The dominant features of the long-period librations of the Trojan minor planets
Long-period librations of Trojan planetary orbits in rotating three-body coordinate system
TROJAN ORBIT↗
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Periodic Trojan orbits in the elliptic restricted problem.
Elliptic restricted problem of periodic Trojan orbit and nonperiodic librational frequency and angular motion of Jupiter
THREE-BODY PROBLEM↗
Third-order stability of the long-period Trojan librations.
Stability analysis of long period Trojan librations treated as short period oscillations about long period reference solution
SECULAR PERTURBATION↗
Analysis of Chemical, REP, and SEP missions to the Trojan asteroids
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.
Trojan asteroids↗
Polyethylene Incorporating Diels–Alder Comonomers: A “Trojan Horse” Strategy for Chemically Recyclable Polyolefins
Abstract Polyolefins with periodic unsaturation in the backbone chain are sought after for synthesizing chemically recyclable polymers or telechelic polyolefin macromonomers. Here we introduce a bottom‐up synthesis of unsaturated high‐density polyethylene (HDPE) via copolymerization of ethylene with dimethyl 7‐oxabicyclo[2.2.1]hepta‐2,5‐diene‐3,5‐dicarboxylate followed by post‐polymerization retro‐Diels–Alder to unveil hidden double bonds in the polymer backbone. The incorporation of this “Trojan Horse” comonomer was varied and a series of unsaturated HDPE polymers with block lengths of 1.2, 1.9, and 3.5 kDa between double bonds was synthesized. Cross metathesis of unsaturated HDPE samples with 2‐hydroxyethyl acrylate yielded telechelic ester terminated PE macromonomers suitable for the preparation of ester‐linked PE. These materials were depolymerized and repolymerized, making them suitable candidates for chemical recycling. The ester‐linked PE displayed thermal and mechanical properties comparable to commercial HDPE.
Parke, Sarah M.↗
Polyethylene Incorporating Diels–Alder Comonomers: A “Trojan Horse” Strategy for Chemically Recyclable Polyolefins
Polyolefins with periodic unsaturation in the backbone chain are sought after for synthesizing chemically recyclable polymers or telechelic polyolefin macromonomers. Here we introduce a bottom-up synthesis of unsaturated high-density polyethylene (HDPE) via copolymerization of ethylene with dimethyl 7-oxabicyclo[2.2.1]hepta-2,5-diene-3,5-dicarboxylate followed by post-polymerization retro-Diels–Alder to unveil hidden double bonds in the polymer backbone. The incorporation of this “Trojan Horse” comonomer was varied and a series of unsaturated HDPE polymers with block lengths of 1.2, 1.9, and 3.5 kDa between double bonds was synthesized. Cross metathesis of unsaturated HDPE samples with 2-hydroxyethyl acrylate yielded telechelic ester terminated PE macromonomers suitable for the preparation of ester-linked PE. These materials were depolymerized and repolymerized, making them suitable candidates for chemical recycling. Here, the ester-linked PE displayed thermal and mechanical properties comparable to commercial HDPE.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The Trojan Horse Method: A Nuclear Physics Tool for Astrophysics
The Trojan Horse Method (THM) represents an indirect path to determine the bare nucleus astrophysical S-factor for reactions among charged particles at astrophysical energies. This is achieved by measuring the quasi-free cross section of a suitable three-body process. The method is also suited to study neutron-induced reactions, especially in the case of radioactive ion beams. A comprehensive review of the theoretical as well as experimental features behind the THM is presented here. An overview is given of some recent applications to demonstrate the method's practical use for reactions that have a great impact on selected astrophysical scenarios.
Physics↗
Notes on the origin of the Trojan asteroids
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.
Yoder, C. F.↗
The composition of the Trojan asteroids
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.
Gradie, J.↗
Spectrophotometry of J8, J9, and four Trojan asteroids from 0.32 to 1.05 microns
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.
Smith, D. W.↗
The 1990 MB: The first Mars Trojan
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.
Bowell, Edward↗
A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka
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.
Mikkola, Seppo↗
Constraints on the Composition of Trojan Asteroid 624 Hektor
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.
Cruikshank, Dale P.↗
Olivine Composition of the Mars Trojan 5261 Eureka: Spitzer IRS Data
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.
Lim, L. F.↗
Collisional Histories of Comets and Trojan Asteroids: Insights from Forsterite and Enstatite Impact Studies
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.
Lederer. S. M.↗
Capabilities of Gamma Ray and Neutron Spectrometers for Studying Trojan Asteroid Composition
A Trojan Tour and Rendezvous mission was specifically targeted by the 2011 Planetary Decadal Survey Committee as a high priority mission for the New Frontiers program.
Parsons, A. M.↗
From Basking Ridge to the Jupiter Trojans
This presentation describes the activities of the Global Trajectory Optimization Lab, a subdivision of the Navigation and Mission Design Branch at NASA GSFC. The students will learn the basics of interplanetary trajectory optimization and then, as an example, the Lucy mission to the Jupiter Trojans will be described from both a science and engineering perspective.
trajectory design↗
The Upcoming Mutual Event Season for the Patroclus-Menoetius Trojan Binary
We present new Hubble Space Telescope and ground-based Keck observations and new Keplerian orbit solutions for the mutual orbit of binary Jupiter Trojan asteroid (617) Patroclus and Menoetius, targets of NASA's Lucy mission. We predict event times for the upcoming mutual event season, which is anticipated to run from late 2017 through mid 2019.
Grundy, W. M.↗