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Long period of nonperiodic librational motion about equilateral points of restricted three-body problem
Stability analysis of long period Trojan librations treated as short period oscillations about long period reference solution
The COllaborative Modeling and Parametric Assessment of Space Systems (COMPASS) team was approached by the NASA Glenn Research Center (GRC) In-Space Project to perform a design session to develop Radioisotope Electric Propulsion (REP) Spacecraft Conceptual Designs (with cost, risk, and reliability) for missions of three different classes: New Frontier s Class Centaur Orbiter (with Trojan flyby), Flagship, and Discovery. The designs will allow trading of current and future propulsion systems. The results will directly support technology development decisions. The results of the Flagship mission design are reported in this document
In the last 100 years, the global population has more than quadrupled to over seven billion people. At the same time, the demand for food and standard of living has been increasing which has amplified the global water use by nearly eight times from approximately 500 to 4000 cu km per yr from 1900 to 2010. With the increasing concern to sustain the growing population on Earth it is necessary to seek other approaches to ensure that our planet will have resources for generations to come. In recent years, the advancement of space travel and technology has allowed the idea of mining asteroids with resources closer to becoming a reality. During the duration of the internship at NASA Kennedy Space Center, several geotechnical tests were conducted on BP-1 lunar simulant and asteroid simulant Orgueil. The tests that were conducted on BP-1 was to practice utilizing the equipment that will be used on the asteroid simulant and the data from those tests will be omitted from report. Understanding the soil mechanics of asteroid simulant Orgueil will help provide basis for future technological advances and prepare scientists for the conditions they may encounter when mining asteroids becomes reality in the distant future. Distinct tests were conducted to determine grain size distribution, unconsolidated density, and maximum density. Once the basic properties are known, the asteroid simulant will be altered to different levels of compaction using a vibrator table to see how compaction affects the density. After different intervals of vibration compaction, a miniature vane shear test will be conducted. Laboratory vane shear testing is a reliable tool to investigate strength anisotropy in the vertical and horizontal directions of a very soft to stiff saturated fine-grained clayey soil. This test will provide us with a rapid determination of the shear strength on the undisturbed compacted regolith. The results of these tests will shed light on how much torque is necessary to drill through the surface of an asteroid. Most of the known asteroids are believed to be left over material during the formation of the solar system that never accreted to form planets. Asteroids can be found in several groups such as Trojan Asteroids, Near Earth Asteroids (NEAs) and the main asteroid belt. The Trojan Asteroids orbit the 4th and 5th Lagrange points of major planets in the Solar System while the NEA's have orbits that are close to and sometimes intersect with Earths orbit and the Main Asteroid Belt which is found between the orbit of Mars and Jupiter. Gravitational perturbations can alter the orbit of asteroids in the Main Asteroid Belt causing them to move closer to earth causing them to become in the NEA class.
Planetesimal orbital evolution in a resisting medium near an accreting protoplanet was studied to explore mechanisms for capture into Trojan and satellite orbits. Various mechanisms for capture into libration were proposed, e.g., increase in Jupiter/Sun mass ratio, change in Jovian orbital radius, and collisions of asteroids with interplanetary dust. Studies include effects of solar nebula gas drag on orbital evolution. In general, the gas deviates from Keplerian motion, causing secular decay of planetesimal orbits, as well as damping eccentricity. The motion of bodies near Jupiter under the effect of a resisting medium was numerically explored. The equations of motion were integrated using the formalism of the planar restricted three body problem, modified to include effects by gas drag and a growing Jupiter.
The most recent NASA Discovery class mission to fly is the Lucy mission to the Trojan Asteroids of Jupiter. Launched in October of 2021, Lucy’s destination will be the unexplored Jupiter Trojan Asteroids that orbit the Sun at the stable L4 and L5 points ahead of, and behind Jupiter. This 12-yearmission will perform close flybys of 1 main belt asteroid, Donaldjohanson, and 7 Trojans asteroids: Eurybates and its satellite Queta, Polymele, Leucus, Orus, and the near equal mass Trojan binary pair, Patroclus andMenoetius. The large distance from earth for the encounters, the high relative velocities and sun incidence angles on approach,and the limited number of Earth observations of the Trojans,make the delivery knowledge highly uncertain. To reduce the delivery uncertainties and maximize science return, Lucy employs a Terminal Tracking System consisting of optical imaging, centroiding and state estimation of the Trojan asteroids on approach and through close approach. This paper presents the Lucy Terminal Tracking System implementation, a brief overview of the mission and the GN&C subsystem.
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.
Cislunar space, encompassing the region from geosynchronous orbit to beyond the Moon, is poised to become a cornerstone for future exploration, scientific discovery, and national security. Missions in this region, spanning durations from weeks to decades, require robust infrastructure and reliable transit capabilities. The complex gravitational influences of the Moon, Sun, and planets, along with thermal radiation from Earth and the Sun, lead to significant trajectory deviations, resulting in kilometer-scale errors within days. Leveraging the high-performance computing resources at Lawrence Livermore National Laboratory (LLNL), we have simulated one million high-fidelity cislunar trajectories, now publicly available via LLNL’s Green Data Oasis and the Unified Data Library. Generated using the open-source Space Situational Awareness Python package, these trajectories match the precision of commercial tools such as AGI’s Systems Tool Kit and NASA’s General Mission Analysis Tool. This data set is a valuable resource for reference, statistical analysis of cislunar orbit populations, and training machine learning models for rapid orbit classification with minimal observational input. Preliminary analysis reveals stable bands in Keplerian element space, particularly around five geosynchronous radii across a range of inclinations and eccentricities. Beyond this threshold, the Moon’s influence disrupts most unassisted orbits, though co-orbiting L4/L5 Lunar Trojans persist throughout the six-year simulation.
Helene, (approximately 17.6 kilometers mean radius) is an L4 Trojan co-orbital of Saturn's moon Dione. Its hemisphere features an unusual morphology consisting of broad depressions and a generally smooth surface patterned with streaks and grooves. The streaks appear to be oriented down-gradient, as are the grooves. This pattern suggests intensive mass-wasting as a dominant process on the leading hemisphere. Kilometer-scale impact craters are very sparse on the leading hemisphere other than the degraded kilometer-scale basins defining the overall satellite shape, and many small craters have a diffuse appearance suggesting ongoing mass wasting. Thus mass wasting must dominate surface-modifying processes at present. In fact, the mass wasting appears to have been sufficient in magnitude to narrow the divides between adjacent basins to narrow septa, similar, but in lower relief, to the honeycomb pattern of Hyperion. The prominent groves occur primarily near topographic divides and appear have cut into a broad, slightly lower albedo surface largely conforming to the present topography but elevated a few meters above the smooth surfaces undergoing mass wasting flow. Low ridges and albedo markings on the surface suggest surface flow of materials traveling up to several kilometers. Diffusive mass wasting produces smooth surfaces - such a pattern characterizes most of the low-lying surfaces. The grooves, however, imply that the transport process is advective at those locations where they occur, that is, erosion tends to concentrate along linear pathways separated by divides. In fact, in many places grooves have a fairly regular spacing of 125-160 meters, defining a characteristic erosional scale. Several questions are prompted by the unusual morphology of Helene: 1) What is the nature of the surface materials? 2) Are the transport processes gradual or catastrophic motion from one or a few events? 3) What mechanisms drive mass wasting and groove development? 4) Have the formative processes been active in the recent past? 5) Finally, is the surface accreting or eroding? The smooth character of the leading edge hemisphere of Helene and the dominance of mass wasting suggest that the surface is composed of fine-grained debris, probably dominated by dust-size to small gravel particles. The Lagrangian points of saturnian satellites are locations where planetesimals might have accreted to form co-orbital satellites such as and they may capture ejecta from their master moon. Published models suggest that Helene is a site of net accretion, but we find no extant explanation for the dominance of fine grain sizes for the surface (and probable subsurface) composition of Helene and the other Lagrangian satellites. Observation of the mass wasting tracks on Helene suggests the presence of well-defined streams of debris with low bordering levees that may be depositional features or remnants of the dissected higher surface. Some flows in grazing illumination appear to have a convex cross-section. This mass-flow morphology might be consistent with the occurrence of large-scale flow events, but which might have occurred through rapid emplacement or slow glacier-like creep. On the other hand, small craters appear to have been "softened" by creep-like processes, indicating ongoing mass wasting.
Abstract We present an analysis of lifetimes and resonances of Earth Trojan Asteroids (ETAs) in the MEGASIM data set. Trojan asteroids co-orbit the Sun with a planet, but remain bound to the Lagrange points, L4 (60° leading the planet) or L5 (60° trailing). In the circular three-body approximation, the stability of a Trojan asteroid depends on the ratio of the host planet mass and the central mass. For the inner planets, the range of stability becomes increasingly small, so perturbations from the planets have made primordial Trojans rare. To date, there have been just two ETAs (2010 TK 7 and 2020 XL 5 ), several Mars Trojans, and a Venus Trojan discovered. The estimated lifetimes of the known inner system Trojans are shorter than a million years, suggesting they are interlopers rather than members of a stable and long-lasting population. With the largest ETA n -body simulation to date, we are able to track their survival across a wide initialized parameter space. We find that the remaining fraction of ETAs over time is well fit with a stretched exponential function that, when extrapolated beyond our simulation run time, predicts zero ETAs by 2.33 Gyr. We also show correlations between ETA ejections and the periods of the Milankovitch cycles. Though Earth’s orbital dynamics dominate the instabilities of ETAs, we provide evidence that ETA ejections are linked to resonances found in the variation of the orbital elements of many if not all of the planets.
As was the case for Jupiter, Saturn formed either as a result of a gas instability within the solar nebula or the accretion of a solid core that induced an instability within the surrounding solar nebula. In either case, the proto-planet's history is divided into three major stages: early, quasi-hydrostatic evolution (stage 1); hydrodynamical collapse (stage 2); and late, quasi-hydrostatic contraction (stage 3). During stage 1, Saturn had a radius of several hundred times that of its present radius, R(s), while stage 3 began when Saturn had a radius of 3.5 R(s). Stages 1 and 2 lasted 10(6) to 10(7) years and 1 year, respectively, while stage 3 is continuing through the present epoch. During the early history of the Saturn system, giant impact events may have catastrophically disrupted most of the original satellites of Saturn. Such disruption, followed by reaccretion, may be responsible, in part for the occurrence of Trojans and co-orbital moons in the Saturn system, the apparent presence of a stochastic component in the trend of satellite density with radial distance, and the present population of ring particles.
As was the case for Jupiter, Saturn formed either as a result of a gas instability within the solar nebula or the accretion of a solid core that induced an instability within the surrounding solar nebula. In either case, the proto-planet's history is divided into three major stages: early, quasi-hydrostatic evolution (stage 1); hydrodynamical collapse (stage 2); and late, quasi-hydrostatic contraction (stage 3). During stage 1, Saturn had a radius of several hundred times that of its present radius, R(s), while stage 3 began when Saturn had a radius of 3.5 R(s). Stages 1 and 2 lasted one-million to 10-million years and one year, respectively, while stage 3 is continuing through the present epoch. During the early history of the Saturn system, giant impact events may have catastrophically disrupted most of the original satellites of Saturn. Such disruption, followed by reaccretion, may be responsible, in part for the occurrence of Trojans and co-orbital moons in the Saturn system, the apparent presence of a stochastic component in the trend of satellite density with radial distance, and the present population of ring particles.
Voyager I and II have revealed the existence of 1980S1 and 1980S3 in the same orbit that add to the discovery of the Lagrange satellite 1980S6 for Dione and 1980S13 - 1980S25 for Thetys as a replica to the Trojan planets in the Jupiter orbit. These bodies may issue from the rupture of a primitive gaseous ring through a disturbance. The Lagrange figures keep stable while the rest of the objects drift in near paths and interact at each transit so as to form a gradual binary. The Moon - Earth system may have a such origin.
Magnitudes and colors on the UBV system are presented for 145 minor planets, including 31 objects in the Eos family, 14 in the Koronis family, 6 in the Nysa family, 11 in the Themis family, 4 Hungarias, 7 Hildas, 8 Trojans, and several objects in unusual orbits. Clearly defined color groups for the Eos, Koronis, Nysa, and Themis family members are strongly suggestive of origin from discrete parent bodies. The Nysas apparently show large light-curve amplitudes. The Mars-orbit crossers 1977RA and 1980 = 1950LA, the earth-orbit crosser 1976UA, and several main-belt asteroids are found to show peculiar colors of unknown significance. The Mars-orbit crosser 1916 = 1953RA appears to be a typical S object, while 1474 Beira and 1977VA show neutral colors. Asteroids at semimajor axis in excess of 4 AU (Trojans preceding and following Jupiter, 279 Thule, and 944 Hidalgo) all belong to a color group centered at B-V = 0.72, U-B = 0.24.
Investigations of Earth's Trojan asteroids will have benefits for science, exploration, and resource utilization. By sending a small spacecraft to the Sun-Earth L4 or L5 Lagrange points to investigate near-Earth objects, Earth's Trojan population can be better understood. This could lead to future missions for larger precursor spacecraft as well as human missions. The presence of objects in the Sun-Earth L4 and L5 Lagrange points has long been suspected, and in 2010 NASA's Wide-field Infrared Survey Explorer (WISE) detected a 300 m object. To investigate these Earth Trojan asteroid objects, it is both essential and feasible to send spacecraft to these regions. By exploring a wide field area, a small spacecraft equipped with an IR camera could hunt for Trojan asteroids and other Earth co-orbiting objects at the L4 or L5 Lagrange points in the near-term. By surveying the region, a zeroth-order approximation of the number of objects could be obtained with some rough constraints on their diameters, which may lead to the identification of potential candidates for further study. This would serve as a precursor for additional future robotic and human exploration targets. Depending on the inclination of these potential objects, they could be used as proving areas for future missions in the sense that the delta-V's to get to these targets are relatively low as compared to other rendezvous missions. They can serve as platforms for extended operations in deep space while interacting with a natural object in microgravity. Theoretically, such low inclination Earth Trojan asteroids exist. By sending a spacecraft to L4 or L5, these likely and potentially accessible targets could be identified.
Abstract We announce the completion of two new Earth Trojan Asteroid (ETA) simulations. ETAs co-orbit the Sun with Earth and remain loosely bound to the fourth or fifth Lagrange points. To date, two ETAs have been detected (2010 TK 7 and 2020 XL 5 ); however, based on their orbits, these are likely temporary captures rather than members of a primordial population. The motivation for our simulations is multi-faceted: (1) the lack of a detected population despite literature claims of stability over the age of the solar system, (2) ETAs are important for both solar system science and planetary defense, and (3) the proximity of ETAs makes them prime candidates for space exploration missions. These simulations are of extremely high fidelity, large in number and long in simulation time. We will be releasing a series of papers based upon these simulations.
This viewgraph presentation analyzes small body targets (Trojan Asteroids), Medium Outer Planet Class (Jupiter Polar Orbiter with Probes), and Main Belt Asteroids and Comets (Comet Surface Sample Return), for Radioisotope Electric Propulsion (REP).
Asteroid 1984 AB, discovered in January 1984, proved to be a unique object with a close dynamical relationship to Mars. A brief history of the discovery and subsequent 'evolution' of the orbit as it was refined is presented. The preliminary orbit of 1984 AB indicated that it might be a Mars Trojan, and an extended discussion of this interesting possibility is presented, but this hypothesis had to be dismissed after further observations had refined the orbit. The semimajor axis and orbital eccentricity are very similar to that of Mars. No other known Mars-crossing asteroid exists with an orbit as closely associated to Mars.