Orbital Integrals Research Articles

Birth sites of young stellar associations and recent star formation in a flocculent corrugated disc

ABSTRACT With backwards orbit integration, we estimate birth locations of young stellar associations and moving groups identified in the solar neighbourhood that are younger than 70 Myr. The birth locations of most of these stellar associations are at a smaller galactocentric radius than the Sun, implying that their stars moved radially outwards after birth. Exceptions to this rule are the Argus and Octans associations, which formed outside the Sun’s galactocentric radius. Variations in birth heights of the stellar associations suggest that they were born in a filamentary and corrugated disc of molecular clouds, similar to that inferred from the current filamentary molecular cloud distribution and dust extinction maps. Multiple spiral arm features with different but near corotation pattern speeds and at different heights could account for the stellar association birth sites. We find that the young stellar associations are located in between peaks in the radial/tangential (UV) stellar velocity distribution for stars in the solar neighbourhood. This would be expected if they were born in a spiral arm, which perturbs stellar orbits that cross it. In contrast, stellar associations seem to be located near peaks in the vertical phase-space distribution, suggesting that the gas in which stellar associations are born moves vertically together with the low-velocity dispersion disc stars.

Collinder 135 and UBC 7: A physical pair of open clusters

Context. Given the closeness of the two open clusters Collinder 135 and UBC 7 on the sky, we investigate the possibility that the two clusters are physically related. Aims. We aim to recover the present-day stellar membership in the open clusters Cr 135 and UBC 7 (300 pc from the Sun) in order to constrain their kinematic parameters, ages, and masses and to restore their primordial phase space configuration. Methods. The most reliable cluster members are selected with our traditional method modified for the use of Gaia DR2 data. Numerical simulations use the integration of cluster trajectories backwards in time with our original high-order Hermite4 code φ−GRAPE. Results. We constrain the age, spatial coordinates, velocities, radii, and masses of the clusters. We estimate the actual separation of the cluster centres equal to 24 pc. The orbital integration shows that the clusters were much closer in the past if their current line-of-sight velocities are very similar and the total mass is more than seven times larger than the mass of the most reliable members. Conclusions. We conclude that the two clusters Cr 135 and UBC 7 might very well have formed a physical pair based on the observational evidence as well as numerical simulations. The probability of a chance coincidence is only about 2%.

Integrated navigation for the approach phase of Mars probe

Considering the navigation for the approach phase of the Chinese Mars probe TIANWEN-1, we present an integrated navigation method based on the data fusion of the ground measurement and optical observation. This method combines the measurements of space and control stations on Earth and the optical observation of the camera carried by the probe. Taking an on-the-ground filter as a subfilter to deal with the data of ground measurement and uploading the results with communication delay considered, we proposed a data fusion method for the uploaded results and optical data. First, a dynamic model for the approach phase of the Mars probe is introduced, and the computational accuracy and efficiency of the orbital integration are analyzed. The measurement models are then subjected to visibility analysis. Second, the algorithms of extended Kalman filter and unscented Kalman filter are formulated for data uploading and fusion. Finally, a simulation is performed under the prior position estimation as 100 km and Priori velocity estimation as 0.1 m/s. Results show that the integrated navigation method has better convergence speed and navigation accuracy.

HST Proper Motions of NGC 147 and NGC 185: Orbital Histories and Tests of a Dynamically Coherent Andromeda Satellite Plane

Abstract We present the first proper-motion (PM) measurements for the dwarf elliptical galaxies NGC 147 and NGC 185, two satellite galaxies of M31, using multiepoch Hubble Space Telescope (HST) imaging data with time baselines of ∼8 yr. For each galaxy, we take an error-weighted average of measurements from HST Advanced Camera for Surveys/WFC and Wide Field Camera 3/UVIS to determine the PMs. Our final results for the PMs are (μ W, μ N)N147 = (−0.0232, 0.0378) ± (0.0143, 0.0146) mas yr−1 for NGC 147 and (μ W, μ N)N185 = (−0.0242, 0.0058) ± (0.0141, 0.0147) mas yr−1 for NGC 185. The 2D direction of motion for NGC 147 about M31 is found to be aligned with its tidal tails. The 3D positions and velocities of both galaxies are transformed into a common M31-centric coordinate system to study the detailed orbital histories of the combined M31+NGC 147+NGC 185 system via numerical orbit integration. We find that NGC 147 (NGC 185) had its closest passage to M31 0.3–0.5 Gyr (≳1.6 Gyr) within the past 6 Gyr at distances of ∼70 kpc (70–260 kpc). The pericentric times of NGC 147/NGC 185 correlate qualitatively well with the presence/absence of tidal tails seen around the galaxies. Our PMs show that the orbital poles of NGC 147, as well as NGC 185, albeit to a lesser degree, agree within the uncertainties with the normal of the Great Plane of Andromeda (GPoA). These are the first measurements of the 3D angular momentum vector of any satellite identified as original GPoA members. Our results strengthen the hypothesis that the GPoA may be a dynamically coherent entity. We revisit previous claims that NGC 147 and NGC 185 are binary galaxies and conclude that it is very unlikely that the two galaxies were ever gravitationally bound to each other.

Particle Trapping in Axisymmetric Electron Holes

AbstractElectron orbits are calculated in solitary two‐dimensional axisymmetric electrostatic potential structures, typical of plasma electron holes, in order to establish the conditions for the particles to remain trapped. Analytic calculations of the evolution of the parallel energy caused by the perturbing radial electric field (breaking magnetic moment invariance) are shown to agree well with full numerical orbit integration Poincaré plots. The predominant mechanism of detrapping is resonance between the gyrofrequency in the parallel magnetic field and harmonics of the parallel bounce frequency. A region of phase space adjacent to the trapped‐passing boundary in parallel energy is generally stochastic because of island overlap of different harmonics, but except for very strong radial electric field perturbation, more deeply trapped orbits have well‐defined islands and are permanently confined. A simple universal quantitative algorithm is given, and its results plotted as a function of magnetic field strength and hole radial scale length, determining the phase space volume available to sustain the electron hole by depression of the permanently trapped distribution function.

Compact Real-Space Representation of Excited States Using Frequency-Dependent Explicitly Correlated Electron-Hole Interaction Kernel.

We present the frequency-dependent geminal-screened electron-hole interaction kernel (FD-GSIK) method for describing electron-hole correlation in electronically excited many-electron systems. The FD-GSIK is a parameter-free, first-principles method derived from excited-state wave function that was both frequency-dependent and r12-explicitly correlated. The FD-GSIK avoids using unoccupied orbitals for kernel construction by performing an infinite-order summation of particle-hole excitation and representing it as a compact real-space operator. It bypasses the computationally demanding steps of evaluation, storage, and transformation of atomic-orbital integrals by directly evaluating molecular orbital integrals in real space using the stratified Monte Carlo method. We demonstrate and discuss the advantages of this method by presenting excitation and electron-hole binding energies of large nanoparticles including Pb140S140, Pb140Se140, Cd144Se144, and Cd72S72.

Basis function expansions for galactic dynamics: Spherical versus cylindrical coordinates

Aims. The orbital structure of galaxies is strongly influenced by the accuracy of the force calculation during orbit integration. We explore the accuracy of force calculations for two expansion methods and determine which one is preferable for orbit integration. Methods. We specifically compare two methods, one was introduced by Hernquist & Ostriker (HO), which uses a spherical coordinate system and was built specifically for the Hernquist model, and the other by Vasiliev & Athanassoula (CylSP) has a cylindrical coordinate system. Our comparisons include the Dehnen profile, its triaxial extension (of which the Hernquist profile is a special case) and a multicomponent system including a bar and disk density distributions for both analytical models and N-body realizations. Results. For the generalized Dehnen density, the CylSP method is more accurate than the HO method for nearly all inner power-law indices and shapes at all radii. For N-body realizations of the Dehnen model, or snapshots of an N-body simulation, the CylSP method is more accurate than the HO method in the central region for the oblate, prolate, and triaxial Hernquist profiles if the particle number is more than 5 × 105. For snapshots of the Hernquist models with spherical shape, the HO method is preferred. For the Ferrers bar model, the force from the CylSP method is more accurate than the HO method. The CPU time required for the initialization of the HO method is significantly shorter than that for the CylSP method, while the HO method costs subsequently much more CPU time than the CylSP method if the input corresponds to particle positions. From surface of section analyses, we find that the HO method creates more chaotic orbits than the CylSP method in the bar model. This could be understood to be due to a spurious peak in the central region when the force is calculated with the HO expansion. Conclusions. For an analytical model, the CylSP method with an inner cutoff radius of interpolation Rmin as calculated by the AGAMA software, is preferred due to its accuracy. For snapshots or N-body realizations not including a disk or a bar component, a detailed comparison between these two methods is needed if a density model other than the Dehnen model is used. For multicomponent systems, including a disk and a bar, the CylSP method is preferable.

Functorial transfer between relative trace formulas in rank 1

According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L -groups of spherical varieties should give rise to a functorial transfer of their local and automorphic spectra. The “beyond endoscopy” proposal predicts that this transfer will be realized as a comparison between limiting forms of the (relative) trace formulas of these spaces. In this paper, we establish the local transfer for the identity map between L -groups, for spherical affine homogeneous spaces X = H \ G whose dual group is SL 2 or PGL 2 (with G and H split). More precisely, we construct a transfer operator between orbital integrals for the ( X × X ) / G -relative trace formula, and orbital integrals for the Kuznetsov formula of PGL 2 or SL 2 . Besides the L -group, another invariant attached to X is a certain L -value, and the space of test measures for the Kuznetsov formula is enlarged to accommodate the given L -value. The transfer operator is given explicitly in terms of Fourier convolutions, making it suitable for a global comparison of trace formulas by the Poisson summation formula, hence for a uniform proof, in rank 1 , of the relations between periods of automorphic forms and special values of L -functions.

The use of Kepler solver in numerical integrations of quasi-Keplerian orbits

ABSTRACT A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the eccentric anomaly relies on the true anomaly that is associated with a unit radial vector calculated by an integrator. This scheme rigorously conserves all integrals and orbital elements except the mean longitude. However, the Kepler energy, angular momentum vector, and Laplace–Runge–Lenz vector for perturbed Kepler problems are slowly varying quantities. However, their integral invariant relations give the quantities high-precision values that directly govern five slowly varying orbital elements. These elements combined with the eccentric anomaly determine the desired numerical solutions. The newly proposed method can considerably reduce various errors for a post-Newtonian two-body problem compared with an uncorrected integrator, making it suitable for a dissipative two-body problem. Spurious secular changes of some elements or quasi-integrals in the outer Solar system may be caused by short integration times of the fourth-order Runge–Kutta algorithm. However, they can be eliminated in a long integration time of 108 yr by the proposed method, similar to Wisdom–Holman second-order symplectic integrator. The proposed method has an advantage over the symplectic algorithm in the accuracy but gives a larger slope to the phase error growth.

Theoretical studies of comets in the 55 Cancri system

ABSTRACT We present orbital integrations for various Jupiter family comets (JFCs) in the 55 Cancri system. This star is known to possess (at least) five planets with masses ranging from super-Earth to Jupiter-type. Furthermore, according to observational constraints, there is a space without planets between ∼0.8 and ∼5.7 au, offering the principal possibility of habitable terrestrial planets, including long-term orbital stability. Hence, there is a stark motivation for the study of comets in the 55 Cnc system noting that comets are viewed a viable candidate mechanism for the delivery of water to Earth-type planets located in stellar habitable zones. However, our study shows that the duration of stability of JFC analogues in the 55 Cnc system is much shorter compared to comets in the Solar system owing to profound differences in the planetary structure of the systems. For example, between planet 55 Cnc-f and 55 Cnc-d, the comets do not undergo close cometary encounters akin to the Earth and Mars in the Solar system as the planetary masses in the 55 Cnc system are much larger than in the Solar system and therefore the comets are much less orbitally stable. Nevertheless, we expect an increased number of comet–planet encounters as well as cometary collisions in the 0.8/5.7 au gap. Future observations and additional theoretical studies are required to shed light on the possibility of habitable terrestrial planets in the 55 Cnc system, including the possible role(s) of exocomets in the facilitation of planetary habitability.

Modified Hermite integrators of arbitrary order

ABSTRACT We present a family of modified Hermite integrators of arbitrary order possessing superior behaviour for the integration of Keplerian and near-Keplerian orbits. After recounting the derivation of Hermite N-body integrators of arbitrary order, we derive a corrector expression that minimizes integrated errors in the argument of periapsis for any such integrator. In addition to providing an alternate derivation of the modified corrector for the fourth-order Hermite integrator, we focus on improved correctors for the sixth- and eighth-order integrators previously featured in the literature. We present a set of numerical examples and find that the higher order schemes improve performance, even when considering their slightly higher cost in floating point operations. The algorithms presented herein hold promise for systems dominated by central potentials, such as planetary systems and the centres of galaxies. Existing Hermite integrators of any order can be modified to use the expressions presented here with minimal effort. Accordingly, the schemes presented herein can be easily implemented on massively parallel architectures.

Finite-temperature coupled cluster: Efficient implementation and application to prototypical systems.

We discuss the theory and implementation of the finite temperature coupled cluster singles and doubles (FT-CCSD) method including the equations necessary for an efficient implementation of response properties. Numerical aspects of the method including the truncation of the orbital space and integration of the amplitude equations are tested on some simple systems, and we provide some guidelines for applying the method in practice. The method is then applied to the 1D Hubbard model, the uniform electron gas (UEG) at warm, dense conditions, and some simple materials. The performance of model systems at high temperatures is encouraging: for the one-dimensional Hubbard model, FT-CCSD provides a qualitatively accurate description of finite-temperature correlation effects even at U = 8, and it allows for the computation of systematically improvable exchange-correlation energies of the warm, dense UEG over a wide range of conditions. We highlight the obstacles that remain in using the method for realistic ab initio calculations on materials.

A Numerical Method for Determining the Elements of Circumbinary Orbits and Its Application to Circumbinary Planets and the Satellites of Pluto-Charon

Abstract Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass ratio is high. A proper description of a circumbinary orbit is in terms of the free eccentricity e free at the epicyclic frequency κ 0, forced eccentricity e forced at the mean motion n 0, and oscillations at higher frequencies forced by the non-axisymmetric components of the binary’s potential. We show that accurate numerical values for the amplitudes and frequencies of these terms can be extracted from numerical orbit integrations by applying fast Fourier transformation (FFT) to the cylindrical distance between the circumbinary object and the center of mass of the binary as a function of time. We apply this method to three Kepler circumbinary planets and the satellites of Pluto-Charon. For the satellite Styx of Pluto-Charon, the FFT results for κ 0 and e free differ significantly from the first-order analytic value and the value reported by Showalter & Hamilton, respectively. We show that the deviation in κ 0 is likely due to the effect of the 3:1 mean-motion resonance and discuss the implications of the lower value for e free.

Hybrid-precision arithmetic for numerical orbit integration towards future satellite gravimetry missions

The precision of numerical orbit integration is crucial in precise orbit determination and gravity field recovery, especially in the context of future satellite gravimetry missions where nanometer-level inter-satellite measurements are provided by laser ranging interferometer. In this paper, we propose a hybrid-precision arithmetic in both Cowell’s and Encke’s formulations for numerical orbit integration after comprehensive analyses on the computational time costs and numerical errors by dividing the integration process into two parts, namely the increment calculation and the orbit propagation. Based on such a separation, we find that the round-off errors basically occur in the least time-consuming orbit propagation part while the more time-demanding increment calculation part is less sensitive to the round-off due to its small numerical magnitude. Therefore, it is natural in the hybrid-precision arithmetic to use the double- and quadruple-precision arithmetic in the increment calculation part and orbit propagation part, respectively. Numerical results demonstrate that the hybrid-precision arithmetic is as efficient as the double-precision method, while far better than its double-precision counterparts in terms of both accuracy and relative precision. In consideration of the ultra-high precision inter-satellite range and range rate measurements of future satellite gravimetry missions, the currently widely-used double-precision arithmetic cannot meet the numerical requirements of one-day arc orbit integration for the inter-satellite range measurement, in which numerical errors should be at least the same level of the measurement precision and had better be one-order magnitude smaller to fully avoid their contaminations, while for the inter-satellite range rate the double-precision Gauss-Jackson integrator is qualified. Instead, by implementation of hybrid-precision arithmetic the range rate precision is easily achieved at 10−12 m/s in terms of the maximum absolute error of the one-day arc by either Cowell’s or Encke’s formulation. Furthermore, the sub-nanometer-level range precision is obtainable in the Encke’s formulation with reference orbit selected as the best-fit one. Therefore, it is recommended to adopt the hybrid-precision arithmetic for orbit integration to fully exploit the ultra-high precise measurement from the pure numerical data processing point of view.

An elastic model of Phobos’ libration

Context. Study the rotation of a celestial body is an efficient way to infer its interior structure, and then may give information of its origin and evolution. In this study, based on the latest shape model of Phobos from Mars Express (MEX) mission, the polyhedron approximation approach was used to simulate the gravity field of Phobos. Then, the gravity information was combined with the newest geophysical parameters such as GM and k2 to construct the numerical model of Phobos’ rotation. And with an appropriate angles transformation, we got the librational series respect to Martian mean equator of date. Aims. The purpose of this paper is to develop a numerical model of Phobos’ rotational motion that includes the elastic properties of Phobos. The frequencies analysis of the librational angles calculated from the numerical integration results emphasize the relationship between geophysical properties and dynamics of Phobos. This work will also be useful for a future space mission dedicated to Phobos. Methods. Based on the latest shape model of Phobos from MEX mission, we firstly modeled the gravity field of Phobos, then the gravity coefficients were combined with some of the newest geophysical parameters to simulate the rotational motion of Phobos. To investigate how the elastic properties of Phobos affect its librational motion, we adopted various k2 into our numerical integration. Then the analysis was performed by iterating a frequency analysis and linear least-squares fit of Phobos’ physical librations. From this analysis, we identified the influence of k2 on the largest librational amplitude and its phase. Results. We showed the first ten periods of the librational angles and found that they agree well with the previous numerical results which Phobos was treated as a perfectly rigid body. We also found that the maximum amplitudes of the three parameters of libration are also close to the results from a rigid model, which is mainly due to the inclination of Phobos and moments of inertia. The other amplitudes are slightly different, since the physics contained in our model is different to that of a previous study, specifically, the different low-degree gravity coefficients and ephemeris. The libration in longitude τ has the same quadratic term with previous numerical study, which is consistent with the secular acceleration of Phobos falling onto Mars. We investigated the influence of the tidal Love number k2 on Phobos’ rotation and found a detectable amplitude changes (0.0005°) expected in the future space mission on τ, which provided a potential possibility to constrain the k2 of Phobos by observing its rotation. We also studied the influence of Phobos’ orbit accuracy on its libration and suggested a simultaneous integration of orbit and rotation in future work.

Long term orbital dynamics of a retrograde Centaur 2006 RJ2

Centaurs are small bodies whose semi-major axes are located between Jupiter and Neptune. They have chaotic orbits and may be in orbital resonances with giant planets. An orbital resonance occurs when a simple commensurability presents between some fundamental frequencies of orbital elements. One of the resonance states is 1:1 (mean motion) resonance or co-orbital with the respected planet. This resonance can also occur in high inclination Centaurs. This study describes the results of long term orbital integration of a retrograde Centaur 2006 RJ2 (inclination of 165°) for 200,000 years. Resonance state of 2006 RJ2 was examined using the FAIR (Fast Identification of Mean Motion Resonance) method for 243 orbital clones with automation by developing Python codes. We report that 2006 RJ2 may be in retrograde 1:1 resonance with Saturn for about 160,000 years in the future. However, the clones exhibit chaotic orbits and show many temporally unstable resonances. Since the quality of its orbital elements is not quite precise, 2006 RJ2 shows a low possibility in the state of long retrograde 1:1 resonance with Saturn.

Targeting Local Osteogenic and Ancillary Cells by Mechanobiologically Optimized Magnesium Scaffolds for Orbital Bone Reconstruction in Canines.

Large-sized orbital bone defects have serious consequences that destroy orbital integrity and result in maxillofacial deformities and vision loss. The treatment of orbital bone defects is currently palliative and not reparative, suggesting an urgent demand for biomaterials that regenerate orbital bones. In this study, via alloying, extrusion and surface modification, we developed mechanobiologically optimized magnesium (Mg) scaffolds (Ca-P-coated Mg-Zn-Gd scaffolds, referred to as Ca-P-Mg) for the orthotopic reconstruction of large-sized orbital bone defects. At 6 months after transplanting the scaffolds to a clinically relevant canine large animal model, large-sized defects were successfully bridged by an abundance of new bone with normal mechanical properties that corresponded to gradual degradation of the implants. The osteogenic and ancillary cells, including vascular endothelial cells and trigeminal neurons, played important roles in this process. The scaffolds robustly enhanced bone marrow mesenchymal stem cell (BMSC) osteogenic differentiation. In addition, the increased angiogenesis including increased ratio of the specific endothelial subtype CD31hi endomucinhi (CD31hiEmcnhi) endothelial cells can facilitate osteogenesis. Furthermore, the scaffolds trigger trigeminal neurons via transient receptor potential vanilloid subtype 1 (Trpv1) to produce the neuropeptide calcitonin gene-related peptide (CGRP), which promotes angiogenesis and osteogenesis. Overall, our investigations revealed the efficacy of Ca-P-Mg scaffolds in healing orbital bone defects and warrant further exploration of these scaffolds for clinical applications.

The M31/M33 tidal interaction: a hydrodynamic simulation of the extended gas distribution

ABSTRACT We revisit the orbital history of the Triangulum galaxy (M33) around the Andromeda galaxy (M31) in view of the recent Gaia Data Release 2 proper motion measurements for both Local Group galaxies. Earlier studies consider highly idealized dynamical friction, but neglect the effects of dynamical mass loss. We show the latter process to be important using mutually consistent orbit integration and N-body simulations. Following this approach, we find an orbital solution that brings these galaxies to within ∼50 kpc of each other in the past, ∼6.5 Gyr ago. We explore the implications of their interaction using an N-body/hydrodynamical simulation with a focus on the origin of two prominent features: (1) M31’s Giant Stellar Stream; and (2) the M31–M33 H i filament. We find that the tidal interaction does not produce a structure reminiscent of the stellar stream that survives up to the present day. In contrast, the M31–M33 H i filament is likely a fossil structure dating back to the time of the ancient encounter between these galaxies. Similarly, the observed outer disc warp in M33 may well be a relic of this past event. Our model suggests the presence of a tidally induced gas envelope around these galaxies, and the existence of a diffuse gas stream, the ‘Triangulum stream’, stretching for tens of kpc from M33 away from M31. We anticipate upcoming observations with the recently commissioned, Five-hundred-metre Aperture Spherical radio Telescope that will target the putative stream in its first years of operation.

Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction

A new method for generating fitting grids for least-squares tensor hypercontraction (LS-THC) is presented. This method draws inspiration from the related interpolative separable density fitting (ISDF) technique, but uses only a pivoted Cholesky decomposition of the metric matrix, S, already computed as a matter of course in LS-THC. The size and quality of the resulting grid is controlled by a user-defined cutoff parameter and the size of the starting grid. Additionally, the Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit. The quality of the grids produced is evaluated for LS-DF-THC-MP2 calculations on retinal and benzene, the former with a large starting grid and small cc-pVDZ basis set, and the latter with a wide range of grids and basis sets. The error and grid size is found to be well-controlled by either the cutoff parameter (with a large starting grid) or the starting grid size (with a tight cutoff) and highly predictable. The Cholesky-based method is also able to generate unique grids tailored to different charge distributions, for example the (ab|, (ai|, and (ij| distributions that arise in the molecular orbital integrals. While only the (ai| grid directly affects the MP2 energy, the relative sizes of the other grids are examined.

Orbital dynamics of highly probable but rare Orionid outbursts possibly observed by the ancient Maya

ABSTRACT Using orbital integrations of particles ejected from Comet Halley’s passages between 1404 and 240 BC, the authors investigate possible outbursts of the Orionids (twin shower of the Eta Aquariids) that may have been observed in the Western hemisphere. In an earlier orbital integration study, the authors determined there was a high probability linking probable outbursts of the Eta Aquariid meteor shower with certain events recorded in inscriptions during the Maya Classic Period, AD 250–900. This prior examination was the first scientific inquiry of its kind into ancient meteor outbursts possibly recorded in the Western hemisphere where previously no pre-Columbian observations had existed. In the current paper, the aim is to describe orbital dynamics of rare but probable Orionid outbursts that would have occurred on or near applicable dates recorded in the Classic Maya inscriptions. Specifically, significant probable outbursts are found in AD 417 and 585 out of 30 possible target years. The driving mechanisms for outbursts in those two years are Jovian 1:6 and 1:7 mean motion resonances acting to maintain compact structures within the Orionid stream for over 1 kyr. Furthermore, an Orionid outburst in AD 585 recorded by China is confirmed.