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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.
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.
Determination and survey of periodic trojan orbits in the restricted problem of three bodies
Periodic trojan orbits and studies of their stability features
Long period libration of trojan minor planet
Short-period Trojan orbits in restricted three- body problem numerically determined, using Jupiter and Sun as principal masses
Long-period librations of Trojan planetary orbits in rotating three-body coordinate system
Elliptic restricted problem of periodic Trojan orbit and nonperiodic librational frequency and angular motion of Jupiter
Stability analysis of long period Trojan librations treated as short period oscillations about long period reference solution
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 dynamic plausibility of various ideas on the origin of the Trojans is briefly discussed. We take the point of view that the present, tightly bound population has secularly evolved through some mechanism from less to more tightly bound orbit configurations. The mechanisms considered are changes in the Jovian mass or semimajor axis during planetary formation, collisional interactions with external, asteroidal material, and cometary outgassing.
Consideration is given to the composition of those Trojan asteroids, Hilda asteroids and 944 Hidalgo with very low albedos and spectral reddening between 0.4 and 1.1 microns with respect to the C asteroids, termed RD objects. It is proposed that the albedo and reddening of these objects can be explained by the presence of very opaque, very red, polymer-type organic compounds structurally similar to kerogen, presumably resulting from Fischer-Tropsch-type reactions in the early solar nebula. The spectra and various mixtures of powdered montmorillonite, magnetite, coal-tar residue containing kerogen substances and carbon black are shown to provide a good match to the RD asteroid spectral properties. It is suggested that the nonsoluble carbonaceous residue may have required lower temperatures for its formation and preservation than carbonaceous materials in the carbonaceous chondrites and C asteroids, and thus explain the absence of RD objects closer than 4 AU from the sun.
New 30-channel narrowband photometry from 0.32 to 1.05 microns of the retrograde Jovian satellites J9 (to 0.7 micron) and J8 and the trailing Trojan asteroids 617, 884, 1172, and 1173 is presented. The data confirm previous measurements of J8, 617, 884, and 1172 at wavelengths less than 0.8 micron, but the extension into the infrared shows that the normalized spectral reflectance of these objects rises steadily from approximately 0.8 at 0.4 micron to approximately 1.4 at 1.05 microns, suggesting they are too bright in the near infrared to be C-type asteroids. The C classification of 1173 is confirmed. J9 is markedly redder than J8 at visible wavelengths. The results indicate a greater taxonomic contrast between these distant objects and main-belt asteroids than previously thought.
Asteroid 1990 MB was discovered 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 longitude led to speculation 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. The most recent orbit shows that the asteroid's semimajor axis is very similar to that of Mars.
Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the pertubations due to other planets.
We present a composite spectrum of Trojan asteroid 624 Hektor, 0.3-3.6 microns, which shows that there is no discernible 3-micron absorption band. Such a band would indicate the presence of OH or H2O- bearing silicate minerals, or macromolecular carbon-rich organic material of the kind seen on the low-albedo hemisphere of Saturn's satellite Iapetus (Owen et al. 2000). The absence of spectral structure is itself indicative of the absence of the nitrogen-rich tholins (which show a distinctive absorption band attributed to N-H). The successful models in this study all incorporate the mineral pyroxene (Mg, Fe SiO3, the composition of hypersthene), which matches the red color of Hektor. Pyroxene is a mafic mineral common in terrestrial and lunar lavas, and is also seen in Main Belt asteroid spectra. An upper limit to the amount of crystalline H20 ice (30-micron grains) in the surface layer of Hektor is 3 weight percent. The upper limit for serpentine, as a representative of hydrous silicates, is much less stringent, at 40 percent, based on the shape of the spectral region around 3 gm. Thus, the spectrum at 3 gm does not preclude the presence of a few weight percent of volatile material in the surface layer of Hektor. All of the models we calculated require elemental carbon to achieve the low geometric albedo that matches Hektor. This carbon could be of organic or inorganic origin. By analogy, other D-type asteroids could achieve their red color, low albedo, and apparent absence of phyllosilicates, from compositions similar to the models presented here.
The largest Mars trojan, 5261 Eureka, is one of two prototype "Sa" asteroids in the Bus-Demeo taxonomy. Analysis of its visible/near-IR spectrum led to the conclusion that it might represent either an angritic analog or an olivine-rich composition such as an R chondrite. Spitzer IRS data (5-30 micrometers) have enabled us to resolve this ambiguity. The thermal-IR spectrum exhibits strong olivine reststrahlen features consistent with a composition of approximately equals Fo60-70. Laboratory spectra of R chondrites, brachinites, and chassignites are dominated by similar features.
Impacts into forsterite and orthoenstatite at speeds typically encountered by comets demonstrate that shock imparted by collisions is detectable in the infrared signatures of their dust. The spectral signatures can be traced to physical alterations in their crystalline structures, as observed in TEM imaging and modeled using a dipole approximation. These results yield tantalizing insights into the collisional history of our solar system, as well as the history of individual comets and Trojan asteroids.