ADDITIONAL PERIODIC TROJAN ORBITS AND FURTHER STUDIES OF THEIR STABILITY FEATURES
Periodic trojan orbits and studies of their stability features
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Periodic trojan orbits and studies of their stability features
Elliptic restricted problem of periodic Trojan orbit and nonperiodic librational frequency and angular motion of Jupiter
Short-period Trojan orbits in restricted three- body problem numerically determined, using Jupiter and Sun as principal masses
Determination and survey of periodic trojan orbits in the restricted problem of three bodies
Oscillating libration orbits with period rigorously commensurable in rational fraction to basic long period
This paper describes the design, testing, and lessons learned during the development of the Lucy Ralph (L'Ralph) Scan Mirror System (SMS), composed of the Scan Mirror Mechanism (SMM), Differential Position Sensor System (DPSS) and Mechanism Control Electronics (MCE). The L'Ralph SMS evolved from the Advanced Topographic Laser Altimeter System (ATLAS) Beam Steering Mechanism (BSM), so design comparisons will be made. Lucy is scheduled to launch in October 2021, embarking upon a 12-year mission to make close range encounters in 2025 and 2033 with seven Trojan asteroids and one main belt asteroid that are within the Jovian orbit. The L'Ralph instrument is based upon the New Horizons Ralph instrument, which is a panchromatic and color visible imager and infrared spectroscopic mapper that slewed the spacecraft for imaging. The L'Ralph SMM is to provide scanning for imaging to eliminate the need to slew the spacecraft. One purpose of this paper is to gain understanding of the reasoning behind some of the design features as compared with the ATLAS BSM. We will identify similarities and differences between the ATLAS BSM and the L'Ralph SMM that resulted from the latter's unique requirements. Another purpose of this paper is to focus upon "Lessons Learned" that came about during the development of the L'Ralph SMM and its MCE, both mechanism engineering issues and solutions as well as Ground Support Equipment (GSE) issues and solutions that came about during the validation of requirements process. At the time of this writing, the L'Ralph SMM has been flight qualified and delivered to the project.
Short period orbit calculations around equilateral libration points in plane restricted three-body problem
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Periodic orbits about the triangular equilibrium points are found for the planar restricted three-body problem using the earth-sun system. The maximum semimajor axis for tadpole orbits ranges from the infinitesimal orbit at 1.000 AU to the near-limiting orbit at 1.00285 AU. Horseshoe orbits are found for 1.0029 to 1.0080 AU, larger horseshoes being unstable because of close approaches to the earth. Using stability tests devised by Rabe (1961, 1962), the limit of stability for nonperiodic orbits is found to occur for maximum semimajor axes near 1.0020 AU. In addition, near-periodic tadpole orbits appear to be stable against perturbations by Jupiter and Venus for periods of at least 10,000 yr. The possibility that minor planets actually exist in such orbits is considered.
Mars is the only terrestrial planet known to have co-orbiting "Trojan" asteroids. We have obtained visible and near-IR reflectance spectra of three of these objects: 5261 Eureka and 1998 VF31 in the L5 region and 1999 UJ7 in the L4 region. We also obtained JHK spectrophotometry and a visible lightcurve for 5261 Eureka. The asteroid 5261 Eureka has a visible spectrum that is classified as Sr in the Bus taxonomy, and has infrared colors consistent with the A-class asteroids. The data for 1998 VF31 have a restricted wavelength range, but are most consistent with the Sr or Sa class, though we note a marginal consistency with the D class. We can rule out a C-class classification. 1999 UJ7 has an X-class or T-class spectrum, which is unlike that of the other two Mars Trojans. The photometric data for Eureka are limited, but we can constrain the period to longer than 5 hours (likely 5.556 hours) and lightcurve amplitude of at least 0.15 magnitude at this viewing geometry. The spectral differences among the Mars Trojans suggests that either they did not all form at their present solar distances or that they have not always been at their present sizes. 0 2003 Elsevier Inc. All rights reserved. Keywords: Asteroids; Asteroids, composition; Spectroscopy; Satellites of Mars
Mars is the only terrestrial planet known to have co-orbiting Trojan asteroids. We have obtained visible and near-IR reflectance spectra of three of these objects: 5261 Eureka and 1998 VF31 in the L5 region and 1999 UJ7 in the LA region. We also obtained JHK spectrophotometry and a visible lightcurve for 5261 Eureka. The asteroid 5261 Eureka has a visible spectrum that is classified as Sr in the Bus taxonomy, and has infrared colors consistent with the A-class asteroids. The data for 1998 VF31 have a restricted wavelength range, but are most consistent with the Sr or Sa class, though we note a marginal consistency with the D class. We can rule out a C-class classification. 1999 UJ7 has an X-class or T-class spectrum, which is unlike that of the other two Mars Trojans. The photometric data for Eureka are limited, but we can constrain the period to longer than 5 hours (likely 5.5-6 hours) and lightcurve amplitude of at least 0.15 magnitude at this viewing geometry. The spectral differences among the Mars Trojans suggests that either they did not all form at their present solar distances or that they have not always been at their present sizes.
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.
A study was conducted that shows how a single Radioisotope Electric Propulsion (REP) spacecraft design could be used for various missions throughout the solar system. This spacecraft design is based on a REP feasibility design from a study performed by NASA Glenn Research Center and the Johns Hopkins University Applied Physics Laboratory. The study also identifies technologies that need development to enable these missions. The mission baseline for the REP feasibility design study is a Trojan asteroid orbiter. This mission sends an REP spacecraft to Jupiter s leading Lagrange point where it would orbit and examine several Trojan asteroids. The spacecraft design from the REP feasibility study would also be applicable to missions to the Centaurs, and through some change of payload configuration, could accommodate a comet sample-return mission. Missions to small bodies throughout the outer solar system are also within reach of this spacecraft design. This set of missions, utilizing the common REP spacecraft design, is examined and required design modifications for specific missions are outlined.
Long-period librations of Trojan planetary orbits in rotating three-body coordinate system
This study assessed the benefits and applicability of REP to missions relevant to the In-Space Propulsion Program (ISPP) using first and second generation RPS with specific powers of 4 We/kg and 8 We/kg, respectively. Three missions representing small body targets, medium outer planet class, and main belt asteroids and comets were evaluated. Those missions were a Trojan Asteroid Orbiter, Comet Surface Sample Return (CSSR), and Jupiter Polar Orbiter with Probes (JPOP). For each mission, REP cost and performance was compared with solar electric propulsion system (SEPS) and SOA chemical propulsion system (SCPS) cost and performance. The outcome of the analysis would be a determinant for potential inclusion in the ISPP investment portfolio.
Trojan asteroids are small bodies orbiting around the L 4 or L 5 Lagrangian points of a Sun-planet system. Due to their peculiar orbits, they provide key constraints to the Solar System evolution models. Despite numerous dedicated observational efforts in the last decade, asteroid 2010 TK 7 has been the only known Earth Trojan thus far. Here we confirm that the recently discovered 2020 XL 5 is the second transient Earth Trojan known. To study its orbit, we used archival data from 2012 to 2019 and observed the object in 2021 from three ground-based observatories. Our study of its orbital stability shows that 2020 XL 5 will remain in L 4 for at least 4 000 years. With a photometric analysis we estimate its absolute magnitude to be ${H}_{r}=18.5{8}_{-0.15}^{+0.16}$, and color indices suggestive of a C-complex taxonomy. Assuming an albedo of 0.06 ± 0.03, we obtain a diameter of 1.18 ± 0.08 km, larger than the first known Earth Trojan asteroid.
Application of limb-fitting methods to the 11 best Voyager 2 images of Enceladus has shown that the shape of this satellite is closely represented by a triaxial ellipsoid. The observed ratio of the differences of the principal axes F = (b - c)/(a - c) is 0.23 (sup +0.04 sub - 0.01), consisting with the value F = 0.23 expected for a synchronously rotating satellite in hydrostatic equilibrium. We also deduce from the Voyager observations, after allowing for limb topography, that the mean radius of the satellite is 249.4 +/- 0.2 km. For satellites of known mass, measurement of the size and shape leads to a determination of the satellite's mean density and moment of inertial. We have used this method to determine the moments of inertia of Mimas (1988) and Tethys (1991). Enceladus appears to be hydrostatically relaxed, making it an ideal candidate for this type of analysis. However, none of the Pioneer or Voyager spacecraft had a close encounter with this satellite and thus its mass is effectively unknown. Enceladus is trapped in a 2:1 orbit-orbit resonance with Dione, but the amplitudes of libration are too small to allow a useful mass determination. Using the observed shape alone, without any other assumptions other than that the satellite is in hydrostatic equilibrium at its present orbital radius, we place an upper bound on the mean density of 1.12 +/- 0.05 g/cu cm. Thus, the mean density of Enceladus is probably little more than that of water-ice and we conclude that this satellite is markedly deficient in rock. If the mass of a satellite is unknown, but the satellite is differentiated and has a deep mantle of known composition, then we show that measurement of the shape alone can lead to a determination of the satellite's mass, mean density, and moment of inertia. Application of this method to Enceladus, assuming that the satellite has a deep mantle of water-ice of density 0.93 g/cu cm, gives the result that the mean density of the satellite is 1.00 +/- 0.03 g/cu cm. This result fills the one remaining gap in our knowledge of the structure of the Saturnian satellite system. We now know the mean densities of all the primary Saturnian satellites in the sequence from the coorbital satellites, Janus and Epimetheus, through to the outer satellite Iapetus (the densities of the small, secondary satellites in Trojan-type orbits are still unknown). The Saturnian system possesses two striking features. (1) Because of significant porosity, the mean material densities of the satellites Janus, Epimetheus, and Mimas could be substantially greater than the apparent mean densities of these satellies. (2) The densities of the satellites are not correlated with their distances from the planet; in particular, the satellites Enceladus and Tethys have lower mean densities than their interior and exterior neighbors, Mimas and Dione. This may be the result of gross postformation redistribution of rock and ice, possibly due to satellite disruptions are suggested by Smith et al. (1982).
Long period libration of trojan minor planet