Multiple-satellite-aided capture trajectories at Jupiter using the Laplace resonance

Satellite-aided capture is a mission design concept used to reduce the delta-v required to capture into a planetary orbit. The technique employs close flybys of a massive moon to reduce the energy of the planet-centered orbit. A sequence of close flybys of two or more of the Galilean moons of Jupiter may further decrease the delta-v cost of Jupiter orbit insertion. A Ganymede-Io sequence can save 207 m/s of delta-v over a single Io flyby. A phase angle analysis based on the Laplace resonance is used to find triple-satellite-aided capture sequences involving Io, Europa, and Ganymede. Additionally, the near-resonance of Callisto and Ganymede is used to find triple-satellite-aided capture sequences involving Callisto, Ganymede, and another moon. A combination of these techniques is used to find quadruple-satellite-aided capture sequences that involve gravity-assists of all four Galilean moons. These sequences can save a significant amount of delta-v and have the potential to benefit both NASA’s Jupiter Europa orbiter mission and ESA’s Jupiter Ganymede orbiter mission.     

On the formation of a neutron star in a close binary system

The effects on a close binary system of one component becoming a neutron star as a result of a supernova explosion are discussed in this paper. In the case of a Type I supernova, the system can remain bound in many cases of interest. For a Type II supernova, the system will probably be disrupted although in some cases a remnant of the companion to the supernova may remain in a bound orbit.Consequently, neutron stars formed in Type I supernova explosions may exist in close binary systems. Such systems may be strong X-ray emitters due to mass flow as suggested by Shklovsky. Photons with energies in the 1–50 MeV region should also be emitted.     

Dynamics of Saturn's magnetodisk near Titan's orbit: Comparison of Cassini magnetometer observations from real and virtual Titan flybys

We analyze the variability of the ambient magnetospheric field along Titan's orbit at 20.3 Saturn radii. However, while our preceding study (Simon et al., 2010) focused on Cassini magnetometer observations from the 62 Titan flybys (TA-T62) between October 2004 and October 2009, the present work discusses magnetic field data that were collected near Titan's orbit when the moon was far away. In analogy to the observations during TA-T62, the magnetospheric fields detected during these 79 “virtual” Titan flybys are strongly affected by the presence of Saturn's bowl-shaped and highly dynamic magnetodisk current sheet. We therefore provide a systematic classification of the magnetic field observations as magnetodisk current sheet or lobe-type scenarios. Among the 141 (62 real+79 virtual) crossings of Titan's orbit between July 2004 and December 2009, only 17 encounters (9 real+8 virtual) took place within quiet, magnetodisk lobe-type fields. During another 50 encounters (21 real+29 virtual), rapid transitions between current sheet and lobe fields were observed around the moon's orbital plane. Most of the encounters (54=22 real+32 virtual) occurred when Titan's orbit was embedded in highly distorted current sheet fields, thereby invalidating the frequently applied idealized picture of Titan interacting with a homogeneous and stationary magnetospheric background field. The locations of real and virtual Titan flybys are correlated to each other. Each of the 62 real Titan flybys possesses at least one virtual counterpart that occurred shortly before or after the real encounter and at nearly the same orbital position. A systematic comparison between Cassini magnetometer observations from the real Titan flybys and their virtual companions suggests that there is no clear evidence of Titan exerting a significant level of control on the vertical oscillatory motion of the magnetodisk near its orbit.     

Possible flyby measurements of Galilean satellite interior structure

Flyby encounters of the Galilean satellites from a Jupiter orbiter spacecraft could yield information about the second-degree gravity harmonics of these satellites. We have calculated the expected values of these harmonics for a range of plausible interior models in hydrostatic equilibrium. Because the satellites respond to comparable perturbations from rotation and tides, an independent test of hydrostatic equilibrium is feasible. For Io and Ganymede, the expected measurement accuracy from a nominal encounter should make possible an excellent discrimination from the ensemble of interior models. For Europa, a qualitative distinction between near-uniform and centrally condensed models seems feasible. Only for Callisto is the proposed experiment of marginal value.     

Evolutionary principles applied to mission planning problems

The space mission planning process is considered as a hybrid optimal control problem. Hybrid optimal control problems are problems that include categorical variables in the problem formulation. For example, an interplanetary trajectory may consist of a sequence of low thrust arcs, impulses and planetary flybys. However, for each choice of the structure of the mission, for example, for a particular choice of the number of planetary flybys to be used, there is a corresponding optimal trajectory. It is not a priori clear which structure will yield the most efficient mission. In this work we present a mathematical framework for describing such problems and solution methods for the hybrid optimal control problem based on evolutionary principles that have the potential for being a robust solver of such problems. As an example, the methods are used to find the optimal choice of three asteroids to visit in sequence, out of a set of eight candidate asteroids, in order to minimize the fuel required.     

Periodic orbits and escapes in dynamical systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central ??bumpy?? black hole. When the energy reaches its escape value, a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.     

Low-energy Lunar Trajectories with Lunar Flybystwo

The low-energy lunar trajectories with lunar flybys are investigated based on the Sun-Earth-Moon bicircular problem (BCP). The characteristics of the distribution of trajectories in the phase space are summarized. Using the invariant manifolds in the BCP system, the low-energy lunar trajectories with lunar flybys are sought. Then, take time as an augmented dimension in the phase space of a nonautonomous system, we present the state space map and reveal the distribution of these lunar trajectories in the phase space. Consequently, we find that the low-energy lunar trajectories exist as families, and that the every moment in the Sun-Earth-Moon synodic period can be the departure date. Finally, we analyse the velocity increment, transfer duration, and system energy for the different trajectory families, and obtain the velocity-impulse optimal family and the transfer-duration optimal family, respectively.     

A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.     

The Rotation of Europa

We present a semi-analytical theory of the rotation of Europa the Galilean satellite of Jupiter. The theory is semi-analytical in the sense that it is based on a synthetic theory of the orbit of Europa developed by Lainey. The theory is developed in the framework of Hamiltonian mechanics, using Andoyer variables and assumes that Europa is a rigid body. We consider this theory as a first step toward the modelization of a non rigid Europa covered by an ocean.     

The Žďár nad Sázavou meteorite fall: Fireball trajectory,photometry, dynamics,fragmentation, orbit,and meteorite recovery

We report a comprehensive analysis of the instrumentally observed meteorite fall ??ár nad Sázavou, which occurred in the Czech Republic on December 9, 2014, at 16:16:45–54 UT. The original meteoroid with an estimated initial mass of 150 kg entered the atmosphere with a speed of 21.89 km s^?1 and began a luminous trajectory at an altitude of 98.06 km. At the maximum, it reached ?15.26 absolute magnitude and terminated after a 9.16 s and 170.5 km long flight at an altitude of 24.71 km with a speed of 4.8 km/s. The average slope of the atmospheric trajectory to the Earth's surface was only 25.66°. Before its collision with Earth, the initial meteoroid orbited the Sun on a moderately eccentric orbit with perihelion near Venus orbit, aphelion in the outer main belt, and low inclination. During the atmospheric entry, the meteoroid severely fragmented at a very low dynamic pressure 0.016 MPa and further multiple fragmentations occurred at 1.4–2.5 MPa. Based on our analysis, so far three small meteorites classified as L3.9 ordinary chondrites totaling 87 g have been found almost exactly in the locations predicted for a given mass. Because of very high quality of photographic and radiometric records, taken by the dedicated instruments of the Czech part of the European Fireball Network, ??ár nad Sázavou belongs to the most reliably, accurately, and thoroughly described meteorite falls in history.     

Additions to the Theory of the Rotation of Europa

In a previous paper (The Rotation of Europa, Henrard, Celest. Mech. Dyn. Astr., 91, 131–149, 2005) we have developed a semi-analytical theory of Europa, one of the Galilean satellites of Jupiter. It is based on a synthetic theory of the orbit of Europa and is developed in the framework of Hamiltonian formalism. It was assumed that Europa is a rigid body and Jupiter a point mass. Several additional effects should be investigated in order to complete the theory. The present contribution considers the effect of the shape of Jupiter and of the gravitational pull of Io. The sensitivity of the main theory to a change in the values of the moments of inertia of Europa is also considered.     

Stochastic models of hot planetary and satellite coronas: Atomic oxygen in Europa’s corona

This paper analyzes the formation, kinetics, and transport of hot oxygen atoms in the atmosphere of the Jovian satellite Europa. Atmospheric sources of suprathermal oxygen atoms are assumed to be represented by the processes of dissociation of molecular oxygen, which is the main component of the atmosphere, by solar UV radiation and electron fluxes from the inner magnetosphere of Jupiter, as well as by the reaction of dissociative recombination of the main ionospheric ion O ₂ ⁺ which thermal electrons. It is shown that dissociation in Europa’s near-surface atmosphere is balanced by the processes of the loss of atomic oxygen due to the effective escape of suprathermal oxygen atoms into the inner magnetosphere of Jupiter along the orbit of Europa and due to ionization by magnetospheric electrons and catalytic recombination of oxygen atoms on the icy surface of the satellite. It thus follows that atomic oxygen is only a small admixture to the main atmospheric component—molecular oxygen—in the near-surface part of the atmosphere. However, the outer exospheric layers of Europa’s atmosphere are populated mostly by suprathermal oxygen atoms. The near-surface molecular envelope of Europa is therefore surrounded by a tenuous extended corona of hot atomic oxygen.     

Determination of the orbit of a natural satellite with hyperbolic flybys

We show that, when a natural satellite like Titan is invisible (e.g., due to an opaque atmosphere) its planetary orbit and its mass can be determined by tracking a spacecraft in close flybys. This is an important problem in the Cassini mission to the Saturnian system, which will be greatly improved by a good astrometric model for all its main components; in particular, an accuracy of a few hundred meters for the orbit of Titan is necessary to allow a measurement of its moment of inertia. The orbit of the spacecraft is the union of elliptical arcs, joined by short hyperbolic transitions: a problem of singular perturbation theory, whose solution leads to a matching condition between the inner hyperbolic orbit and the elliptical orbital elements. Since the inner elements are given in terms of the relative position and velocity of the spacecraft, accurate Doppler measurements in both regions can provide a satisfactory determination of Titan's position and velocity, hence of its Keplerian elements. The errors in this determination are discussed on the basis of the expected Allan deviation of the Doppler method; it is found that the driving errors are those in the elliptical arcs; the fractional errors in Titan's orbital elements are expected to be 10^–7. It is also possible to measure the mass of the satellite; however, when the eccentricity e of the flybys is large, the mass and a scaling transformation are highly correlated and the fractional error in the mass is expected to be e times worse.     

Optimal transfers between unstable periodic orbits using invariant manifolds

This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between unstable periodic orbits in the Sun–Earth, Earth–Moon, and Jupiter-Europa three-body systems. Multiple solutions are found between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost is accompanied by an increase in transfer time of flight.     

Compositional mapping of planetary moons by mass spectrometry of dust ejecta

Classical methods to analyze the surface composition of atmosphereless planetary objects from an orbiter are IR and gamma ray spectroscopy and neutron backscatter measurements. The idea to analyze surface properties with an in-situ instrument has been proposed by Johnson et al. (1998). There, it was suggested to analyze Europa's thin atmosphere with an ion and neutral gas spectrometer. Since the atmospheric components are released by sputtering of the moon's surface, they provide a link to surface composition. Here we present an improved, complementary method to analyze rocky or icy dust particles as samples of planetary objects from which they were ejected. Such particles, generated by the ambient meteoroid bombardment that erodes the surface, are naturally present on all atmosphereless moons and planets. The planetary bodies are enshrouded in clouds of ballistic dust particles, which are characteristic samples of their surfaces. In situ mass spectroscopic analysis of these dust particles impacting onto a detector of an orbiting spacecraft reveals their composition. Recent instrumental developments and tests allow the chemical characterization of ice and dust particles encountered at speeds as low as 1 km/s and an accurate reconstruction of their trajectories. Depending on the sampling altitude, a dust trajectory sensor can trace back the origin of each analyzed grain with about 10 km accuracy at the surface. Since the detection rates are of the order of thousand per orbit, a spatially resolved mapping of the surface composition can be achieved. Certain bodies (e.g., Europa) with particularly dense dust clouds, could provide impact statistics that allow for compositional mapping even on single flybys. Dust impact velocities are in general sufficiently high at orbiters about planetary objects with a radius >1000 km and with only a thin or no atmosphere. In this work we focus on the scientific benefit of a dust spectrometer on a spacecraft orbiting Earth's Moon as well as Jupiter's Galilean satellites. This ‘dust spectrometer' approach provides key chemical and isotopic constraints for varying provinces or geological formations on the surfaces, leading to better understanding of the body's geological evolution.     

Impact-generated dust clouds around planetary satellites: model versus Galileo data

This paper focuses on tenuous dust clouds of Jupiter's Galilean moons Europa, Ganymede and Callisto. In a companion paper (Srem?evi? et al., Planet. Space Sci. 51 (2003) 455-471) an analytical model of impact-generated ejecta dust clouds surrounding planetary satellites has been developed. The main aim of the model is to predict the asymmetries in the dust clouds which may arise from the orbital motion of the parent body through a field of impactors. The Galileo dust detector data from flybys at Europa, Ganymede and Callisto are compatible with the model, assuming projectiles to be interplanetary micrometeoroids. The analysis of the data suggests that two interplanetary impactor populations are most likely the source of the measured dust clouds: impactors with isotropically distributed velocities and micrometeoroids in retrograde orbits. Other impactor populations, namely those originating in the Jovian system, or interplanetary projectiles with low orbital eccentricities and inclinations, or interstellar stream particles, can be ruled out by the statistical analysis of the data. The data analysis also suggests that the mean ejecta velocity angle to the normal at the satellite surface is around 30°, which is in agreement with laboratory studies of the hypervelocity impacts.     

Trajectory Analysis and Design for A Jupiter Exploration Mission

The trajectory design for a Jupiter exploration mission is investigated in this paper. The differences between the Jupiter exploration trajectory and the Mars or Venus exploration trajectory are mainly concerned about. Firstly, the selection of the Jupiter-centered orbit is analyzed based on the Galileo Jupiter mission. As for the Earth-Jupiter transfer orbit, the fuel consumption of the direct transfer is too large. So the energy-saving technologies such as the planetary gravity assist should be used for the trajectory to the Jupiter. The different sequences of planetary gravity assists are examined by applying the Particle Swarm Optimization (PSO). According to the searched result, the Venus-Earth-Earth sequence (VEEGA) is the most effective one for the Jupiter mission. During the Jupiter mission, the spacecraft will pass though the main asteroid belt between the orbits of Mars and Jupiter, and may encounter multiple asteroids. Therefore the Jupiter mission is able to combine with the main-belt asteroid flyby mission. The design method of the intermediate asteroid flyby trajectory is also considered. At last, an entire trajectory for the Jupiter mission launched in 2023 is presented.     

Selection and trajectory design to mission secondary targets

Recently, with new trajectory design techniques and use of low-thrust propulsion systems, missions have become more efficient and cheaper with respect to propellant. As a way to increase the mission’s value and scientific return, secondary targets close to the main trajectory are often added with a small change in the transfer trajectory. As a result of their large number, importance and facility to perform a flyby, asteroids are commonly used as such targets. This work uses the Primer Vector theory to define the direction and magnitude of the thrust for a minimum fuel consumption problem. The design of a low-thrust trajectory with a midcourse asteroid flyby is not only challenging for the low-thrust problem solution, but also with respect to the selection of a target and its flyby point. Currently more than 700,000 minor bodies have been identified, which generates a very large number of possible flyby points. This work uses a combination of reachability, reference orbit, and linear theory to select appropriate candidates, drastically reducing the simulation time, to be later included in the main trajectory and optimized. Two test cases are presented using the aforementioned selection process and optimization to add and design a secondary flyby to a mission with the primary objective of 3200 Phaethon flyby and 25143 Itokawa rendezvous.     

The energy transfer process in planetary flybys

We illustrate the energy transfer during planetary flybys as a function of time using a number of flight mission examples. The energy transfer process is rather more complicated than a monotonic increase (or decrease) of energy with time. It exhibits temporary maxima and minima with time which then partially moderate before the asymptotic condition is obtained. The energy transfer to angular momentum is exhibited by an approximate Jacobi constant for the system.We demonstrate this with flybys that have shown unexplained behaviors: (i) the possible onset of the “Pioneer anomaly” with the gravity assist of Pioneer 11 by Saturn to hyperbolic orbit (as well as the Pioneer 10 hyperbolic gravity assist by Jupiter) and (ii) the Earth flyby anomalies of small increases in energy in the geocentric system (Galileo-I, NEAR, and Rosetta, in addition discussing the Cassini and Messenger flybys). Perhaps some small, as yet unrecognized effect in the energy-transfer process can shed light on these anomalies.     

Hydrated minerals on Europa’s surface: An improved look from the Galileo NIMS investigation

The surface composition of Europa is of great importance for understanding both the internal evolution of Europa and its putative ocean. The Near Infrared Mapping Spectrometer (NIMS) investigation on Galileo observed Europa and the other Galilean satellites from 0.7 to 5.2 μm with spatial resolution down to a few kilometers during flybys by the spacecraft as it orbited Jupiter. These data have been analyzed and results published over the life of the Galileo mission and afterward. One result was the discovery of hydrated minerals at some locations on Europa and Ganymede. The data are noisy, especially for Europa, due to radiation affecting the NIMS electronics and detectors, and other artifacts are also present. The NIMS data are now being reprocessed using the accumulated knowledge gained over the entire missions to remove noise spikes and compensate for some other defects in the data. We are analyzing these reprocessed data in an attempt to defined better the nature of the hydrate spectral features and improve their interpretation. We report here on analyses of two NIMS reprocessed observations for the 0.7-3-μm region. A revised hydrate spectrum is calculated and mapped in detail across two lineaments. The spectrum shows the expected distorted water features but little or no spectral structure in these features. A narrow, weak spectral feature appears at 1.344 μm, which is weakly correlated with lower albedo. Several other weak features may be present but are difficult to confirm in these limited data sets. The hydrate signature shows the greatest strength within and toward the center of the lineaments, confirming and strengthening the association of the hydrate with these endogenic features. This trend may indicate that the material in the lineaments is youngest toward the center and has more water frost coverage toward the edge. A small, visually dark, circular feature has a spectrum that shows both hydrate and crystalline water ice features and perhaps contains a hydrate different in spectral characteristics and perhaps composition than found in the lineament.