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Stability analysis of highly eccentric satellite orbits about earth in lunar-solar gravitational disturbing field, deriving approximate criteria from planetary perturbation theory
A preliminary analysis of the relative motion of a free flying experiment module in the vicinity of a space station under the perturbative effects of drag and earth oblateness was made. A listing of a computer program developed for determining the relative motion of a module utilizing the Cowell procedure is presented, as well as instructions for its use.
The extent to which the low latitude dawn-dusk magnetic asymmetry is controlled by the dawn-dusk solar wind motional electric field VBs and/or substorm processes measured by the westward auroral electrojet index AL is studied using the technique of empirical linear prediction filters. A new index, (ASYM), defined as the difference between dawn and dusk deviations in the X (geomagnetic Northward) magnetic field component, is used to measure the dawn-dusk asymmetry. Quantitative information which characterizes the coupling processes are provided by the empirically determined filters obtained from this analysis. Results indicate that some currents are directly driven by the solar wind-magnetosphere interaction and that their magnetic perturbations contribute to both the AL and ASYM indices. However, a portion of the AL index that is uncorrelated with VBs is correlated with ASYM which suggests that internal magnetospheric processes also contribute to AL and ASYM.
An effective computational strategy is presented for the analysis of large and complex structures. The strategy is based on generating the response of the complex structure using large perturbations from that of a lower-order (simpler) model associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). The three key elements of the strategy are: (a) mixed (or primitive variable) formulation with the fundamental unknowns consisting of generalized displacements and stress parameters; (2) operator splitting, or a reduction method to relate the arrays and degrees of freedom of the original complex structure ot those of the simpler system; and (3) efficient iterative process for the generation of the response of the complex structure starting from that of the simpler system. The effectiveness of the proposed strategy is demonstrated by means of two numerical examples.
Novel computational strategies are presented for the analysis of large and complex structures. The strategies are based on generating the response of the complex structure using large perturbations from that of a simpler model, associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). Numerical examples are presented to demonstrate the effectiveness of the strategies developed.
Novel computational strategies are presented for the analysis of large and complex structures. The strategies are based on generating the response of the complex structure using large perturbations from that of a simpler model, associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). Numerical examples are presented to demonstrate the effectiveness of the strategies developed.
A radial-azimuthal stability analysis of a thin, alpha disk accretion flow is presented. The proportion of radiation pressure, Pr, of the unperturbed flow is allowed to vary according to the parameter beta = Pr/P, where P is the total pressure. As is the case for a purely radial analysis, the disk is stable for beta equal to or less than 0.6. However, the coupling of radial and azimuthal perturbations eliminates the viscous instability for such nonradial modes for all values of beta. The group velocity of the retrograde thermal mode is calculated as a function of beta.
The effects of gravity on the dynamic performance of structural control actuators and sensors are dual forms of an additive perturbation that can attenuate or amplify the device response (input or output). The modal modeling of these perturbations is derived for the general case of arbitrarily oriented devices and arbitrarily oriented planes of deformation. A nondimensional sensitivity analysis to identify the circumstances under which the effects of gravity are important is presented. Results show that gravity effects become important when the product of the ratio of the normalized modal slope and the modal displacement is comparable to the ratio of the gravitational acceleration and the product of the beam length and the squared eigenfrequency for a given mode.
It is generally accepted that some kind of non-baryonic dark matter accounts for most of the mass density of the universe. Considering such a component has become, in the last decade, a key ingredient in current theories of structure formation. In particular, the Cold Dark Matter (CDM) scenario has proven to be quite successful in explaining most of the observed properties of galaxies and of their large-scale distribution. The standard CDM model is characterized by a primordial Zel'dovich spectrum, of random-phase adiabatic perturbations in a universe with density parameter omega sub 0 = 1 and vanishing cosmological constant. This poster paper presents an analysis of observational data on peculiar motion of optical galaxies in comparison to the predictions of CDM models where the assumptions of the standard scenario: omega sub 0 = 1, n = 1, and bias parameter b = 1 are relaxed. In particular, CDM models with 0 less than n less than 1 and 0.4 less than omega sub 0 less than 1 are considered.
A complete analytic theory of dynamic linear reconnection at an X-type neutral point is developed. An eigenmode analysis, using cylindrical coordinates centered on the neutral point, extends the work of Craig & McClymont (1991) to include nonazimuthally symmetric perturbations on the flux function. It is demonstrated that all physically significant disturbances, both reconnective and nonreconnective, decay resistively on a 'fast' time scale. The significance of the linear theory is discussed within the general context of steady state and dynamic reconnection studies. Disturbances can be expected to focus explosively in the vicinity of the neutral point. This suggests the formation of a 'flux pile-up' current layer in which the bulk of the magnetic energy is released as heat rather than kinetic energy of mass motion.
Ethyl alcohol (ethanol) is known to possess a pair of closely spaced excited torsional substates (gauche+, gauche-) at an energy of approximately 57 K above the ground (trans) torsional substate. We report an extended analysis of some gauche - gauche+ Q-branch ((Delta)J = 0) transitions with a three-substate fixed frame axis method (FFAM) Hamiltonian. Our approach accounts for complex trans-gauche interactions for the first time. In addition, we are able to obtain intensities for perturbed rotational transitions, and to determine the trans to gauche+ separation to be 1185399.1 MHz. A complete ground state rotational-torsional partition function accounting for the previously neglected gauche substates is presented. Based on our analysis, a total of 14 U lines obtained towards Orion KL can now be assigned to gauche substates of ethanol. Analysis of these lines yields a rotational temperature of 223 K and a total (trans + gauche) column density of 7.0 x 10(exp 15)/sq cm. The column density is in reasonable agreement with the recent value of 2-3 x 10(exp 15)/sq cm based on observations of trans-ethanol by Ohishi et al., although there is some disparity in the rotational temperatures. Eight additional U lines in the literature are assigned to transitions of gauche ethanol.
We describe the calibration and data processing methods used to generate full-sky maps of the cosmic microwave background (CMB) from the first year of Wilkinson Microwave Anisotropy Probe (WMAP) observations. Detailed limits on residual systematic errors are assigned based largely on analyses of the flight data supplemented, where necessary, with results from ground tests. The data are calibrated in flight using the dipole modulation of the CMB due to the observatory's motion around the Sun. This constitutes a full-beam calibration source. An iterative algorithm simultaneously fits the time-ordered data to obtain calibration parameters and pixelized sky map temperatures. The noise properties are determined by analyzing the time-ordered data with this sky signal estimate subtracted. Based on this, we apply a pre-whitening filter to the time-ordered data to remove a low level of l/f noise. We infer and correct for a small (approx. 1 %) transmission imbalance between the two sky inputs to each differential radiometer, and we subtract a small sidelobe correction from the 23 GHz (K band) map prior to further analysis. No other systematic error corrections are applied to the data. Calibration and baseline artifacts, including the response to environmental perturbations, are negligible. Systematic uncertainties are comparable to statistical uncertainties in the characterization of the beam response. Both are accounted for in the covariance matrix of the window function and are propagated to uncertainties in the final power spectrum. We characterize the combined upper limits to residual systematic uncertainties through the pixel covariance matrix.
The scintillations of phase and amplitude in terms of signal-to-noise ratio (SNR) of the GPS radio occultation signal are caused by thin ionization layers. These thin irregular electron density layers in the E region ionosphere are often called sporadic E (Es). For a monthly retrieval of Es morphology we use the variances of the phase and SNR fluctuations of worldwide ~6000 GPS/CHAMP occultations in the E region. The Es climatology is studied globally with the SNR and phase variances in terms of monthly zonal means, seasonal maps, and diurnal and long-term variations. The zonal mean variances reveal strong, extended Es activities at summertime midlatitudes but weak, confined activities in wintertime high latitudes, peaking at ~105 km. Global maps at 105-km altitude show clear dependence of Es activities on the geomagnetic dip angle, where the summertime midlatitude Es occurs mostly at dip angles of 30 deg. - 60 deg. and the wintertime high-latitude enhancement occurs mostly at dip angles greater than 80 deg. The midlatitude Es variances exhibit a strong semidiurnal variation with peak hours near 0800 1000 and 2000 local solar time, respectively. The peak hours are delayed slightly with decreasing height, suggesting influences from the semidiurnal tide. To provide more insights on the observed SNR and phase variances, we model radio wave propagation for the CHAMP observing geometry under several perturbed cases in the E region ionosphere. The model simulations indicate that the SNR variance has the maximum response to Es perturbations at vertical wavelengths of 1.2 km, whereas the phase response maximizes at ~2 km (for the 1-s variance analysis). The characteristic scale depends little on the truncation time used in the SNR variance analysis, but it increases with the truncation time for the phase variances. Initial studies show that reasonable global Es morphology can be produced on a monthly and seasonal basis with the CHAMP one-antenna occultations. Better results from other existing and upcoming GPS occultation missions are anticipated in future studies, and they will significantly improve our understanding of this important phenomenon.
The traditional approach used in the design of stability critical thin-walled circular cylin- ders, is to reduce unconservative buckling load predictions with an empirical knockdown factor. An alternative analysis-based approach to determine a lower bound buckling load for cylinders under axial compression is to use a lateral perturbation load to create an initial imperfection and determine the buckling load while that load is applied. This paper describes a preliminary e ort to develop a test capability to verify this approach. Results from tests of three aluminum alloy cylinders are described and compared to nite element predictions.
The NASA GMAO seasonal (9 months) and subseasonal (45 days) forecasts are produced with the Goddard Earth Observing System (GEOS) Atmosphere-Ocean General Circulation Model and Data Assimilation System Version S2S-2_1. The new system replaces version S2S-1.0 described in Borovikov et al (2017), and includes upgrades to many components of the system. The atmospheric model includes an upgrade from a pre-MERRA-2 version running on a latitude-longitude grid at approx. 1 degree resolution to a current version running on a cubed sphere grid at approximately 1/2 degree resolution. The important developments are related to the dynamical core (Putman et al., 2011), the moist physics (''two-moment microphysics'' of Barahona et al., 2014) and the cryosphere (Cullather et al., 2014). As in the previous GMAO S2S system, the land model is that of Koster et al (2000). GMAO S2S-2_1 now includes the Goddard Chemistry Aerosol Radiation and Transport (GOCART, Colarco et al., 2010) single moment interactive aerosol model that includes predictive aerosols including dust, sea salt and several species of carbon and sulfate. The previous version of GMAO S2S specified aerosol amounts from climatology, which were used to inform the atmospheric radiation only. The ocean model includes an upgrade from MOM4 to MOM5 (Griffies 2012), and continues to be run on the tripolar grid at approximately 1/2 degree resolution in the tropics with 40 vertical levels. As in S2S-1.0, the sea ice model is from the Los Alamos Sea Ice model (CICE4, Hunke and Lipscomb 2010). The Ocean Data Assimilation System (ODAS) has been upgraded from the one described in Borovikov et al., 2017 to one that uses a modified version of the Penny, 2014 Local Ensemble Transform Kalman Filter (LETKF), and now assimilates along-track altimetry. The ODAS also does a nudging to MERRA-2 SST and sea ice boundary conditions. The atmospheric data assimilation fields used to constrain the atmosphere in the ODAS have been upgraded from MERRA to a MERRA-2 like system. The system is initialized using a MERRA-2-like atmospheric reanalysis (Gelaro et al. 2017) and the GMAO S2S-2_1 ocean analysis. Additional ensemble members for forecasts are produced with initial states at 5-day intervals, with additional members based on perturbations of the atmospheric and ocean states. Both subseasonal and seasonal forecasts are submitted to the National MultiModel Ensemble (NMME) project, and are part of the US/Canada multimodel seasonal forecasts (http://www.cpc.ncep.noaa.gov/products/NMME/). A large suite of retrospective forecasts (''hindcasts'') have been completed, and contribute to the calculation of the model's baseline climatology and drift, anomalies from which are the basis of the seasonal forecasts.
In this study, we examine a low-altitude Lunar Position, Navigation, and Timing (LPNT) constellations and the localization performance of Centralized Extended Kalman Filter (CEKF) and Decentralized Extended Kalman Filter (DEKF) algorithms. The primary investigation involves a 100-node swarm operating at a 100 km altitude, in contrast to previous studies that examined a 21-node asset in a frozen-orbit at 5,500 km. The autonomous operation of large-scale swarm is based on two-way Inter-Satellite Link (ISL) measurements, which involve pseudoranges and relative velocities among swarm nodes. We perform a numerical assessment of the two filtering approaches, utilizing ‘fully sampled’ measurements from all available assets as well as ‘two ISL’ measurements where each spacecraft is restricted to only two antennas. This research includes an analysis of CEKF under 2-ISL constraints and evaluates the performance of DEKF in a 100-node swarm, which has not been explored in previous studies. In addition, we examine the impact of increasing the sampling frequency for DEKF, showing that the update cycle can be shortened from a 10-minute interval. A novel approach for ‘2-ISL limited’ DEKF will also be introduced, using a matching formulation that exhaustively enumerates all potential matches. This study provides valuable insights into large-scale distributed swarm operations, considering various filter configurations, sampling frequencies, matching strategies, and scalability of CEKF and DEKF for low-altitude LPNT applications. The Lunar PNT technology plays a key role in providing reliable and robust navigation services on the Moon's surface and the South pole, where the primary Lunar missions are planned. To support upcoming Lunar missions, including small satellites from NASA's Commercial Lunar Payload Services program, the Lunar PNT system must be adaptable to smaller platforms like CubeSats. Driven by the growing involvement of public and private exploration partnerships, the traditional low Earth orbit missions are shifting to beyond geosynchronous orbit [1]. These upcoming missions aim to foster a sustainable and innovative exploration program, in collaboration with commercial and international partners, to facilitate human expansion throughout the solar system and return new knowledge and opportunities to Earth [2]. As part of this trend, there are increasing efforts to utilize science missions in Lunar orbit to develop a non-dedicated and ad-hoc PNT network system. Two traditional approaches, the Deep Space Network (DSN) and the weak signal Global Positioning System (GPS), are established deep-space navigation technologies for missions beyond the geosynchronous orbit. Beginning in 1958, the DSN was developed to communicate with the Explorer 1 spacecraft based on the use of radiometric tracking in spacecraft navigation [3]. The DSN is capable of providing nearly unfettered coverage to spacecraft beyond low-Earth orbit (LEO), however, increased space mission volume has created concerns about future expectations of DSN usage for spacecraft navigation [4]. For cislunar mission applications, the position accuracy using DSN achieves 100 m (3σ) with at least three geometrically diverse ground stations when using radiometric tracking alone [5]. The DSN's dependence on Earth-based ground stations restricts its operational capabilities to periods of Earth visibility. This limitation, coupled with its poor localization performance, renders the DSN unsuitable for future lunar missions that demand continuous tracking and precise positioning. To satisfy the increasing requirements of DSN in Lunar applications, spacecrafts are also required to improve their onboard antenna power and efficiency of the transmission. However, there is an important aggregate cost trade between adding capabilities to every spacecraft and adding to a capacity on the ground that serves multiple spacecraft [6]. A weak GPS system can provide PNT service while the user spacecraft is bound to the Moon, leveraging a single, steerable high gain antenna with the relatively narrow beam which includes all the sources in its field of view [7]. However, the higher the altitude the receiver is above the GPS constellations, the poorer and the weaker are the relative geometry and the received signal powers, respectively, leading to a significant navigation accuracy reduction [8]. The transmitted power becomes weaker with increasing distance from the Earth as well as signals tracked from one of the side lobes of the GPS antenna pattern. As a results, the number of visible satellites and relative geometric condition of the GPS satellites at very high altitude drops dramatically and reduces the navigation solution accuracy. Therefore, the weak GPS system is also not an ideal way to provide PNT service to upcoming Lunar missions when considering its limited geometric condition and the recued navigation accuracy. Another navigation approach on the Moon is being developed, similar to the Global Navigation Satellite System (GNSS) on Earth, aiming to offer navigation service with continuous 24/7 coverage across the entire Lunar surface. For example, lunar communications relay and navigation systems (LCRNS) by NASA and Lunar navigation satellite systems (LNSS) by JAXA are designed to serve as dedicated Position, Navigation, and Timing (PNT) systems for the Moon. However, designing a dedicated LNSS and PNT service involves additional challenges, which are unique to the lunar environment, including limited payload capacity for the CubeSat platform, i.e., the size, weight, and power (SWaP) of the onboard clock, limited lunar ground monitoring stations, and limited financial investment as compared to the legacy Earth-GPS [9]. NASA’s focus on utilizing CubeSat platforms on the Moon leads to an alternative Lunar navigation platform that leverages the existing Lunar science and exploration assets. The small satellites used in Lunar missions can be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions [10]. As upcoming Lunar missions will often operate at low-altitude about 30 km to 100 km for scientific observations and mapping purposes, the low-altitude orbital constellations could be employed to create an ad-hoc Lunar PNT system. However, several issues must be addressed, such as the instability of these orbits, which often require maintenance or are only suitable for short-duration missions, operating for fewer than 90 days. Additionally, at an altitude of 100 km, the satellites have a limited period during which they are above the horizon and capable of providing PNT service to users. The implementation of a non-dedicated, ad-hoc Lunar navigation constellation facilitates on-demand PNT services. A preliminary study of ad-hoc Lunar PNT system was conducted using 21 spacecraft in 5,5000 km altitude frozen orbits to test its feasibility and a basic performance of orbital asset localization among ad-hoc Lunar constellations in small satellites format [10]. These swarm assets are designed for autonomous localization with minimal Earth interaction, reducing dependency on bandwidth and ground resources. The design in [10] demonstrated the feasibility of a decentralized PNT approach, specifically employing a DEKF approach for state estimation, which helps minimize onboard operating costs. The DEKF method distributes computation across individual satellites, which lightens the computational load while maintaining accuracy in orbit ephemeris and clock offsets, similar to centralized systems [11]. In a follow-on study [12], each spacecraft was limited to 2 communications antennae, forcing the selection of measurements and scheduling spacecraft activities to perform the measurements. A matching algorithm is implemented to select the best measurements and schedule position estimation updates. The decentralized localization performance is also investigated with increasing levels of network degradation for swarm assets considering the impact of intermittent and permanent communication failure, to demonstrate the robustness and fidelity of the decentralized Lunar PNT service [13]. This study confirmed that the ad-hoc PNT constellations in frozen orbit are highly robust and resilient to communication failures. However, unlike frozen orbit swarm assets, the low-altitude satellites have a limited ground view at an altitude of 100 km, where the ad-hoc Lunar constellation consists of 98 low-altitude satellites, evenly distributed across seven circular polar orbital planes, alongside two satellites in a frozen orbit at an altitude of 5,500 km (Figure 1). Therefore, the number of satellites visible to ground users is significantly limited in low-altitude orbit constellations. As each visibility of a spacecraft remains intact for only a few ticks before it moves out of the field of view, the ground user encounters challenges in maintaining continuous navigation service, resulting in sparse availability and provision of Lunar PNT system. Consequently, service availability is primarily restricted to the Lunar South Pole region (Figure 2). Given these limitations and concerns, the localization performance of low-altitude swarm assets will be assessed in this study. We focus on the investigation of the localization performance of low-altitude swarm assets and ground users near the Lunar South Pole. The overall flow of the Lunar PNT simulation incorporates the DEKF approach of asset localization and the weighted least-squares approach in user localization (Figure 3). The autonomous Lunar PNT simulation is primarily implemented in MATLAB, where the DEKF based on the matching scheduler is implemented with Google’s OR-tools as a model builder and Gurobi optimization tool as a backend solver. The General Mission Analysis Tool (GMAT) is utilized to generate ephemeris data for swarm assets, and accounts for satellite orbital details, mass, and perturbations like solar radiation pressure and drag coefficients. Each ephemeris dataset is produced in the Moon International Celestial Reference Frame (ICRF) inertial coordinate system. For state estimation, the distributed swarm assets rely on two-way Inter-Satellite Link (ISL) measurements, which involve tracking pseudoranges and relative velocities between visible satellites and anchor nodes during each observation. Numerical evaluations of the decentralized localization process are conducted to demonstrate the feasibility of the low-altitude PNT system in providing reliable navigation services. The main approach involves using DEKF and CEKF to localize 100 satellites in low-altitude constellations, where the CEKF is implemented to serve as a baseline for comparing the performance of distributed algorithms. In both cases, we evaluate ‘fully sampled’ measurements from all available assets, and ‘two ISL’ measurements when spacecraft are constrained to have only two antennas. We test four estimation techniques: CEKF fully sampled, CEKF two ISL, DEKF fully sampled, and DEKF two ISL filters. As the DEKF update cycle is comprised of network setup, communication, and computations, a global broadcast network and 2-way ISL network setup will take from 4 to 6 minutes as maximum [12]. In this simulation, the DEKF update cycle is set to 10 minutes, including a 4-minute latency for obtaining and computing the actual measurement updates. We experiment an increased update cycle to demonstrate the feasibility and evaluate the impact on localization performance using various tuning values for measurement noise covariances (Figures 4 and 5). By comparing centralized and decentralized approaches using a matching algorithm, we analyze the influence of cross-correlation factors in the covariance matrix, assuming 100% reliability of all assets and measurements. The increased frequency and the adjustments of tuning parameters reveal distinct error patterns between the two scenarios. The localization accuracy of the swarm assets and ground users is assessed by taking the median error across 100 assets and one ground user (84.9°S, 137.5°E) over 7-day simulation period (Table 1). Since the user localization accuracy is significantly affected by the performance of the swarm assets, it is crucial to maintain high localization accuracy within the swarm. This study will continue to explore decentralized filtering for autonomous LPNT operations, with further investigation of an 'iterative' matching approach which enumerates every valid matching pair, planned for the following month.
Large-scale spiral arms have been revealed in scattered light images of a few protoplanetary disks. Theoretical models suggest that such arms may be driven by and corotate with giant planets, which has called for remarkable observational efforts to look for them. By examining the rotation of the spiral arms for the MWC 758 system over a 10 year timescale, we are able to provide dynamical constraints on the locations of their perturbers. We present reprocessed Hubble Space Telescope (HST)/NICMOS F110W observations of the target in 2005, and the new Keck/NIRC2 L'-band observations in 2017. MWC 758's two well-known spiral arms are revealed in the NICMOS archive at the earliest observational epoch. With additional Very Large Telescope (VLT)/SPHERE data, our joint analysis leads to a pattern speed of 0.°6(sup +3.°3, sub -0.°6)/yr at 3σ for the two major spiral arms. If the two arms are induced by a perturber on a near-circular orbit, its best-fit orbit is at 89 au (0."59), with a 3σ lower limit of 30 au (0."20). This finding is consistent with the simulation prediction of the location of an arm-driving planet for the two major arms in the system.
An improved dynamic analysis for liquid annular seals with arbitrary profile based on a method, first proposed by Nelson and Nguyen, is presented. An improved first order solution that incorporates a continuous interpolation of perturbed quantities in the circumferential direction, is presented. The original method uses an approximation scheme for circumferential gradients, based on Fast Fourier Transforms (FFT). A simpler scheme based on cubic splines is found to be computationally more efficient with better convergence at higher eccentricities. A new approach of computing dynamic coefficients based on external specified load is introduced. This improved analysis is extended to account for arbitrarily varying seal profile in both axial and circumferential directions. An example case of an elliptical seal with varying degrees of axial curvature is analyzed. A case study based on actual operating clearances of an interstage seal of the Space Shuttle Main Engine High Pressure Oxygen Turbopump is presented.