Trojan

About: Trojan is a research topic. Over the lifetime, 2028 publications have been published within this topic receiving 33209 citations.

A near-infrared search for silicates in jovian trojan asteroids

Abstract: We obtained near-infrared (NIR; 0.8–2.5 μm) spectra of seven Jovian Trojan asteroids that have been formerly reported to show silicate-like absorption features near 1 μm. Our sample includes the Trojan (1172) Aneas, which is one of the three Trojans known to possess a comet-like 10 μm emission feature, indicative of fine-grained silicates. Our observations show that all seven Trojans appear featureless in high signal-to-noise ratio spectra. The simultaneous absence of the 1 μm band and the presence of the 10 μm emission can be understood if the silicates on (1172) Aneas are iron-poor. In addition, we present NIR observations of five optically gray Trojans, including three objects from the collisionally produced Eurybates family. The five gray Trojans appear featureless in the NIR with no diagnostic absorption features. The NIR spectrum of Eurybates can be best fitted with the spectrum of a CM2 carbonaceous chondrite, which hints that the C-type Eurybates family members may have experienced aqueous alteration.

Effective stability of the Trojan asteroids

Abstract: We study the spatial circular restricted problem of three bodies in the light of Nekhoroshev theory of stability over large time intervals. We consider in particular the Sun-Jupiter model and the Trojan asteroids in the neighborhood of the Lagrangian point L 4 . We find a region of effective stability around the point L 4 such that if the initial point of an orbit is inside this region the orbit is confined in a slightly larger neighborhood of the equilibrium (in phase space) for a very long time interval. By combining analytical methods and numerical approximations we are able to prove that stability over the age of the universe is guaranteed on a realistic region, big enough to include one real asteroid. By comparing this result with the one obtained for the planar problem we see that the regions of stability in the two cases are of the same magnitude.

Resonant and Secular Families of the Kuiper Belt

Abstract: We review ongoing efforts to identify occupants of mean-motion resonances (MMRs) and collisional families in the Edgeworth—Kuiper belt. Direct integrations of trajectories of Kuiper belt objects (KBOs) reveal the 1:1 (Trojan), 5:4, 4:3, 3:2 (Plutino), 5:3, 7:4, 9:5, 2:1 (Twotino), and 5:2 MMRs to be inhabited. Apart from the Trojan, resonant KBOs typically have large orbital eccentricities and inclinations. The observed pattern of resonance occupation is consistent with resonant capture and adiabatic excitation by a migratory Neptune; however, the dynamically cold initial conditions prior to resonance sweeping that are typically assumed by migration simulations are probably inadequate. Given the dynamically hot residents of the 5:2 MMR and the substantial inclinations observed in all exterior MMRs, a fraction of the primordial belt was likely dynamically pre-heated prior to resonance sweeping. A pre-heated population may have arisen as Neptune gravitationally scattered objects into trans-Neptunian space. The spatial distribution of Twotinos offers a unique diagnostic of Neptune’s migration history. The Neptunian Trojan population may rival the Jovian Trojan population, and the former’s existence is argued to rule out violent orbital histories for Neptune. Finally, lowest-order secular theory is applied to several hundred non-resonant KBOs with well-measured orbits to update proposals of collisional families. No convincing family is detected.

Detection of trojans using a combined ring oscillator network and off-chip transient power analysis

Abstract: Verifying the trustworthiness of Integrated Circuits (ICs) is of utmost importance, as hardware Trojans may destroy ICs bound for critical applications. A novel methodology combining on-chip structure with external current measurements is proposed to verify whether or not an IC is Trojan free. This method considers Trojans' impact on neighboring cells and on the entire IC's power consumption, and effectively localizes the measurement of dynamic power. To achieve this, we develop a new on-chip ring oscillator network structure distributed across the entire chip and place each ring oscillator's components in different rows of a standard-cell design. By developing novel statistical data analysis, the effect of process variations on the ICs' transient power will be separated from the effect of Trojans. Simulation results using 90nm technology and experimental results on Xilinx Spartan-6 FPGAs demonstrate the efficiency of our proposed method.

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

Abstract: The possibility that giant extrasolar planets could have small Trojan co-orbital companions has been examined in the literature from both viewpoints of the origin and dynamical stability of such a configuration. Here we aim to investigate the dynamics of hypothetical small Trojan exoplanets in domains of secondary resonances embedded within the tadpole domain of motion. To this end, we consider the limit of a massless Trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of additional planets (hereafter referred to as the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the dynamics of the Trojan body. The paper contains a theoretical and a numerical part. In the theoretical part, we develop a Hamiltonian formalism in action-angle variables, which allows us to treat in a unified way resonant dynamics and secular effects on the Trojan body in both the ERTBP or the RMPP. In both cases, our formalism leads to a decomposition of the Hamiltonian in two parts, $$H=H_b+H_{sec}$$ . $$H_b$$ , called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom, while $$H_{sec}$$ contains only terms depending trigonometrically on slow (secular) angles. $$H_b$$ is formally identical in the ERTBP and the RMPP, apart from a re-definition of some angular variables. An important physical consequence of this analysis is that the slow chaotic diffusion along resonances proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism. We found that this is best approximated by the paradigm of ‘modulational diffusion’. In the paper’s numerical part, we then focus on the ERTBP in order to make a detailed numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we first provide a survey of the resonant web for characteristic mass parameter values of the primary, in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the synodic period), as well as their transverse resonant multiplets, appear. We give numerical examples of diffusion of weakly chaotic orbits in the resonant web. We finally make a statistics of the escaping times in the resonant domain, and find power-law tails of the distribution of the escaping times for the slowly diffusing chaotic orbits. Implications of resonant dynamics in the search for Trojan exoplanets are discussed.