Accelerating frames of reference and the clock paradox.
Lorentz-Einstein transformations, coordinate transformation between accelerating systems and inertial frames of reference and clock paradox
RELATIVITY THEORY↗
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Decoupling the Role of Inertia and Gravity on Particle Dispersion
Turbulent gas flows laden with small, dense particles are encountered in a wide number of important applications in both industrial settings and aerodynamics applications. Particle interactions with the underlying turbulent flow are exceedingly complex and, consequently, difficult to accurately model. The difficulty arises primarily due to the fact that response of a particle to the local environment is dictated by turbulence properties in the reference frame moving with the particle (particle-Lagrangian). The particle-Lagrangian reference frame is in turn dependent upon the particle relaxation time (time constant) as well as gravitational drift. The combination of inertial and gravitational effects in this frame complicates our ability to accurately predict particle-laden flows since measurements in the particle-Lagrangian reference frame are difficult to obtain. Therefore, in this work we will examine separately the effects of inertia and gravitational drift on particle dispersion through a combination of physical and numerical experiments. In this study, particle-Lagrangian measurements will be obtained in physical experiments using stereo image velocimetry. Gravitational drift will be varied in the variable-g environments of the NASA DC-9 and in the zero-g environment at the drop tower at NASA-Lewis. Direct numerical simulations will be used to corroborate the measurements from the variable-g experiments. We expect that this work will generate new insight into the underlying physics of particle dispersion and will, in turn, lead to more accurate models of particle transport in turbulent flows.
Rogers, Chris↗
Global and regional kinematics with GPS
The inherent precision of the doubly differenced phase measurement and the low cost of instrumentation made GPS the space geodetic technique of choice for regional surveys as soon as the constellation reached acceptable geometry in the area of interest: 1985 in western North America, the early 1990's in most of the world. Instrument and site-related errors for horizontal positioning are usually less than 3 mm, so that the dominant source of error is uncertainty in the reference frame defined by the satellites orbits and the tracking stations used to determine them. Prior to about 1992, when the tracking network for most experiments was globally sparse, the number of fiducial sites or the level at which they could be tied to an SLR or VLBI reference frame usually, set the accuracy limit. Recently, with a global network of over 30 stations, the limit is set more often by deficiencies in models for non-gravitational forces acting on the satellites. For regional networks in the northern hemisphere, reference frame errors are currently about 3 parts per billion (ppb) in horizontal position, allowing centimeter-level accuracies over intercontinental distances and less than 1 mm for a 100 km baseline. The accuracy of GPS measurements for monitoring height variations is generally 2-3 times worse than for horizontal motions. As for VLBI, the primary source of error is unmodeled fluctuations in atmospheric water vapor, but both reference frame uncertainties and some instrument errors are more serious for vertical than horizontal measurements. Under good conditions, daily repeatabilities at the level of 10 mm rms were achieved. This paper will summarize the current accuracy of GPS measurements and their implication for the use of SLR to study regional kinematics.
King, Robert W.↗
Hydrodynamic Stability And Frames Of Reference
Criteria of stability different in different sets of coordinates. Report discusses dependence of criteria of hydrodynamic instability upon frame of reference used to analyze motion of fluid.
Zak, Michail A.↗
Speckle interferometry of Hipparcos link stars. III
A third list of stars is presented which have been tested by speckle interferometry for use in the Hubble Space Telescope link between the Hipparcos astrometric reference frame and the extragalactic VLBI reference frame. Structural information on angular scales of 0.15-1.2 arcsec for 34 Southern Hemisphere stars is reported from observations made with the Imperial College Speckle Interferometer mounted on the Mount Stromlo 1.9-m telescope. Twenty-four percent of the stars (8 out of the 34) show evidence of multiplicity, in agreement with previous observations in this program.
White, Graeme L.↗
Global Positions and Velocities from One Year of GPS Data
A generalized no-fiducial approach has been developed to obtain global positions and velocities without fixing any individual position or velocity components. The method used can be applied to any global geodetic technique and proceeds in three general steps. First, daily solutions derived with weak constraints are combined to yield one global set of positions and velocities. Second, 14 minimal constraints are applied to remove uncertainties due to the loosely defined reference frame. Third, transformation from one reference frame to another is accomplished with a 14 parameter transformation. One year of daily FLINN solutions, each made with data from about 40 sites, have been combined to yield our best fit global model...
Heflin, M. B.↗
Laser-Camera Vision Sensing for Spacecraft Mobile Robot Navigation
The advent of spacecraft mobile robots-free-flyng sensor platforms and communications devices intended to accompany astronauts or remotely operate on space missions both inside and outside of a spacecraft-has demanded the development of a simple and effective navigation schema. One such system under exploration involves the use of a laser-camera arrangement to predict relative positioning of the mobile robot. By projecting laser beams from the robot, a 3D reference frame can be introduced. Thus, as the robot shifts in position, the position reference frame produced by the laser images is correspondingly altered. Using normalization and camera registration techniques presented in this paper, the relative translation and rotation of the robot in 3D are determined from these reference frame transformations.
Maluf, David A.↗
Using XR for Improving Scientific Discovery With Numerical Weather Models
Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.
Thomas Grubb↗
The effects of gravity darkening on the ultraviolet continuum polarization produced by circumstellar disks
We investigate the effects of gravity darkening on the UV continuum polarization produced by an axisymmetric disk that surrounds a rapidly rotating star. Although the model is a single scattering approximation, we do include the effects of attenuation (electron scattering plus hydrogen bound-free absorption) by the disk, using an approach similar to that of Sobolev (1963). Because of the gravity darkening of the star and the attenuation within the disk, the radiation field is not axially symmetric about the radius vector. This implies that the polarization source functions are no longer provided by the finite disk depolarization factors of Cassinelli, Nordsieck, & Murison (1987), which are functions of the intensity moments in a spherically symmetric atmosphere. We reformulate the polarization source functions using generalized intensity moment tensors (J, H(sub i), K(sub ij)) that are valid for an arbitrary radiation field and envelope geometry. We find that the polarization source functions are simplest when using intensity moments in the observer's reference frame. On the other hand, the intensity moments are most easily evaluated in the stellar reference frame. Using the rotation transformation properties of the generalized intensity moments, we relate the observer's moments to those evaluated in the stellar reference frame. Our procedure for determining the polarization source functions thus merely involves choosing a set of Euler angles for the coordinate rotations, and then evaluating the associated rotation matrix. The geometrical complications of polarization transfer are thus reduced to obtaining a coordinate rotation matrix.
Bjorkman, J. E.↗
Coupled rotor-fuselage vibration reduction with multiple frequency blade pitch control
A nonlinear coupled rotor/flexible fuselage analysis has been developed and used to study the effects of higher harmonic blade pitch control on the vibratory hub loads and fuselage acceleration levels. Previous results, obtained with this model have shown that conventional higher harmonic control (HHC) inputs aimed at hub shear reduction cause an increase in the fuselage accelerations and vice-versa. It was also found that for simultaneous reduction of hub shears and fuselage accelerations, a pitch input representing a combination of two higher harmonic components of different frequencies was needed. Subsequently, it was found that this input could not be implemented through a conventional swashplate. This paper corrects a mistake originally made in the representation of the multiple frequency pitch input and shows that such a pitch input can be only implemented in the rotating reference frame. A rigorous mathematical solution is found, for the pitch input in the rotating reference frame, which produces simultaneous reduction of hub shears and fuselage acceleration. New insight on vibration reduction in coupled rotor/fuselage systems is obtained from the sensitivity of hub shears to the frequency and amplitude of the open loop HHC signal in the rotating reference frame. Finally the role of fuselage flexibility in this class of problems is determined.
Papavassiliou, I.↗
Transformation from proper time on earth to coordinate time in solar system barycentric space-time frame of reference
An expression was derived for the time transformation t - tau, where t is coordinate time in the solar system barycentric space-time frame of reference and tau is proper time obtained from a fixed atomic clock on earth. This transformation is suitable for use in the computation of high-precision earth-based range and Doppler observables of a spacecraft or celestial body located anywhere in the solar system; it can also be used in obtaining computed values of very long baseline interferometry data types. The formulation for computing range and Doppler observables, which is an explicit function of the transformation t - tau, is described briefly.
Moyer, T. D.↗
Local Gravitomagnetism
In quasi-inertial reference frame, geodetic precession is gravitomagnetic phenomenon. Report presents theoretical analysis of gravitomagnetism as perceived by observer in quasi-inertial reference frame near spinning body. Study addresses manifestations of gravitomagnetism in this reference frame, with emphasis on two measurable phenomena: precession of gyroscope in orbit about Earth, and perturbation of trajectory of satellite in orbit around Earth.
Shahid-Saless, Bahman↗
Errors in fixed and moving frame of references - Applications for conventional and Doppler radar analysis
Techniques for the correction of errors in Doppler radar scans due to advection effects are presented. A moving frame of reference is shown to be useful in least-squares estimates with stationary observations expressed in scalars or Cartesian coordinates. For non-Cartesian coordinates, such as the deduction of radial velocities from triple Doppler radar data, an integral is defined for accounting for advection effects and consequent coordinate transformations. The multiple radars are necessary for unambiguous characterization of the horizontal wind velocity. A scale analysis is employed to estimate errors with and without the error correction procedure. Improvements in correlations between scans are demonstrated when the error correction method is used.
Tzvi, G.-C.↗
Global VLBI Observations of Weak Extragalactic Radio Sources: Imaging Candidates to Align the VLBI and Gaia Frames
The space astrometry mission Gaia will construct a dense optical QSO-based celestial reference frame. For consistency between optical and radio positions, it will be important to align the Gaia and VLBI frames (International Celestial Reference Frame) with the highest accuracy. In this respect, it is found that only 10% of the ICRF sources are suitable to establish this link (70 sources), either because most of the ICRF sources are not bright enough at optical wavelengths or because they show extended radio emission which precludes reaching the highest astrometric accuracy. In order to improve the situation, we initiated a multi-step VLBI observational project, dedicated to finding additional suitable radio sources for aligning the two frames. The sample consists of about 450 optically-bright radio sources, typically 20 times weaker than the ICRF sources, which have been selected by cross-correlating optical and radio catalogs. The initial observations, aimed at checking whether these sources are detectable with VLBI, and conducted with the European VLBI Network (EVN) in 2007, showed an excellent 90% detection rate. This paper reports on global VLBI observations carried out in March 2008 to image 105 from the 398 previously detected sources. All sources were successfully imaged, revealing compact VLBI structure for about half of them, which is very promising for the future.
Bourda, Geraldine↗
Estimation Filter for Alignment of the Spitzer Space Telescope
A document presents a summary of an onboard estimation algorithm now being used to calibrate the alignment of the Spitzer Space Telescope (formerly known as the Space Infrared Telescope Facility). The algorithm, denoted the S2P calibration filter, recursively generates estimates of the alignment angles between a telescope reference frame and a star-tracker reference frame. At several discrete times during the day, the filter accepts, as input, attitude estimates from the star tracker and observations taken by the Pointing Control Reference Sensor (a sensor in the field of view of the telescope). The output of the filter is a calibrated quaternion that represents the best current mean-square estimate of the alignment angles between the telescope and the star tracker. The S2P calibration filter incorporates a Kalman filter that tracks six states - two for each of three orthogonal coordinate axes. Although, in principle, one state per axis is sufficient, the use of two states per axis makes it possible to model both short- and long-term behaviors. Specifically, the filter properly models transient learning, characteristic times and bounds of thermomechanical drift, and long-term steady-state statistics, whether calibration measurements are taken frequently or infrequently. These properties ensure that the S2P filter performance is optimal over a broad range of flight conditions, and can be confidently run autonomously over several years of in-flight operation without human intervention.
Bayard, David↗
A Joint Analysis of GPS Displacement and GRACE Geopotential Data for Simultaneous Estimation of Geocenter Motion and Gravitational Field
Gravitational potential data from GRACE are being used to study mass redistribution within and between the atmosphere, hydrosphere, cryosphere, and solid Earth. The GRACE data are made available in a reference frame with its origin at the center of mass of the Earth system (geocenter) while many other geophysical models and data sets refer to a reference frame attached to the Earth's surface. Changes in the offset between these reference frames (geocenter motion) must be accounted for when GRACE data are used to quantify surface mass changes. In this study, we developed a technique for co‐estimation of geocenter motion and gravitational potential field seamlessly from degree 1 to 90 by simultaneously inverting a set of globally‐distributed GPS displacement time series and the temporally‐varying GRACE gravity data. We found that the effect of geocenter motion was evident particularly in the GPS time series of horizontal displacements. Our estimates of geocenter motion are most consistent with the Satellite Laser Ranging (SLR) results within 1 mm in X and Z components and a submillimeter in Y component, when compared to monthly variability averaged over the period of 2003–2016. The overall magnitude of the degree‐1 (l = 1) surface mass load is estimated to be ~3 cm in equivalent water height annually migrating south‐westward from Europe (December–January) to the South Pacific (June–July). Our results also show that dense GPS network data improve water storage recovery in major river basins in the United States and Europe by contributing significantly to the recovery of higher‐degree (l ≥ ~20) geopotential coefficients.
Razeghi, Mahdiyeh↗
Spatial coding of eye movements relative to perceived earth and head orientations during static roll tilt
This purpose of this study was to examine the spatial coding of eye movements during static roll tilt (up to +/-45 degrees) relative to perceived earth and head orientations. Binocular videographic recordings obtained in darkness from eight subjects allowed us to quantify the mean deviations in gaze trajectories along both horizontal and vertical coordinates relative to the true earth and head orientations. We found that both variability and curvature of gaze trajectories increased with roll tilt. The trajectories of eye movements made along the perceived earth-horizontal (PEH) were more accurate than movements along the perceived head-horizontal (PHH). The trajectories of both PEH and PHH saccades tended to deviate in the same direction as the head tilt. The deviations in gaze trajectories along the perceived earth-vertical (PEV) and perceived head-vertical (PHV) were both similar to the PHH orientation, except that saccades along the PEV deviated in the opposite direction relative to the head tilt. The magnitude of deviations along the PEV, PHH, and PHV corresponded to perceptual overestimations of roll tilt obtained from verbal reports. Both PEV gaze trajectories and perceptual estimates of tilt orientation were different following clockwise rather than counterclockwise tilt rotation; however, the PEH gaze trajectories were less affected by the direction of tilt rotation. Our results suggest that errors in gaze trajectories along PEV and perceived head orientations increase during roll tilt in a similar way to perceptual errors of tilt orientation. Although PEH and PEV gaze trajectories became nonorthogonal during roll tilt, we conclude that the spatial coding of eye movements during roll tilt is overall more accurate for the perceived earth reference frame than for the perceived head reference frame.
NASA Discipline Neuroscience↗
Development of an Extended Reality (XR) Tool for Earth Science Visualization
In this presentation, we will discuss our work in adapting the NASA open source XR software, the Mixed Reality Exploration Toolkit (MRET), to an earth science domain. MRET is a NASA open source XR software for rapidly building extended reality (XR) environments for NASA domain problems, e.g., pulling in CAD models of thermal vac chamber and Roman Space Telescope to do fit checks. Primarily used for hardware integration & test, we have been adapting and extending MRET for science problems. Traditionally, scientists view and analyze the result of calculated or measured observables with static 1-D, 2-D or 3-D plots. It can be difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. Additionally, numerical models, such as the NASA GEOS climate model, are almost exclusively formulated and analyzed on Eulerian grids with points fixed in space and time. However, atmospheric phenomena such as convective clouds, hurricanes and wildfire smoke plumes move with the 3-D flow field, and it is often difficult and unnatural to understand these phenomena in an Eulerian reference frame as opposed to the Lagrangian reference frame in which nature operates. As part of an Earth Science Technology Office (ESTO) proposal, we have been adapting MRET to be a scientific exploration and analysis XR tool with integrated Lagrangian Dynamics (LD) for the Goddard Earth Observing System (GEOS) numerical weather prediction model. We believe this will help scientists identify, track, and understand the evolution of Earth Science phenomena. This presentation will discuss current results in our work in developing this XR tool for Earth Science.
Thomas G Grubb↗