case study, we consider Apophis’ risk assessment for the 2036 and 2068 keyholes based on information available as of 2013. Within the framework of epistemic uncertainties, under
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Analytical stability in the Caledonian Symmetric Five-Body Problem Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-25 B. A. Steves, M. Shoaib, Winston L. Sweatman
In this paper, we develop an analytical stability criterion for a five-body symmetrical system, called the Caledonian Symmetric Five-Body Problem (CS5BP), which has two pairs of equal masses and a fifth mass located at the centre of mass. The CS5BP is a planar problem that is configured to utilise past–future symmetry and dynamical symmetry. The introduction of symmetries greatly reduces the dimensions
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Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman–Deprit coordinates Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-25 S. Ferrer, F. Crespo, J. L. Zapata
We study the reduction and regularization processes of perturbed Keplerian systems from an astronomical point of view. Our approach connects axially symmetric perturbed 4-DOF oscillators with Keplerian systems, including the case of rectilinear solutions. This is done through a preliminary reduction recently studied by the authors. Then, the reduction program continues by removing the Keplerian energy
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Higher-order sensitivity matrix method for probabilistic solution to uncertain Lambert problem and reachability set problem Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-11-01 Zach Hall, Puneet Singla
This paper presents a derivative-free method for computing approximate solutions to the uncertain Lambert problem (ULP) and the reachability set problem (RSP) while utilizing higher-order sensitivity matrices. These sensitivities are analogous to the coefficients of a Taylor series expansion of the deterministic solution to the ULP and RSP, and are computed in a derivative-free and computationally
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The Manifold Of Variations: hazard assessment of short-term impactors Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-10-30 Alessio Del Vigna
When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to overcome this problem is based on the systematic ranging and combined with the Admissible Region theory to constrain the poorly-determined topocentric range and range-rate
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Science orbit design with a quasi-frozen beta angle: effects of body obliquity on J2-perturbed dynamics Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-10-11 Kenshiro Oguri, Gregory Lantoine, William Hart, Jay McMahon
The beta angle, an angle formed by the sunlight and a spacecraft orbital plane, is an important parameter for science orbit design of orbiter missions. This angle defines lighting conditions and eclipse occurrences, and is used for science observation planning. Not only is this parameter perturbed by the irregular gravity field of the primary body, it varies with the body’s motion around the Sun. Investigating
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The precession and nutations of a rigid Mars Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-09-29 Rose-Marie Baland, Marie Yseboodt, Sébastien Le Maistre, Attilio Rivoldini, Tim Van Hoolst, Véronique Dehant
The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and
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Analysis of regular precession conditions for asymmetrical liquid-filled rigid bodies Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-09-28 V. Yu. Ol’shanskii
To describe the rotation of a “rigid mantle + liquid core” system, the Poincaré–Hough–Zhukovsky equations are used. An analysis is made of the previously obtained (Ol’shanskii in Celest Mech Dyn Astron 131(12):Article number:57, 2019) conditions for regular precession of a system that does not have an axial symmetry. Upon receipt of the conditions, it is considered that the external torque can be neglected
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The effect of zonal harmonics on dynamical structures in the circular restricted three-body problem near the secondary body Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-09-25 Luke Bury, Jay McMahon
The circular restricted three-body model is widely used for astrodynamical studies in systems where two major bodies are present. However, this model relies on many simplifications, such as point-mass gravity and planar, circular orbits of the bodies, and limiting its accuracy. In an effort to achieve higher-fidelity results while maintaining the autonomous simplicity of the classic model, we employ
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On the dynamical origins of retrograde Jupiter Trojans and their connection to high-inclination TNOs Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-09-19 Tobias Köhne, Konstantin Batygin
Over the course of the last decade, observations of highly inclined (orbital inclination i > 60\(^\circ \)) trans-Neptunian objects (TNOs) have posed an important challenge to current models of solar system formation (Levison et al. in Icarus 196(1):258–273, 2008; Nesvorný in Astron J 150:73, 2015). These remarkable minor planets necessitate the presence of a distant reservoir of strongly out-of-plane
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Long-period comets as a tracer of the Oort cloud structure Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-09-02 Marc Fouchard; Vacheslav Emel’yanenko; Arika Higuchi
A previous study showed that a fingerprint of the initial shape of synthetic Oort clouds was detectable in the flux of “new” long-period comets. The present study aims to explain in detail how such a fingerprint is propagated by different classes of observable comets to improve the detection of fingerprints. It appears that three main long-term behaviors of observable comets are involved in this propagation:
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Impact probability computation of near-Earth objects using Monte Carlo line sampling and subset simulation Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-08-27 Matteo Romano; Matteo Losacco; Camilla Colombo; Pierluigi Di Lizia
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the initial uncertainty region in different ways, with the result of either providing a more accurate estimate of the impact probability or reducing the number of required
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Transfers from distant retrograde orbits to low lunar orbits Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-08-25 Ruikang Zhang; Yue Wang; Hao Zhang; Chen Zhang
The stable distant retrograde orbits (DROs) around the Moon are considered as potential parking orbits for cislunar stations that are important facilities in cislunar space. Transfer orbits from DROs to lunar orbits will be fundamental and routine for operations of the cislunar stations. This paper studies transfer orbits from DROs to low lunar orbits with inclinations between 0° and 90°. Ten DROs
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Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-08-13 Stefano Marò
We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A solution to this problem goes back to Gauss and leads to the least squares method. Since the observations admit errors, the solution comes with a confidence region
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Periodic orbits of the two fixed centers problem with a variational gravitational field Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-08-04 Fabao Gao; Jaume Llibre
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
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Homoclinic dynamics in a spatial restricted four-body problem: blue skies into Smale horseshoes for vertical Lyapunov families Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-28 Maxime Murray; J. D. Mireles James
The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admits certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection—or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this
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Correction to: The Lagrange coefficients of Vinti theory Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-06-25 Ashley D. Biria
In the first paragraph of the Introduction, the last sentence should read as “ Vinti.
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Evolution of orbits about comets with arbitrary comae Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-21 Mark Moretto; Jay McMahon
Spacecraft and natural objects orbiting an active comet are perturbed by gas drag from the coma. These gases expand radially at about 0.5 km/s, much faster than orbital velocities that are on the order of meters per second. The coma has complex gas distributions and is difficult to model. Accelerations from gas drag can be on the same order of gravity and are currently poorly understood. Semi-analytical
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Lunar close encounters compete with the circumterrestrial Lidov–Kozai effect Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-20 Davide Amato; Renu Malhotra; Vladislav Sidorenko; Aaron J. Rosengren
Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semimajor axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov–Kozai effect. However, the classical Lidov–Kozai
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Retrograde periodic orbits in 1/2, 2/3 and 3/4 mean motion resonances with Neptune Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-20 T. Kotoulas; G. Voyatzis
We study planar and three-dimensional retrograde periodic orbits, using the model of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and focusing on the dynamics of resonant trans-Neptunian objects (TNOs). The position and the stability character of the periodic orbits can provide important piece of information on the stability and long-term evolution of small TNOs in
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Analysing the Main Belt asteroid distributions by wavelets Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-20 R. V. Baluev; E. I. Rodionov
We perform statistical wavelet analysis of the Main Belt asteroids, seeking statistically significant asteroid families. The goal is to test the new wavelet analysis algorithm and to compare its results with more traditional methods like the hierarchic clustering. We first consider several 1D distributions for various physical and orbital parameters of asteroids. Then, we consider three bivariate distributions
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Centaur and giant planet crossing populations: origin and distribution Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-20 Romina P. Di Sisto; Natalia L. Rossignoli
The current giant planet region is a transitional zone where transneptunian objects (TNOs) cross in their way to becoming Jupiter Family Comets. Their dynamical behavior is conditioned by the intrinsic dynamical features of TNOs and also by the encounters with the giant planets. We address the Giant Planet Crossing (GPC) population (those objects with 5.2 au \(< q < 30\,\hbox {au}\)) studying their
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Pfaffians and the inverse problem for collinear central configurations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-13 D. L. Ferrario
We consider, after Albouy–Moeckel, the inverse problem for collinear central configurations: Given a collinear configuration of n bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy–Moeckel Pfaffians: We show that for any homogeneity \(\alpha \) and \(n\le 6\) or \(n\le 10\) and \(\alpha =1\) (computer assisted) the Pfaffians are positive
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Inner third-body perturbations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-07-11 Guy Marcus; Pini Gurfil
Third-body perturbations have been extensively studied in recent years. Almost all previous works, however, assumed that the perturbations are caused by a third body that orbits the primary on a radius larger than the semimajor axis of the perturbed object. This assumption is justified as long as the primary is not accompanied by a third body in close orbit. In this work, we present an analytic model
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Analytical shape uncertainties in the polyhedron gravity model Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-06-23 Benjamin Bercovici; Paolo Panicucci; Jay McMahon
The exploration of small bodies in the Solar system and the ability to perform remote or in situ science is tied to the understanding of the dynamical environment of such objects. As such, the evaluation of the gravity field arising from small bodies is key to this understanding. However, remote observations can only produce shape estimates, from which only uncertain gravity fields can be computed
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Near rectilinear halo orbits and nearby higher-period dynamical structures: orbital stability and resonance properties Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-06-13 Emily M. Zimovan-Spreen; Kathleen C. Howell; Diane C. Davis
Near rectilinear halo orbits (NRHOs), a subset of the \(L_1\) and \(L_2\) halo orbit families, are strong candidates for a future inhabited facility in line with the goals for NASA’s long-term cislunar transportation network. Higher-period dynamical structures that bifurcate from the NRHO region of the \(L_2\) halo family offer additional insight into motion departing from or arriving into the vicinity
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An analytically treatable model of long-term dynamics in a mean motion resonance with coexisting resonant modes Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-06-05 Sergey S. Efimov; Vladislav V. Sidorenko
We examine a 2-DOF Hamiltonian system modeling some previously unexplored dynamical effects in first-order mean motion resonances in the spatial circular restricted three-body problem “star-planet-asteroid.” In distinction from the well-known integrable model of Sessin and Ferraz-Mello (Celest Mech Dyn Astron 32:307–332, 1984) and Wisdom (Celest Mech Dyn Astron 38:175–180, 1986), in our analysis, we
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The Lagrange coefficients of Vinti theory Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-06-01 Ashley D. Biria
The existence of Lagrange coefficients under two-body dynamics is well known, and the concept forms the basis of robust algorithms for solving a variety of fundamental astrodynamics problems. The Lagrange coefficients are generalized to Vinti theory in the present work, where the Vinti potential describes the dynamics of small objects like spacecraft orbiting an oblate body. Exact expressions for the
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Test of the equivalence principle for galaxy’s dark matter by lunar laser ranging Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-05-14 Mingyue Zhang; Jürgen Müller; Liliane Biskupek
Having 50 years of unique observations, lunar laser ranging (LLR) is used to test central elements of Einstein’s theory of relativity, like a possible temporal variation of the gravitational constant or metric parameters. Here, we focused on a possible violation of the equivalence principle (EP) due to assumed dark matter in the galactic center. According to the EP, Earth and Moon experience the same
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Analytical solution of the Colombo top problem Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-29 J. Haponiak; S. Breiter; D. Vokrouhlický
The Colombo top is a basic model in the rotation dynamics of a celestial body moving on a precessing orbit and perturbed by a gravitational torque. The paper presents a detailed study of analytical solution to this problem. By solving algebraic equations of degree 4, we provide the expressions for the extreme points of trajectories as functions of their energy. The location of stationary points (known
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Uncertainties in the gravity spherical harmonics coefficients arising from a stochastic polyhedral shape Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-22 Paolo Panicucci; Benjamin Bercovici; Emmanuel Zenou; Jay McMahon; Michel Delpech; Jérémy Lebreton; Keyvan Kanani
The increasing interest towards exploring small bodies in the Solar system has paved the way for the investigation of different gravity field models allowing robust orbit design and dynamical environment characterization. Among these, the spherical harmonics representation and the polyhedral gravity model are the most employed and studied—the former for historical reasons and the latter due to the
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The geometry of isochrone orbits: from Archimedes’ parabolae to Kepler’s third law Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-18 Paul Ramond; Jérôme Perez
The Kepler potential \(\propto {-1/r}\) and the harmonic potential \(\propto r^2\) share the following remarkable property: In either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and harmonic potentials are called isochrone. In this paper, we solve the following general problem: Are there any other isochrone
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Cassini states of a rigid body with a liquid core Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-13 Gwenaël Boué
The purpose of this work is to determine the location and stability of the Cassini states of a celestial body with an inviscid fluid core surrounded by a perfectly rigid mantle. Both situations where the rotation speed is either non-resonant or trapped in a \(p\!:\!1\) spin–orbit resonance where p is a half integer are addressed. The rotation dynamics is described by the Poincaré–Hough model which
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Use of the semilinear method to predict the impact corridor on ground Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-11 Linda Dimare; Alessio Del Vigna; Davide Bracali Cioci; Fabrizio Bernardi
We propose an adaptation of the semilinear algorithm for the prediction of the impact corridor on ground of an Earth-impacting asteroid. The proposed algorithm provides an efficient tool, able to reliably predict the impact regions at fixed altitudes above ground with 5 orders of magnitudes less computations than Monte Carlo approaches. Efficiency is crucial when dealing with imminent impactors, which
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Nominal definition of satellite constellations under the Earth gravitational potential Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-04-01 David Arnas; Daniel Casanova
This work focuses on the definition of satellite constellations whose secular relative distributions are invariant under the perturbation produced by the Earth gravitational potential. This is done by defining the satellite distribution directly in the Earth-Centered–Earth-Fixed frame of reference and using the along-track time distances between satellites to define the satellite constellation configuration
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A dissipative Kepler problem with a family of singular drags Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-03-29 Alessandro Margheri; Mauricio Misquero
In this work, we consider the Kepler problem with a family of singular dissipations of the form \(-\frac{k}{|x|^\beta }\dot{x},\quad k>0, \beta >0.\) We present some results about the qualitative dynamics as \(\beta \) increases from zero (linear drag) to infinity. In particular, we detect some threshold values of \(\beta \), for which qualitative changes in the global dynamics occur. In the case \(\beta
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Interplanetary gravity-assist fuel-optimal trajectory optimization with planetary and Solar radiation pressure perturbations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-03-02 Mohammadreza Saghamanesh; Ehsan Taheri; Hexi Baoyin
Designing optimal spacecraft trajectories is a critical task for any mission design. In particular, mission designers seek to exploit from the combined effects of planetary gravity-assist maneuvers and electric propulsions systems to reduce both the flight time and propellant consumption. In order to obtain more realistic results, disturbances such as (1) gravitational force of secondary bodies, (2)
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Probabilistic data association: the orbit set Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-23 Laura Pirovano; Daniele A. Santeramo; Roberto Armellin; Pierluigi Di Lizia; Alexander Wittig
This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus
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Bounded motion design in the Earth zonal problem using differential algebra based normal form methods Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-20 A. Weisskopf; R. Armellin; M. Berz
Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. In this work, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè
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Impulsive orbit correction using second-order Gauss’s variational equations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-10 Gang Zhang; Daniele Mortari
Based on Gauss’s variational equations (GVEs), the impulsive orbital-element corrections are investigated in orbit transfer problems. Both single impulse and multiple impulses are considered for the first-order and second-order GVEs. For the single impulse, a nonlinear least-squares iteration method for the minimum orbit error is provided to simultaneously solve for the impulse vector and the impulse
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Long-term orbital dynamics of trans-Neptunian objects Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-07 Melaine Saillenfest
This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, and secular effects) to external perturbations (galactic tides and passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms
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The vicinity of the Earth–Moon $$L_1$$L1 point in the bicircular problem Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-07 Àngel Jorba; Marc Jorba-Cuscó; José J. Rosales
The bicircular model is a periodic time-dependent perturbation of the Earth–Moon restricted three-body problem that includes the direct gravitational effect of the Sun on the infinitesimal particle. In this paper, we focus on the dynamics in the neighbourhood of the \(L_1\) point of the Earth–Moon system. By means of a periodic time-dependent reduction to the centre manifold, we show the existence
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Uniform formulation for orbit computation: the intermediate elements Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-07 Giulio Baù; Javier Roa
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e. constants of the unperturbed motion. The proposed elements are uniformly valid for any value of the total energy. Their definition stems from the idea of applying Sundman’s time transformation
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Three-dimensional structure of mean motion resonances beyond Neptune Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-02-01 Tabaré Gallardo
We propose a semianalytical method for the calculation of widths, libration centers and small-amplitude libration periods of the mean motion resonances \(k_p\):k in the framework of the circular restricted three-body problem valid for arbitrary eccentricities and inclinations. Applying the model to the trans-Neptunian region, we obtain several atlas of resonances between 30 and 100 au, showing their
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Observing Mercury by a quasi-propellantless mission Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-01-27 Andrea Carbone; Marco Cinelli; Christian Circi; Emiliano Ortore
In this paper, the feasibility of exploiting the Sun’s gravitational force to design the final phase (capture and orbit circularisation) to Mercury with a low propellant consumption has been investigated. The initial conditions, on the eccentricity and argument of pericentre, for the circularisation phase are obtained from a prime integral of motion, which takes place when the probe moves over a polar
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Numerical integration in Celestial Mechanics: a case for contact geometry Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-01-03 Alessandro Bravetti; Marcello Seri; Mats Vermeeren; Federico Zadra
Several dynamical systems of interest in Celestial Mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin–orbit model and the Lane–Emden equation all belong to such class. In this work, we start an investigation of these models from the point of view of contact geometry. In particular, we focus
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On the nodal distance between two Keplerian trajectories with a common focus Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-01-02 Giovanni Federico Gronchi; Laurent Niederman
We study the possible values of the nodal distance \(\delta _\mathrm{nod}\) between two non-coplanar Keplerian trajectories \(\mathcal{A}, \mathcal{A}'\) with a common focus. In particular, given \(\mathcal{A}'\) and assuming it is bounded, we compute optimal lower and upper bounds for \(\delta _\mathrm{nod}\) as functions of a selected pair of orbital elements of \(\mathcal{A}\), when the other elements
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Data association and uncertainty pruning for tracks determined on short arcs Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-01-02 Laura Pirovano; Gennaro Principe; Roberto Armellin
When building a space catalogue, it is necessary to acquire multiple observations of the same object for the estimated state to be considered meaningful. A first concern is then to establish whether different sets of observations belong to the same object, which is the association problem. Due to illumination constraints and adopted observation strategies, small objects may be detected on short arcs
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Disassociation energies for the finite-density N -body problem Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2020-01-01 D. J. Scheeres
This paper considers the energy required for collections of finite-density bodies to undergo escape under internal gravitational interactions alone. As the level of the system energy is increased, there are different combinations of components that can escape, until the total energy becomes positive, when the entire system can undergo mutual disruption. The results are also defined for bodies modeled
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Effects of protoplanetary nebula on orbital dynamics of planetesimals in the outer Solar system Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2019-12-24 David Vokrouhlický; David Nesvorný
Massive gaseous nebula has been a key element to formation of large solid objects (planetesimals, giant planet cores) in the early phase of the Solar system evolution. Here, we focus on its effects during the stage when giant planets have already fully formed. Dynamical effects of the nebula on motion of planetesimals stirred by planets were twofold: (i) global gravitational acceleration, and (ii)
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The detection of relativistic corrections in cosmological N-body simulations Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2019-12-21 Jean-Pierre Eckmann; Farbod Hassani
Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (Nat Phys 12:346, 2016), Barrera-Hinojosa and Li (GRAMSES: a new route to general relativistic N-body simulations in cosmology—I. Methodology and code description, 2019) have developed
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Secular resonance sweeping and orbital excitation in decaying disks Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2019-12-13 Athanasia Toliou; Kleomenis Tsiganis; Georgios Tsirvoulis
We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in light of recent models of Solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance
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Correction to: Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2019-12-02 Dmitry A. Pavlov,James G. Williams,Vladimir V. Suvorkin
In the original, the bottom-right diagonal element of the
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Correction to: Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015 Celest. Mech. Dyn. Astr. (IF 1.613) Pub Date : 2019-12-02 B. A. Archinal,C. H. Acton,A. Conrad,T. Duxbury,D. Hestroffer,J. L. Hilton,L. Jorda,R. L. Kirk,S. A. Klioner,J.-L. Margot,K. Meech,J. Oberst,F. Paganelli,J. Ping,P. K. Seidelmann,A. Stark,D. J. Tholen,Y. Wang,I. P. Williams
We point out some errors in the most recent report from the International Astronomical Union (IAU) Working Group on Cartographic Coordinates and Rotational Elements (Archinal et al. 2018).
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