Showing papers on "Trojan published in 2001"

A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system

Abstract: We focus on the dynamics of a small particle near the Lagrangian points of the Sun-Jupiter system. To try to account for the effect of Saturn, we develop a specific model based on the computation of a true solution of the planar three-body problem for Sun, Jupiter and Saturn, close to the real motion of these three bodies. Then, we can write the equations of motion of a fourth infinitesimal particle moving under the attraction of these three masses. Using suitable coordinates, the model is written as a time-dependent perturbation of the well-known spatial Restricted Three-Body Problem. Then, we study the dynamics of this model near the triangular points. The tools are based on computing, up to high order, suitable normal forms and first integrals. From these expansions, it is not difficult to derive approximations to invariant tori (of dimensions 2, 3 and 4) as well as bounds on the speed of diffusion on suitable domains. We have also included some comparisons with the motion of a few Trojan asteroids in the real Solar system.

Planetary Migration and the Effects of Mean Motion Resonances on Jupiter’s Trojan Asteroids

Abstract: We present results of several numerical simulations of fictitious Trojan asteroids under different resonant configurations of the outer planets, especially between Jupiter and Saturn. Although the present outer solar system is not locked in mean motion resonances, such commensurabilities may have been temporarily attained in the past if current theories of planetary migration are correct. By studying the evolution of Trojan-like test particles under these conditions, it is possible to obtain information related to the maximum variation of the semimajor axes of the two major Jovian planets, as well as insights on the duration of the migration itself. Results show that the 2S : 1J and 5S : 2J Jupiter-Saturn resonances introduce large instabilities in the Trojan region. In the case of 2S : 1J, a few thousand years are sufficient to expel all particles initially in tadpole orbits. For 5S : 2J, these may survive for up to 106 yr. The 7S : 3J commensurability, on the other hand, is much less disruptive. These results seem to indicate that the observed presence of the Jovian Trojans is compatible with a planetary migration as proposed by Han & Malhotra, in which the orbital distance between Jupiter and Saturn did not vary by more about 1 AU. Larger variations of the semimajor axes seem unlikely.

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.

Why do Trojan ASCs (not) Escape

Abstract: The orbits of 12 Trojan asteroids, which have Lyapunov times T L ~ 105 years and were previously classified as ASCs(=asteroids in stable chaos), are integrated for 50 Myrs, along with a group of neighbouring initial conditions for each nominal orbit. About 40% of the orbits present strong instabilities in the inclination, which may be attributed primarily to the action of the v16 secular resonance; two escapes are also recorded. Higher-order secular resonances, involving the nodes of the outer planets, are also found to be responsible for chaotic motion. Orbital stability depends critically on the choice of initial conditions and, thus, these objects can be regarded as being on the edge of strong chaos.

Planetary migration and the effects of mean motion resonances on jupiters

Abstract: We present results of several numerical simulations of —ctitious Trojan asteroids under diUerent resonant con—gurations of the outer planets, especially between Jupiter and Saturn. Although the present outer solar system is not locked in mean motion resonances, such commensurabilities may have been temporarily attained in the past if current theories of planetary migration are correct. By studying the evolution of Trojan-like test particles under these conditions, it is possible to obtain information related to the maximum variation of the semimajor axes of the two major Jovian planets, as well as insights on the duration of the migration itself. Results show that the 2S:1J and 5S:2J Jupiter-Saturn resonances introduce large instabilities in the Trojan region. In the case of 2S:1J, a few thousand years are sufficient to expel all particles initially in tadpole orbits. For 5S:2J, these may survive for up to 106 yr. The 7S:3J commensurability, on the other hand, is much less disruptive. These results seem to indicate that the observed presence of the Jovian Trojans is compatible with a planetary migration as proposed by Han & Malhotra, in which the orbital distance between Jupiter and Saturn did not vary by more about 1 AU. Larger variations of the semimajor axes seem unlikely.

SKETHIC: Secure Kernel Extension against Trojan Horses with Information-Carrying Codes

Abstract: Trojan-horses are hard to detect since they pretend normal programs [14]. This paper proposes 'SKETHIC (Secure Kernel Extension against Trojan Horses with Information-carrying Codes)', an anti-Trojan method based on resource access information attached to codes. This information serves as criteria for users' decision on installation of programs and forms access control policies for the runtime monitoring system. Compared to the previous approaches, SKETHIC introduces a way of reducing the users' decision-making overhead. To show clearly how it keeps a host secure from Trojans, we describe the mechanism in a formal way.

IA and Software

Abstract: No discussion of information assurance is complete without at least an overview of IA as it relates to operating systems and application software. This chapter will discuss information assurance problems and possible solutions as they relate to operating systems and application software. The discussion will include views on malicious codes such as viruses, logic bombs and Trojan horses.

Elementary celestial mechanics using Matlab

Abstract: The Trojan asteroids, discovered almost a century ago, are direct evidence for stability in the pure three-body problem. Two groups of asteroids share Jupiter's orbit, preceding or trailing it by an angle of 60 degrees. Because the Sun and Jupiter are by far the heaviest bodies, the restricted three body model is perfectly adequate to describe the relevant dynamics, and the perturbations due to the attraction of other planets do not significantly modify the orbit. For a hypothetical Lagrangian satellite bound to Earth and the Moon, we cannot discard the Sun's influence a priori. The problem of stability in this case is very hard; no analytic result is known, up to now. However, numerical analysis can give us a plausible answer. In spring 1999, I made this problem a classroom activity for my physics undergraduate students at the University of Parma. These students had an elementary background in classical mechanics but no computational-physics training. The choice of Matlab as a working environment was rather natural. With a little sacrifice in speed compared to Fortran or C, Matlab let us build a working program in a few days, including visualization and a friendly user interface. We easily found clear numerical evidence that the equilateral orbits L/sub 4/ and L/sub 5/ in the Earth-Moon system are unstable. I describe the program's setup, its Matlab implementation and the results.

The F airy Ta le o f ,What Yo u S ee I s W hat Yo u S ign' - Trojan H orse A ttacks o n Software f or D igital S ignatures

Abstract: Software for the creation of digital signatures performs a delicate task. The signatory has to trust the manufacturer of the software that it will work in the intended way. Signing a document electronically will have legal consequences in a growing number of countries, therefore the security of the signing software is an important issue. In the past, Trojan horse programs have shown to be of grow- ing concern for end-user computers. Software for digital signatures must provide protection against Trojan horses attacking the legally relevant signing process. In a survey of commercially-of-the-shelf signature software programs we found severe vulnerabilities that can easily be exploited by an attacker.