Showing papers on "Trojan published in 2005"

Chaotic capture of Jupiter's Trojan asteroids in the early Solar System.

Abstract: A collection of three papers in this issue, tackling seemingly unrelated planetary phenomena, marks a notable unification of Solar System dynamics. The three problems covered are the hard-to-explain orbits of giant planets, the evolution of the orbits of Jupiter's Trojan asteroids, and the cause of the ‘Late Heavy Bombardment’ that peppered the Moon with meteors, comets and asteroids some 700 million years after the planets were formed. Key to all these events, on this new model, was a rapid migration of the giant planets (Saturn, Jupiter, Neptune and Uranus) after a long period of stability within the Solar System. Jupiter's Trojans are asteroids that follow essentially the same orbit as Jupiter, but lead or trail the planet by an angular distance of ∼60 degrees (co-orbital motion). They are hypothesized to be planetesimals that formed near Jupiter and were captured onto their current orbits while Jupiter was growing1,2, possibly with the help of gas drag3,4,5,6 and/or collisions7. This idea, however, cannot explain some basic properties of the Trojan population, in particular its broad orbital inclination distribution, which ranges up to ∼40 degrees (ref. 8). Here we show that the Trojans could have formed in more distant regions and been subsequently captured into co-orbital motion with Jupiter during the time when the giant planets migrated by removing neighbouring planetesimals9,10,11,12. The capture was possible during a short period of time, just after Jupiter and Saturn crossed their mutual 1:2 resonance, when the dynamics of the Trojan region were completely chaotic. Our simulations of this process satisfactorily reproduce the orbital distribution of the Trojans and their total mass.

Size Distribution of Faint Jovian L4 Trojan Asteroids

Abstract: We detected 51 faint Jovian Trojan asteroids in the L4 Lagrangian swarm in survey observations near opposition and the ecliptic using a wide-field mosaicked CCD camera on the 8.2 m Subaru Telescope. We report the Trojan size distributions in this paper. The surveyed sky area was about 3 deg2 and located ~30° in longitude ahead of the L4 point. From trailed-image simulations of hypothetical Trojans, we measured the 90% complete detection limiting magnitudes for our Trojan asteroids on a CCD chip-by-chip basis. The limiting magnitudes varied by 0.4–0.5 mag between chips; therefore, we introduce a new measure of detection limit appropriate for multichip CCD cameras. By statistically comparing the observed number of Trojans with the predictions from theoretical size distributions near the limiting magnitude calculated in this way, we determined a limiting diameter of D ~ 2 km, corresponding to the detection limit of this survey. On the other hand, the detected Trojans covered a size range of 0.7 km 1 km. Finally, we discuss, from a cosmogonic viewpoint, a possible relation between Trojans and short-period comets on the basis of their size distribution slopes.

Neptune Trojans as a Test Bed for Planet Formation

Abstract: The problem of accretion in the Trojan 1 : 1 resonance is akin to the standard problem of planet formation, transplanted from a star-centered disk to a disk centered on the Lagrange point. The newly discovered class of Neptune Trojans promises to test theories of planet formation by coagulation. Neptune Trojans resembling the prototype 2001 QR322 ("QR")—whose radius of ~100 km is comparable to that of the largest Jupiter Trojan—may outnumber their Jovian counterparts by a factor of ~10. We develop and test three theories for the origin of large Neptune Trojans: pull-down capture, direct collisional emplacement, and in situ accretion. These theories are staged after Neptune's orbit anneals, that is, after dynamical friction eliminates any large orbital eccentricity and after the planet ceases to migrate. We discover that seeding the 1 : 1 resonance with debris from planetesimal collisions and having the seed particles accrete in situ naturally reproduces the inferred number of QR-sized Trojans. We analyze accretion in the Trojan subdisk by applying the two-groups method, accounting for kinematics specific to the resonance. We find that a Trojan subdisk comprising decimeter-sized seed particles and having a surface density ~10-3 times that of the local minimum-mass disk produces ~10 QR-sized objects in ~1 Gyr, in accord with observation. Further growth is halted by collisional diffusion of seed particles out of resonance. In our picture, the number and sizes of the largest Neptune Trojans represent the unadulterated outcome of dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the most newly accreted objects in our solar system, may today have a dispersion in orbital inclination of less than ~10°, despite the existence of niches of stability at higher inclinations. Such a vertically thin disk, born of a dynamically cold environment necessary for accretion and raised in minimal contact with external perturbations, contrasts with the thick disks of other minor body belts.

Neptune Trojans as a Testbed for Planet Formation

Abstract: The problem of accretion in the Trojan 1:1 resonance is akin to the standard problem of planet formation, transplanted from a star-centered disk to a disk centered on the Lagrange point. The newly discovered class of Neptune Trojans promises to test theories of planet formation by coagulation. Neptune Trojans resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is comparable to that of the largest Jupiter Trojan--may outnumber their Jovian counterparts by a factor of ~10. We discover that seeding the 1:1 resonance with debris from planetesimal collisions and having the seed particles accrete in situ naturally reproduces the inferred number of QR-sized Trojans. We analyze accretion in the Trojan sub-disk by applying the two-groups method, accounting for kinematics specific to the resonance. We find that a Trojan sub-disk comprising decimeter-sized seed particles and having a surface density 1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1 Gyr, in accord with observation. Further growth is halted by collisional diffusion of seed particles out of resonance. In our picture, the number and sizes of the largest Neptune Trojans represent the unadulterated outcome of dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the most newly accreted objects in our Solar System, may today have a dispersion in orbital inclination of less than ~10 degrees, despite the existence of niches of stability at higher inclinations. Such a vertically thin disk, born of a dynamically cold environment necessary for accretion, and raised in minimal contact with external perturbations, contrasts with the thick disks of other minor body belts.

On the construction of the Kolmogorov normal form for the Trojan asteroids

Abstract: In this paper, we focus on the stability of the Trojan asteroids for the planar restricted three-body problem, by extending the usual techniques for the neighbourhood of an elliptic point to derive results in a larger vicinity. Our approach is based on numerical determination of the frequencies of the asteroid and effective computation of the Kolmogorov normal form for the corresponding torus. This procedure has been applied to the first 34 Trojan asteroids of the IAU Asteroid Catalogue, and it has worked successfully for 23 of them. The construction of this normal form allows computer-assisted proofs of stability. To show this, we have implemented a proof of existence of families of invariant tori close to a given asteroid, for a high order expansion of the Hamiltonian. This proof has been successfully applied to three Trojan asteroids.

Trojan pairs in the HD 128311 and HD 82943 planetary systems

Abstract: Two nearby stars, HD 128311 and HD 82943, are believed to host pairs of Jupiter-like planets involved in a strong first order 2:1 mean motion resonance (MMR). In this work we reanalyze available radial velocity (RV) measurements and demonstrate that it is also possible to explain the observed RV variations of the parents stars as being induced by a pair of Trojan planets (i.e., in a 1:1 MMR). We show that these Trojan configurations reside in extended zones of stability in which such systems may easily survive in spite of large masses of the planets, large eccentricities and nonzero mutual inclinations of their orbits. We also show that HD 82943 could harbor a previously unknown third planet about of 0.5 Jupiter masses in 2.1 AU orbit.

Chaotic diffusion and effective stability of jupiter trojans

Abstract: It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T L and the escape time, T E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T E = 1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T L and T E is found.

The observed trojans and the global dynamics around the lagrangian points of the sun-jupiter system

Abstract: In this paper, we make a systematic study of the global dynamical structure of the Sun-Jupiter L 4 tadpole region. The results are based on long-time simulations of the Trojans in the Sun, Jupiter, Saturn system and on the frequency analysis of these orbits. We give some initial results in the description of the resonant structure that guides the long-term dynamics of this region. Moreover, we are able to connect this global view of the phase space with the observed Trojans and identify resonances in which some of the real bodies are located.

Malicious cryptography: kleptographic aspects

Abstract: In the last few years we have concentrated our research efforts on new threats to the computing infrastructure that are the result of combining malicious software (malware) technology with modern cryptography. At some point during our investigation we ended up asking ourselves the following question: what if the malware (i.e., Trojan horse) resides within a cryptographic system itself? This led us to realize that in certain scenarios of black box cryptography (namely, when the code is inaccessible to scrutiny as in the case of tamper proof cryptosystems or when no one cares enough to scrutinize the code) there are attacks that employ cryptography itself against cryptographic systems in such a way that the attack possesses unique properties (i.e., special advantages that attackers have such as granting the attacker exclusive access to crucial information where the exclusive access privelege holds even if the Trojan is reverse-engineered). We called the art of designing this set of attacks “kleptography.” In this paper we demonstrate the power of kleptography by illustrating a carefully designed attack against RSA key generation.

The instability of venus trojans

Abstract: Using Laskar's frequency map analysis, we investigate the long-term stability of Venus Trojan orbits. By measuring the diffusion rate of proper frequencies, we outline in phase space the most stable region. It is located between 5° and 10° in proper inclination with libration amplitudes ranging from 50° to 110°. The proper eccentricity is lower than 0.13. The stable region is surrounded by secular resonances that destabilize orbits on short timescales. The dynamical half-life of orbits within the stable region is about 6 × 108 yr. The Yarkovsky effect further reduces the dynamical lifetime. Therefore, primordial Venus Trojans, if any, cannot have survived until the present. Transient Trojans, on the other hand, cannot be excluded.

On the stability regions of the Trojan asteroids

Abstract: The orbits of fictitious bodies around Jupiter’s stable equilibrium points L 4 and L 5 were integrated for a fine grid of initial conditions up to 100 million years. We checked the validity of three different dynamical models, namely the spatial, restricted three body problem, a model with Sun, Jupiter and Saturn and also the dynamical model with the Outer Solar System (Jupiter to Neptune). We determined the chaoticity of an orbit with the aid of the Lyapunov Characteristic Exponents (=LCE) and used also a method where the maximum eccentricity of an orbit achieved during the dynamical evolution was examined. The goal of this investigation was to determine the size of the regions of motion around the equilibrium points of Jupiter and to find out the dependance on the inclination of the Trojan’s orbit. Whereas for small inclinations (up to i = 20°) the stable regions are almost equally large, for moderate inclinations the size shrinks quite rapidly and disappears completely for i > 600. Additionally, we found a difference in the dynamics of orbits around L 4 which — according to the LCE — seem to be more stable than the ones around L 5.

Trojans in habitable zones.

Abstract: With the aid of numerical experiments we examined the dynamical stability of fictitious terrestrial planets in 1:1 mean motion resonance with Jovian-like planets of extrasolar planetary systems. In our stability study of the so-called "Trojan" planets in the habitable zone, we used the restricted three-body problem with different mass ratios of the primary bodies. The application of the three-body problem showed that even massive Trojan planets can be stable in the 1:1 mean motion resonance. From the 117 extrasolar planetary systems only 11 systems were found with one giant planet in the habitable zone. Out of this sample set we chose four planetary systems—HD17051, HD27442, HD28185, and HD108874—for further investigation. To study the orbital behavior of the stable zone in the different systems, we used direct numerical computations (Lie Integration Method) that allowed us to determine the escape times and the maximum eccentricity of the fictitious "Trojan planets." Astrobiology 5, 579–586.

MarsSat: assured communication with Mars.

Abstract: The author developed the MarsSat concept during the 1990s. For this task, he designed a class of orbits to solve the problem of communicating with crews on Mars when the planet is in solar conjunction as seen from Earth, a planetary configuration that occurs near the midpoint of a conjunction class mission to Mars. This type of orbit minimizes the distance between Mars and the communications satellite; thus, minimizing the size, weight, and power requirements, while providing a simultaneous line-of-sight to both Earth and Mars. The MarsSat orbits are solar orbits that have the same period as Mars, but are inclined a few degrees out of the plane of the Mars orbit and also differ in eccentricity from the orbit of Mars. These differences cause a spacecraft in this orbit to rise North of Mars, then fall behind Mars, then drop South of Mars, and then pull ahead of Mars, by some desired distance in each case-typically about 20 million kilometers-in order to maintain an angular separation of a couple of degrees as seen from a point in the orbit of Earth on the opposite side of the Sun. A satellite in this type of orbit would relay communications between Earth and Mars during the period of up to several weeks, when direct communication is blocked by the Sun. These orbits are far superior for this purpose when compared to stationing a satellite at one of the Sun-Mars equilateral Lagrangian points, L 4 or L 5 , for two reasons. First, L 4 and L 5 are 228 million kilometers from Mars, about 10 times the distance of a spacecraft in one of the MarsSat orbits, and by virtue of the inverse-square law, all other things being equal, the signal strength received at L 4 or L 5 would be one percent of the signal strength received by a spacecraft in one of the MarsSat orbits. Thus, a relay satellite stationed at L 4 or L 5 would have to be that much more powerful to receive data at the same rate, with concomitant increases in spacecraft size and weight. Second, a number of Martian Trojan asteroids have been discovered at the Sun-Mars L 4 and L 5 points, and there are probably countless smaller objects that have collected in these regions that pose a significant threat to any spacecraft located there.

Euripides' Trojan women

Abstract: In this dissertation, I approach the interpretation of a classical text in performance by examining the practical elements (directorial and design choices: set, costumes, lighting, music, etc.) and promotional materials (programmes, press releases, photographs, etc.) for a selection of significant test cases in order to determine how these production decisions engage with external factors of political, intellectual, and cultural import. Trojan Women is a particularly useful case study to explore within the parameters of this method because the dynamism and immediacy of the play is most powerfully articulated when production choices allow for it to be wielded as a weapon of protest or reaction against contemporary policy, especially the waging of war. Using a chronological approach, this analysis of Trojan Women as a text for performance provides a broad and in-depth discussion of the reception of the play in the twentieth century, the period in which the ancient text was most frequently performed. Through the investigation of several influential productions on the international stage, and through an examination of the roles of key players (particularly Gilbert Murray and Jean-Paul Sartre), Trojan Women emerges as a play that offers theatre artists a unique and effective forum for debating issues of human responsibility in times of war a central theme in the play and a considerable preoccupation during a century of armed conflict. Chapter One discusses how the play was used to criticize imperial activity and promote ideological causes in the first half of the century. Chapters Two and Three draw attention to a major cluster of performances reflecting the spirit of international war protest in the 1960s and 1970s. Chapter Four addresses productions of the play affected by delayed responses to the Holocaust. Chapter Five features performances in the 1990s that respond to crises of civil conflict and genocide.

Euripides' Trojan women : a 20th century war play in performance

Abstract: Euripides' Trojan Women: A 20th Century War Play in Performance Avery T. Willis, Balliol College Faculty of Classics, Sub-Faculty of Classical Languages and Literature Submitted for Degree of Doctor of Philosophy, Trinity Term 2005 Supervisor: Professor Oliver Taplin, Magdalen College In this dissertation, I approach the interpretation of a classical text in performance by examining the practical elements (directorial and design choices: set, costumes, lighting, music, etc.) and promotional materials (programmes, press releases, photographs, etc.) for a selection of significant test cases in order to determine how these production decisions engage with external factors of political, intellectual, and cultural import. Trojan Women is a particularly useful case study to explore within the parameters of this method because the dynamism and immediacy of the play is most powerfully articulated when production choices allow for it to be wielded as a weapon of protest or reaction against contemporary policy, especially the waging of war. Using a chronological approach, this analysis of Trojan Women as a text for performance provides a broad and in-depth discussion of the reception of the play in the twentieth century, the period in which the ancient text was most frequently performed. Through the investigation of several influential productions on the international stage, and through an examination of the roles of key players (particularly Gilbert Murray and Jean-Paul Sartre), Trojan Women emerges as a play that offers theatre artists a unique and effective forum for debating issues of human responsibility in times of war a central theme in the play and a considerable preoccupation during a century of armed conflict. Chapter One discusses how the play was used to criticize imperial activity and promote ideological causes in the first half of the century. Chapters Two and Three draw attention to a major cluster of performances reflecting the spirit of international war protest in the 1960s and 1970s. Chapter Four addresses productions of the play affected by delayed responses to the Holocaust. Chapter Five features performances in the 1990s that respond to crises of civil conflict and genocide.

Analysis of Chemical, REP, and SEP missions to the Trojan asteroids

Abstract: Recent studies suggest significant benefits from using 1st and 2nd generation Radioisotope Power Systems (RPS) as a power source for electric propulsion (EP) missions to the outer planets. This study focuses on trajectories to the Trojan asteroids. A high level analysis is performed with chemical trajectories to determine potential canidates for REP trajectory optimization. Extensive analysis of direct trajectories using REP is performed on these candidates. Solar Electric Propulsion (SEP) trajectories are also considered for comparison against REP trajectories.

The Trojan War

Abstract: Series Foreword Author's Preface Timeline The Trojan War in History and Legend Troy and the World of the Late Bronze Age Finding Troy and the Trojan War Homer and the Epic Tradition The Force of Legend Troy in the Twenty-First Century Biographical Sketches Readings From Primary Documents and Other Sources Glossary of Selected Terms Annotated Bibliography Index

Hawking radiation from trojan states in muonic hydrogen in a strong laser field

Abstract: We show that the Unruh-Davis effect is measurable from Trojan wavepackets in muonic hydrogen as the acceleration on the first muonic Bohr orbit reaches 10 25 of the earth's acceleration. It is the biggest acceleration achievable in the laboratory environment ever predicted for the cyclotronic configuration. We calculate the ratio between the power of the Larmor radiation and the power of the Hawking radiation. The Hawking radiation is measurable even for Rydberg quantum numbers of the muon due to suppression of spontaneous emission in Trojan hydrogen.

Librations with Mass Transfer in the Sun-Jupiter System

Abstract: Trojan-type motion is analytically and numerically studied under mass transfer between the primaries with conservation of their total orbital angular momentum. We prove theoretically and numerically our new result that angular libration widths change as m^1/4, (m - Jupiter mass) if they are throughout smaller than about 60 arcd. Numerical examples show that for initial libration widths larger than about 60 arcd, the Trojan is ultimately driven out of the libration domain, becoming an ordinary asteroid, if Jupiter's transferred mass increases by a factor less than about two. Certain processes occurring in our solar system and in extrasolar planetary systems lead to a decrease of the Trojan's libration amplitude, while other processes lead to an increase, respectively.

Trojan: Trojans & spyware: an electronic achilles

Abstract: ICSTIS, the body that regulates premium rate phone numbers in the UK, recently received about 50,000 complaints from PC users who claimed that secret Trojan software had changed their Internet dial-up settings to connect automatically to premium rate phone numbers.