Ballistic Orbits Research Articles

Ballistic Capture Analysis Using the Energy Transition Domain

In the framework of the planar Circular Restricted Three-Body Problem (CR3BP) and for a given value of the Jacobi constant, a necessary condition for a ballistic capture is a passage through zero two-body energy, which defines a region in the synodic plane called energy transition domain (ETD). The latter is the locus of points where the zero-energy condition and selected Jacobi constant are simultaneously fulfilled. This paper shows how an ETD can be described analytically and exploited for the efficient computation and insightful classification of the complete set of ballistic capture trajectories in the planar problem. The new methodology is applied to different three-body systems and highlights the influence of the three-body energy on key aspects of the capture mechanism, such as prograde to retrograde transition. Other interesting results concern three-body energy limits, collisions, long-duration captures, altitude range throughout the capture process, and the origin of ballistic capture orbits.

Design of Mars global longitudinal coverage constellation leveraging resonant and periodic orbits in Mars-Phobos-Deimos system

Over the last decades, the exploration of Phobos and Deimos has acquired relevance from both scientific and human missions standpoint. Both moons can play a key role on supporting the Martian Exploration program improving teleoperation capabilities and infrastructure support. The purpose of this work is to propose a different approach to the problem of global longitudinal coverage of Mars, exploiting the characteristic of natural satellites of the planet itself. The proposed constellation can be an alternative to the Mars Areostationary Orbit (MAO), in fact, three satellites equally spaced at Deimos height are enough to provide global longitudinal coverage, with a reduced cost. The main source of perturbation at areostationary height is due to the second degree, second order sectorial harmonic of Mars gravitational field (J2,2), which requires high maintenance cost for an equivalent configuration in MAO. By leveraging Lyapunov orbits in the Mars-Deimos perturbed Three Body Problem, it’s possible to achieve long term stable orbits with lower cost, as well as ballistic orbits with bounded variations. The characteristics and the performance of the constellation are analyzed, as well as the transfer orbits between the Mars-Deimos Lagrange points leveraging resonant orbits. The possibility of placing an extra satellite in an orbit around Phobos with the purpose of increasing performance is also detailed, as well as the transfer trajectory from the Deimos L3 point to a DRO orbit around Phobos.

A Semi-Lagrangian Computation of Front Speeds of G-equation in ABC and Kolmogorov Flows with Estimation via Ballistic Orbits

The Arnold-Beltrami-Childress (ABC) flow and the Kolmogorov flow are three dimensional periodic divergence free velocity fields that exhibit chaotic streamlines. We are interested in front speed enhancement in G-equation of turbulent combustion by large intensity ABC and Kolmogorov flows. We give a quantitative construction of the ballistic orbits of ABC and Kolmogorov flows, namely those with maximal large time asymptotic speeds in a coordinate direction. Thanks to the optimal control theory of G-equation (a convex but non-coercive Hamilton-Jacobi equation), the ballistic orbits serve as admissible trajectories for front speed estimates. To study the tightness of the estimates, we compute the front speeds of G-equation based on a semi-Lagrangian (SL) scheme with Strang splitting and weighted essentially non-oscillatory (WENO) interpolation. Time step size is chosen so that the Courant number grows sublinearly with the flow intensity. Numerical results show that the front speed growth rate in terms of the flow intensity may approach the analytical bounds from the ballistic orbits.

A flow-informed strategy for ballistic capture orbit generation

Ballistic capture is a phenomenon by which a spacecraft approaches its target body, and performs a number of revolutions around it, without requiring manoeuvres in between. Capture orbits are characterized by specific dynamics, defining regions that guide transport phenomena. Because of the limitations associated with existing approaches, the development of heuristics informed by Lagrangian Coherent Structures appears desirable. In fact, such structures identify transport barriers in dynamical systems, separating regions with qualitatively different dynamics. In this work, different flow-informed approaches are presented, and their relations with ballistic capture are discussed. A new heuristic, the time-varying strainline, is introduced. This new tool is applied to compute ballistic capture orbits around Mars. Different degrees of model fidelity have been investigated, mainly in order to test the robustness of the proposed technique with respect to different features of the underlying dynamical model. We show that time-varying strainlines are useful in identifying ballistic capture orbits.

Structural Design and Dynamics Simulation Analysis of A Certain Type of Co-frame Launcher

To study the dynamic response of a certain type of co-frame launcher during launch, this article uses the 3D modeling software Pro/E to import the model into Adams from the perspective of launch dynamics. the launch dynamics model of the shared-frame launcher is established. We apply the ejection thrust of the two types of missiles to the corresponding ejection devices and measure and collect the dynamic parameters of the cartridge system. The simulation results show that the dynamic parameters of the A and B missiles are in line with the available overload design requirements. The B-type missiles are superior to the A-type missiles in terms of ballistic orbit contact force and ejection attitude.

The influence of upper boundary conditions on molecular kinetic atmospheric escape simulations

Molecular kinetic simulations are typically used to accurately describe the tenuous regions of the upper atmospheres on planetary bodies. These simulations track the motion of particles representing real atmospheric atoms and/or molecules subject to collisions, the object's gravity, and external influences. Because particles can end up in very large ballistic orbits, upper boundary conditions (UBC) are typically used to limit the domain size thereby reducing the time for the atmosphere to reach steady-state. In the absence of a clear altitude at which all molecules are removed, such as a Hill sphere, an often used condition is to choose an altitude at which collisions become infrequent so that particles on escape trajectories are removed. The remainder are then either specularly reflected back into the simulation domain or their ballistic trajectories are calculated analytically or explicitly tracked so they eventually re-enter the domain. Here we examine the effect of the choice of the UBC on the escape rate and the structure of the atmosphere near the nominal exobase in the convenient and frequently used 1D spherically symmetric approximation. Using Callisto as the example body, we show that the commonly used specular reflection UBC can lead to significant uncertainties when simulating a species with a lifetime comparable to or longer than a dynamical time scale, such as an overestimation of escape rates and an inflated exosphere. Therefore, although specular reflection is convenient, the molecular lifetimes and body's dynamical time scales need to be considered even when implementing the convenient 1D spherically symmetric simulations in order to accurately estimate the escape rate and the density and temperature structure in the transition regime.

Dayside-to-nightside dust coma brightness asymmetry and its implications for nightside activity at Comet 67P/Churyumov–Gerasimenko

We have determined the dust coma brightness ratio between the dayside and the nightside (DS:NS) in OSIRIS images of comet 67P/Churyumov–Gerasimenko and compared them to results from numerical dust coma simulations to learn more about the dynamic processes that are involved in coma formation. The primary focus of this paper lies in the analysis of a subset of OSIRIS images acquired during one comet rotation on 11. April 2015 when the spacecraft was at a phase angle of 90∘ and therefore directly above the terminator. The DS:NS ratio was found to be 2.49 ± 0.18 on average - a very low value if insolation-driven sublimation of water dominates dust emission. We investigated two possible hypotheses: First, the influence of direct activity from non-illuminated (nightside) areas of the comet and second, the brightness contribution of large gravity-dominated particles in the innermost coma. For our numerical simulations, we used a combination of DSMC gas dynamics simulation and particle propagation by an equation of motion to simulate the dust coma. Our simulations show that direct activity from the nightside is preferred, contributing ≈ 10% of the total emission. We show that intensity profiles, used to quantify dust outflow behaviour, fit the observations better when nightside activity is present and we suggest that nightside gas emission by CO2 or CO is responsible for the observed dust flux. With the help of a simplified Keplerian modelling approach we exclude large particles on gravitationally bound or ballistic orbits from being the major contributor to the observed dust coma brightness. Additionally, we show the DS:NS ratio as a function of days to perihelion and observe that it is on a similar level as in the April OSIRIS time series from February to mid-June 2015, but increases towards a maximum of ≥4.07± 0.49 shortly after perihelion passage. We suggest that this is correlated to the increasing importance of H2O production when approaching perihelion.

Dynamics of three-dimensional capture orbits from libration region analysis

Low-energy trajectories take advantage of the mutual action of multiple celestial bodies on the spacecraft, and can conclude with ballistic capture about the arrival body, thus allowing significant savings in terms of propellant consumption, if compared to more traditional transfers. Because of the chaotic nature of multibody environments, the design of low-energy trajectories with given constraints can be complex and it is often obtained after a long, iterative, and eventually computationally expensive process.This work is aimed at identifying a limited set of characteristic parameters related both to the time behavior of three-dimensional ballistic capture orbits and to some osculating orbit elements (i.e., inclination, semimajor axis, and eccentricity), relative either to the departure or to the arrival body. The analysis is performed using the linear expansion of the Hamiltonian equations of motion in the equilibrium region around the collinear libration point L1 (or L2), in the dynamical framework of the 3 dimensional circular restricted 3-body problem. A correlation among some Hamiltonian parameters in the equilibrium region and the trajectory osculating orbital elements at capture is established. This result is used to design missions with ballistic capture having required orbital parameters at the arrival planet and it provides a strategy to control the target orbital elements at capture by small thrust maneuvers at the equilibrium region. Because of the long flight time, the solar perturbation is considered in the analysis, and suitable launch dates for the ballistically captured missions are determined.

Normal and Anomalous Diffusion in Soft Lorentz Gases.

Motivated by electronic transport in graphenelike structures, we study the diffusion of a classical point particle in Fermi potentials situated on a triangular lattice. We call this system a soft Lorentz gas, as the hard disks in the conventional periodic Lorentz gas are replaced by soft repulsive scatterers. A thorough computational analysis yields both normal and anomalous (super)diffusion with an extreme sensitivity on model parameters. This is due to an intricate interplay between trapped and ballistic periodic orbits, whose existence is characterized by tonguelike structures in parameter space. These results hold even for small softness, showing that diffusion in the paradigmatic hard Lorentz gas is not robust for realistic potentials, where we find an entirely different type of diffusion.

Torques on Low-mass Bodies in Retrograde Orbit in Gaseous Disks

We evaluate the torque acting on a gravitational perturber on a retrograde circular orbit in the midplane of a gaseous disk. We assume that the mass of this satellite is so low it weakly disturbs the disk (type I migration). The perturber may represent the companion of a binary system with a small mass ratio. We compare the results of hydrodynamical simulations with analytic predictions. Our two-dimensional (2D) simulations indicate that the torque acting on a perturber with softening radius $R_{\rm soft}$ can be accounted for by a scattering approach if $R_{\rm soft}<0.3H$, where $H$ is defined as the ratio between the sound speed and the angular velocity at the orbital radius of the perturber. For $R_{\rm soft}>0.3H$, the torque may present large and persistent oscillations, but the resultant time-averaged torque decreases rapidly with increasing $R_{\rm soft}/H$, in agreement with previous analytical studies. We then focus on the torque acting on small-size perturbers embedded in full three-dimensional (3D) disks and argue that the density waves propagating at distances $\lesssim H$ from the perturber contribute significantly to the torque because they transport angular momentum. We find a good agreement between the torque found in 3D simulations and analytical estimates based on ballistic orbits. We compare the radial migration timescales of prograde versus retrograde perturbers. For a certain range of the perturber's mass and aspect ratio of the disk, the radial migration timescale in the retrograde case may be appreciably shorter than in the prograde case. We also provide the smoothing length required in 2D simulations in order to account for 3D effects.

The Sun–Earth saddle point: characterization and opportunities to test general relativity

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun–Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on $$L_{1,2}$$ Lagrange point orbits. Sun–Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.

Effects of space weather on the ionosphere and LEO satellites’ orbital trajectory in equatorial, low and middle latitude

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites’ orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite’s orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October–14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute r,h and ODR in three regimes viz. (i) excluding solar indices (or effect), where r=r0,h=h0 and ODR=ODR0 (ii) with mean value of solar indices for the interval, where r=rm,h=hm and ODR=ODRm and (iii) with actual daily values of solar indices for the interval (r,h and ODR). For a typical LEO satellite at h = 450 km, we show that the total decay in r during the period is about 4.20 km, 3.90 km and 3.20 km in EQL, LLT and MLT respectively; the respective nominal decay (r0) is 0.40 km, 0.34 km and 0.22 km, while solar-induced orbital decay (rm) is about 3.80 km, 3.55 km and 2.95 km. h also varied in like manner. The respective nominal ODR0 is about 13.5 m/day, 11.2 m/day and 7.2 m/day, while solar-induced ODRm is about 124.3 m/day, 116.9 m/day and 97.3 m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite’s trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.

Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs

In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of looking for a fixed point of a high order smoothing Picard-like operator. We then develop a rigorous computational method based on a Newton-Kantorovich type argument (the radii polynomial approach) to prove existence of a fixed point of the Picard-like operator. We present all necessary estimates in full generality and for any nonlinearities. With our approach, we study two systems of nonlinear equations: the Lorenz system and the ABC flow. For the Lorenz system, we solve Cauchy problems and prove existence of periodic and connecting orbits at the classical parameters, and for ABC flows, we prove existence of ballistic spiral orbits.

Risk Assessment of Hypervelocity Impact of Saturn Dust on Cassini Sun Sensors

Cassini is one of the most sophisticated interplanetary spacecraft that humans have ever built and launched. Since achieving orbit at Saturn in 2004, Cassini has collected science data throughout its four-year prime mission (2004–2008), and it has since been approved for first and second extended missions through September 2017. In April 2017, the Cassini spacecraft will begin a daring set of ballistic orbits that will hop the rings and dive between the upper atmosphere of Saturn and its innermost D ring. The “dusty” environment of the inner D-ring region the spacecraft must fly through is hazardous because of the possible damage that dust particles, travelling at speeds as high as (relative to the spacecraft), can do to spacecraft hardware. During proximal ring-plane crossings, the mission operation team plans to point the high-gain antenna to the spacecraft velocity relative to dust particles in order to protect most of spacecraft instruments from the incoming dust particles. However, this attitude exposes two sun sensors (that are mounted on the antenna) to the incoming particles. High-velocity impacts on the sun sensor coverglass might penetrate it. Moreover, craters created by these impacts on the coverglass will degrade the transmissibility of light through it. Analyses performed to quantify the risks that the sun sensors must contend with during these hazardous ring-plane crossings are given in this paper.

Analysis of medium-energy transfers to the Moon

This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.

Computer Aided Ballistic Orbit Classification Around Small Bodies

Orbital dynamics around small bodies are as varied as the shapes and dynamical states of these bodies. While various classes of orbits have been analyzed in detail, the global overview of relevant ballistic orbits at particular bodies is not easily computed or organized. Yet, correctly categorizing these orbits will ease their future use in the overall trajectory design process. This paper overviews methods that have been used to organize orbits, focusing on periodic orbits in particular, and introduces new methods based on clustering approaches.

Tidal disruption events by a massive black hole binary

Massive black hole binaries (MBHBs) are a natural byproduct of galaxy mergers. Previous studies have shown that flares from stellar tidal disruption events (TDEs) are modified by the presence of a secondary perturber, causing interruptions in the light curve. We study the dynamics of TDE debris in the presence of a milliparsec-separated MBHB by integrating ballistic particle orbits in the time-varying potential of the binary. We find that gaps in the light curve appear when material misses the accretion radius on its first return to pericentre. Subsequent recurrences can be decomposed into "continuous" and "delayed" components, which exhibit different behaviour. We find that this potential can substantially alter the locations of stream self-intersections. When debris is confined to the plane, we find that close encounters with the secondary BH leave noticeable signatures on the fallback rate and can result in significant accretion onto the secondary BH. Tight, equal-mass MBHBs accrete equally, periodically trading the infalling stream.

Ballistic Orbits and Front Speed Enhancement for ABC Flows

We study the two main types of trajectories of the ABC flow in the near-integrable regime: spiral orbits and edge orbits. The former are helical orbits which are perturbations of similar orbits that exist in the integrable regime, while the latter exist only in the nonintegrable regime. We prove existence of ballistic (i.e., linearly growing) spiral orbits by using the contraction mapping principle in the Hamiltonian formulation, and we also find and analyze ballistic edge orbits. We discuss the relationship of existence of these orbits with questions concerning front propagation in the presence of flows, in particular the question of linear (i.e., maximal possible) front speed enhancement rate for ABC flows.

Ballistic Transport in Graphene Antidot Lattices.

The bulk carrier mobility in graphene was shown to be enhanced in graphene-boron nitride heterostructures. However, nanopatterning graphene can add extra damage and drastically degrade the intrinsic properties by edge disorder. Here we show that graphene embedded into a heterostructure with hexagonal boron nitride (hBN) on both sides is protected during a nanopatterning step. In this way, we can prepare graphene-based antidot lattices where the high mobility is preserved. We report magnetotransport experiments in those antidot lattices with lattice periods down to 50 nm. We observe pronounced commensurability features stemming from ballistic orbits around one or several antidots. Due to the short lattice period in our samples, we can also explore the boundary between the classical and the quantum transport regime, as the Fermi wavelength of the electrons approaches the smallest length scale of the artificial potential.

Conductance fluctuations in chaotic bilayer graphene quantum dots.

Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit.