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The 1990 MB: The first Mars Trojan

Asteroid 1990 MB was discovered by D. H. Levy and H. E. Holt during the course of the Mars and Earth Crossing Asteroid and Comet Survey. An orbit based on a 9 day arc and the asteroid's location near Mars' L5 (trailing Lagrangean) longitude led E. Boswell to speculate that it might be in 1:1 resonance with Mars, analogous to the Trojan asteroids of Jupiter. Subsequent observations strengthened the possibility, and later calculations confirmed it. Thus 1990 MB is the first known asteroid in 1:1 resonance with a planet other than Jupiter. The existence of 1990 MB (a small body most likely between 2 and 4 km in diameter) provides remarkable confirmation of computer simulations. These self consistent n-body simulations demonstrated this sort of stability for Trojans of all the terrestrial planets over at least a 2 million year time base. The discovery of 1990 MB suggests that others of similar or smaller diameter may be found. Using hypothetical populations of Mars Trojans, their possible sky plane distributions were modeled as a first step in undertaking a systematic observational search of Mars' L4 and L5 libration regions.

Innanen, Kimmo A.↗

Mapping the stability field of Jupiter Trojans

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Levison, H. F.↗

JHK photometry of selected Trojan and Hilda asteroids

No entirely satisfactory match has been established between the present JHK photometry of selected Hilda and Trojan asteroids and photometry for both main belt asteroids and laboratory samples. It is noted that while the leading Trojans and Hildas exhibit similar and homogeneous JHK colors, the trailing Trojans appear to be more heterogeneous. Charcoal and magnetite provide the best match in terms of JHK colors.

Smith, Dale W.↗

Spectroscopy and Photometry of Mars Trojans

Mars is the only terrestrial planet known to have co-orbiting "Trojan" asteroids. We have obtained visible and near-IR reflectance spectra of three of these objects: 5261 Eureka and 1998 VF31 in the L5 region and 1999 UJ7 in the L4 region. We also obtained JHK spectrophotometry and a visible lightcurve for 5261 Eureka. The asteroid 5261 Eureka has a visible spectrum that is classified as Sr in the Bus taxonomy, and has infrared colors consistent with the A-class asteroids. The data for 1998 VF31 have a restricted wavelength range, but are most consistent with the Sr or Sa class, though we note a marginal consistency with the D class. We can rule out a C-class classification. 1999 UJ7 has an X-class or T-class spectrum, which is unlike that of the other two Mars Trojans. The photometric data for Eureka are limited, but we can constrain the period to longer than 5 hours (likely 5.556 hours) and lightcurve amplitude of at least 0.15 magnitude at this viewing geometry. The spectral differences among the Mars Trojans suggests that either they did not all form at their present solar distances or that they have not always been at their present sizes. 0 2003 Elsevier Inc. All rights reserved. Keywords: Asteroids; Asteroids, composition; Spectroscopy; Satellites of Mars

Rivkin, A. S.↗

Spectroscopy and Photometry of Mars Trojans

Mars is the only terrestrial planet known to have co-orbiting Trojan asteroids. We have obtained visible and near-IR reflectance spectra of three of these objects: 5261 Eureka and 1998 VF31 in the L5 region and 1999 UJ7 in the LA region. We also obtained JHK spectrophotometry and a visible lightcurve for 5261 Eureka. The asteroid 5261 Eureka has a visible spectrum that is classified as Sr in the Bus taxonomy, and has infrared colors consistent with the A-class asteroids. The data for 1998 VF31 have a restricted wavelength range, but are most consistent with the Sr or Sa class, though we note a marginal consistency with the D class. We can rule out a C-class classification. 1999 UJ7 has an X-class or T-class spectrum, which is unlike that of the other two Mars Trojans. The photometric data for Eureka are limited, but we can constrain the period to longer than 5 hours (likely 5.5-6 hours) and lightcurve amplitude of at least 0.15 magnitude at this viewing geometry. The spectral differences among the Mars Trojans suggests that either they did not all form at their present solar distances or that they have not always been at their present sizes.

Rivkin, A. S.↗

MEGASIM: Distribution and Detection of Earth Trojan Asteroids

Abstract Using N -body simulation results from the MEGASIM data set, we present spatial distributions of Earth Trojan Asteroids and assess the detectability of the population in current and next-generation ground-based astronomical surveys. Our high-fidelity Earth Trojan Asteroid (ETA) distribution maps show never-before-seen high-resolution spatial features that evolve over timescales up to 1 Gyr. The simulation was synchronized to start times and timelines of two observational astronomy surveys: (1) the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) and (2) the Zwicky Transient Facility (ZTF). We calculate upper limits for the number of ETAs potentially observable with both the ZTF and LSST surveys. Due to the Yarkovsky Effect, we find no stable ETAs on billion-year timescales likely to be detected by any ETA survey, as no C-type or S-type ETAs (with H < 22 and H < 24, respectively) are likely to be stable on billion-year timescales, and ETAs large enough to remain stable on billion-year timescales are very rare relative to the rest of the ETA population. We find that a twilight ETA survey will not drastically increase the likelihood of individual ETA detection, but it would provide orders of magnitude more observations of select ETA populations. The null detection to date from ZTF restricts the potential ETA population to hundreds of objects larger than 100 m (at H ≈ 22), while a null detection by LSST will further restrict the ETA population to tens of objects larger than 100 m.

79 ASTRONOMY AND ASTROPHYSICS↗

Automated Design of Propellant-Optimal, End-to-End, Low-Thrust Trajectories for Trojan Asteroid Tours

The Sun-Jupiter Trojan asteroids are celestial bodies of great scientific interest as well as potential resources offering water and other mineral resources for longterm human exploration of the solar system. Previous investigations under this project have addressed the automated design of tours within the asteroid swarm. This investigation expands the current automation scheme by incorporating options for a complete trajectory design approach to the Trojan asteroids. Computational aspects of the design procedure are automated such that end-to-end trajectories are generated with a minimum of human interaction after key elements and constraints associated with a proposed mission concept are specified.

Trojan asteroid↗

Multiple Encounter Missions with the Trojan and Main Belt Asteroids

The clustering of asteroids, the Trojans, at the Jupiter liberation points L4 and L5 offer yearly launch opportunities for double flybys. Also, passage through the main belt can add one or two additional flybys to make this an attractive mission for small spacecraft. The Trojans represent important clusters of main-belt sized bodies. This study explores the possibilities of multiple asteroid encounters.

astrodynamics↗

Trojan horse method as an indirect approach to study resonant reactions in nuclear astrophysics

The primary goal of the Trojan horse method (THM) is to analyze resonant rearrangement reactions when the density of the resonance levels is low and statistical models cannot be applied. The main difficulty of the analysis is related with the facts that in the final state the THM reaction involves three particles and that the intermediate particle, which is transferred from the Trojan horse particle to the target nucleus to form a resonance state, is virtual. Another difficulty is associated with the Coulomb interaction between the particles, especially, taking into account that the goal of the THM is to study resonant rearrangement reactions at very low energies important for nuclear astrophysics. The exact theory of such reactions with three charged particles is very complicated and is not available. This is why different approximations are used to analyze THM reactions. In this review paper we describe a new approach based on a few-body formalism that provides a solid basis for deriving the THM reaction amplitude taking into account rescattering of the particles in the initial, intermediate and final states of the THM reaction. Since the THM uses a two-step reaction in which the first step is the transfer reaction populating a resonance state, we address the theory of the transfer reactions. The theory is based on the surface-integral approach and R-matrix formalism. We also discuss application of the THM to resonant reactions populating both resonances located on the second energy sheet and subthreshold resonances, which are subthreshold bound states located at negative energies close to thresholds. We consider the application of the THM to determine the astrophysical factors of resonant radiative-capture reactions at energies so low that direct measurements can hardly be performed due to the negligibly small penetrability factor in the entry channel of the reaction. Here, we elucidated the main ideas of the THM and outline necessary conditions to perform the THM experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

The $^3$He+$^5$He$\rightarrow $ $\alpha $+$\alpha $ reaction below the Coulomb barrier via the Trojan Horse Method

For the first time in an application to nuclear astrophysics, a process induced by the unstable 5 He = ( 4 He-n) nucleus, the 3 He+ 5 He→2α reaction, has been studied through the Trojan Horse Method (THM). For that purpose, the quasi-free (QF) contribution of the 9 Be( 3 He,αα) 4 He reaction was selected at E 3 He =4 MeV incident energy. The reaction was studied in a kinematically complete experiment following a recent publication, where for the quasi free contribution the momentum distribution between α and 5 He particle cluster in the 9 Be nucleus in the ground state have been extracted. The angular distribution of the QF 3 He+ 5 He→2α reaction was measured at θ cm = 78°–115°. The energy dependence of the differential cross section of the 3 He+ 5 He→2α virtual reaction was extracted in the energy range E cm = 0–650 keV. In conclusion, the total cross section obtained from the Trojan-horse method was normalized to absolute cross sections from a theoretical calculation in the energy range E cm =300–620 keV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Autonomous System Inference, Trojan, and Adversarial Reprogramming Attack and Defense (Final)

In the world of ever-advancing technology, Autonomous Systems (AS) find extensive application, bolstering functionalities of critical infrastructures such as nuclear power plants. These systems, however, are increasingly becoming a target for nefarious activities, namely through inference attacks, trojan attacks, and adversarial reprogramming. This paper delves into a comprehensive exploration of machine learning (ML)-driven autonomous control systems within advanced nuclear reactor designs, revealing the vulnerabilities and proposing strategies for defense against potential cyber-attacks. Advanced cyber-attacks against critical infrastructure and the energy sector are becoming more common. With the invention of autonomous control systems (ACS) within advanced nuclear reactor designs, system designers, reactor operators, and regulators must consider cybersecurity during the design and operational phases. This article provides a cyber threat assessment of machine learning (ML)- based digital twinning (DT) technologies in the context of advanced reactor ACS. A cyber-physical testbed was created to emulate nuclear reactor digital instrumentation and controls (I&C) and act as a basis for the ACS. The ACS was designed as two plant-level DTs predicting reactor malfunctions and determining control actions and two component-level DTs responsible for classifying component states and forecasting component inputs and outputs (I/O). Two duplicate ACS designs– one using a traditional ML framework and one using an automated ML (AutoML) framework– were created and tested against cyber-attacks on training data, real-time process data, and ML model architectures to determine their respective qualitative cyber-risk in terms of likelihood and impact. Both frameworks showed similar cyber-resilience against training, real-time, and ML architecture attacks, proving that neither is inherently more secure. Recommended safeguard and security measures are posed to system designers, reactor operators, and regulators to maintain the cybersecurity of ML-based DT technologies such as ACS, prompting a holistic view of shared responsibility for maintaining cyber-secure ML-based systems. As global reliance on generation III reactors begins to be critically assessed, the evolution towards advanced reactor systems utilizing digital instrumentation and controls (I&C) becomes not merely preferable, but essential. The integration of semi and fully autonomous control systems (ACS), powered by digital I&C and machine learning (ML)-based digital twinning (DT) technologies, emerges as a potent strategy to mitigate operations and maintenance costs, thereby enhancing the economic feasibility of novel reactor designs. However, with a staggering 500% and 380% increase in cyber-attacks reported against the energy sector by the United States Department of Energy (DoE) and the European Union respectively, a surge in cyber vulnerabilities specifically targeting the nuclear industry has been 2 markedly observed. Notable incidents, such as the W32.Ramnit spyware infiltration at the Gundremmingen nuclear power plant in Germany and the Dtrack spyware intrusion at the Kudankulam nuclear power plant in India, while not directly compromising core industrial control systems (ICS), underscore a compelling necessity to fortify cybersecurity protocols in safeguarding reactor systems against increasingly adept digital adversaries. In light of this, our investigation extends beyond conventional cybersecurity parameters, diving into the intricate web of potential vulnerabilities woven into ML-based DTs and ACS in advanced reactor systems. A crafted cyber-physical testbed and preliminary ACS were devised to act as a mirror, reflecting potential configurations of advanced reactor control designs. Moreover, this study is intertwined with a scrutinization of ML models, developed either through conventional, manually tuned methodologies or via automated means through AutoML, probing into their cyber-risk profiles within operational technology (OT) environments. Expanding on this, two distinct ACS blueprints were forged – one navigating through the corridors of traditional ML and the other traversing the path of AutoML – in an effort to holistically encapsulate the considerations pivotal to ML-based DT control system design. Employing the SANS Institute Industrial Control System (ICS) Kill Chain and the MITRE ATT&CK Tactics, Techniques, and Procedures (TTP) framework, a structured analysis was conducted, launching three targeted attacks against the training dataset, real-time dataset, and ML models, therein dissecting the potential cyber-attack implications against both ML frameworks within an ACS milieu. It is essential to note that three distinct categories of attacks were conducted against both ACS configurations, each encompassing three distinct ML-based DTs, cumulating in a total of 18 varied attacks. This exploration extends into the realms of Autonomous System Inference, Trojan, and Adversarial Reprogramming Attack and Defense, unraveling vulnerabilities, and opportunities for fortified defenses against such intrusions, particularly where ML-driven technologies, and by extension, ACS, are deployed. Final recommendations, articulated through a lens of security, safeguard, and implementation considerations, are presented for both traditional and AutoML models, anchoring upon the existing knowledge landscape and ML-based DT modeling for ACS, and are offered as a beacon to guide the nuclear industry through the intricate cybersecurity challenges that lie ahead.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Comet nuclei and Trojan asteroids - A new link and a possible mechanism for comet splittings

Relatively elongated shapes, implied by recent evidence of a greater incidence of high amplitude lightcurves for comet nuclei and Trojan asteroids than for similarly scaled main belt asteroids, are suggested to have evolved among comet nuclei and Trojans due to volatile loss. It is further suggested that such an evolutionary course may account for observed comet splitting; rotational splitting may specifically occur as a result of evolution in the direction of an elongated shape through sublimation. Supporting these hypotheses, the few m/sec separation velocities projected for rotationally splitting elongated nuclei are precisely in the observed range.

Hartmann, William K.↗

On the dynamical structure of the Trojan group of asteroids

Using a semi-analytical approach, domains of possible motion for Trojan asteroids were established. It is shown that stable librating motion is possible for both high inclination and high eccentricity. Frequency distributions were also produced for real Trojan asteroids, against differing libration amplitudes and libration periods.

Zagretdinov, R. V.↗

Lucy: Navigating a Jupiter Trojan Tour

In January 2017, NASA selected the Lucy mission to explore six Jupiter Trojan asteroids. These six bodies, remnants of the primordial material that formed the outer planets, were captured in the Sun-Jupiter L4 and L5 Lagrangian regions early in the solar system formation. These particular bodies were chosen because of their diverse spectral properties and the chance to observe up close for the first time two orbiting approximately equal mass binaries, Patroclus and Menoetius. KinetX, Inc. is the primary navigation supplier for the Lucy mission. This paper describes preliminary navigation analyses of the approach phase for each Trojan encounter.

trajectory design↗