Determination of ellipsoidal surface mass change from GRACE time-variable gravity data
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Khosro Ghobadi-Far↗
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Results for “Ellipsoids”
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Modeling Chondrule Dust Rim Growth with Ellipsoidal Monomers
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C. Xiang↗
Small-Body Extensions for the Satellite Orbit Analysis Program (SOAP)
An extension to the SOAP software allows users to work with tri-axial ellipsoid-based representations of planetary bodies, primarily for working with small, natural satellites, asteroids, and comets. SOAP is a widely used tool for the visualization and analysis of space missions. The small body extension provides the same visualization and analysis constructs for use with small bodies. These constructs allow the user to characterize satellite path and instrument cover information for small bodies in both 3D display and numerical output formats. Tri-axial ellipsoids are geometric shapes the diameters of which are different in each of three principal x, y, and z dimensions. This construct provides a better approximation than using spheres or oblate spheroids (ellipsoids comprising two common equatorial diameters as a distinct polar diameter). However, the tri-axial ellipsoid is considerably more difficult to work with from a modeling perspective. In addition, the SOAP small-body extensions allow the user to actually employ a plate model for highly irregular surfaces. Both tri-axial ellipsoids and plate models can be assigned to coordinate frames, thus allowing for the modeling of arbitrary changes to body orientation. A variety of features have been extended to support tri-axial ellipsoids, including the computation and display of the spacecraft sub-orbital point, ground trace, instrument footprints, and swathes. Displays of 3D instrument volumes can be shown interacting with the ellipsoids. Longitude/latitude grids, contour plots, and texture maps can be displayed on the ellipsoids using a variety of projections. The distance along an arbitrary line of sight can be computed between the spacecraft and the ellipsoid, and the coordinates of that intersection can be plotted as a function of time. The small-body extension supports the same visual and analytical constructs that are supported for spheres and oblate spheroids in SOAP making the implementation of the more complex algorithms largely transparent to the user.
Carnright, Robert↗
Multispectral glancing incidence X-ray telescope
A multispectural glancing incidence X-ray telescope is illustrated capable of broadband, high-resolution imaging of solar and stellar X-ray and extreme ultraviolet radiation sources which includes a primary optical system preferably of the Wolter I type having a primary mirror system. The primary optical system further includes an optical axis having a primary focus at which the incoming radiation is focused by the primary mirrors. A plurality of ellipsoidal mirrors are carried at an inclination to the optical axis behind the primary focus. A rotating carrier is provided on which the ellipsoidal mirrors are carried so that a desired one of the ellipsoidal mirrors may be selectively positioned in front of the incoming radiation beam. In the preferred embodiment, each of the ellipsoidal mirrors has an identical concave surface carrying a layered synthetic microstructure coating tailored to reflect a desired wavelength of 1.5A or longer. Each of the identifical ellipsoidal mirrors has a second focus at which a detector is carried. Thus the different wavelength image is focused upon the detector irregardless of which mirror is positioned in front of the radiation beam.
Hoover, R. B.↗
Variable magnification glancing incidence x ray telescope
A multispectral glancing incidence x ray telescope is disclosed, which capable of broadband, high resolution imaging of solar and stellar x ray and extreme ultraviolet radiation sources includes a primary optical system which focuses the incoming radiation to a primary focus. Two or more ellipsoidal mirrors are positioned behind the primary focus at an inclination to the optical axis, each mirror having a concave surface coated with a multilayer synthetic microstructure coating to reflect a desired wavelength. The ellipsoidal mirrors are segments of respective ellipsoids having a common first focus coincident with the primary focus. A detector such as an x ray sensitive photographic film is positioned at the second focus of each of the ellipsoids so that each of the ellipsoidal mirrors may reflect the image at the first focus to the detector. In one embodiment the mirrors are inclined at different angles and has its respective second focus at a different location, separate detectors being located at the respective second focus. The mirrors are arranged so that the magnification and field of view differ, and a solenoid activated arm may withdraw at least one mirror from the beam to select the mirror upon which the beam is to impinge so that selected magnifications and fields of view may be detected.
Hoover, Richard↗
Magnetopause shape as a bivariate function of interplanetary magnetic field B(sub z) and solar wind dynamic pressure
We present a new method for determining the shape of the magnetopause as a bivariate function of the hourly averaged solar wind dynamic pressure (p) and the north-south component of the interplanetary magnetic field (IMF) B(sub z). We represent the magnetopause (for X(sub GSE) greater than -40 R(sub E)) as an ellipsoid of revolution in solar-wind-aberrated coordinates and express the (p, B(sub z)) dependence of each of the three ellipsoid parameters as a second-order (6-term) bivariate expansion in Inp and B(sub z). We define 12 overlapping bins in a normalized dimensionless (p, B(sub z)) `control space' and fit an ellipsoid to those magnetopause crossings having (p, B(sub z)) values within each bin. We also calculate the bivariate (Inp, B(sub z)) moments to second order over each bin in control space. We can then calculate the six control-space expansion coefficients for each of the three ellipsoid parameters in configuration space. From these coefficients we can derive useful diagnosis of the magnetopause shape as joint functions of p and B(sub z): the aspect ratio of the ellipsoid's minor-to-major axes; the flank distance, radius of curvature, and flaring angle (at X(sub GSE) = 0); and the subsolar distance and radius of curvature. We confirm and quantify previous results that during periods of southward B(sub z) the subsolar magnetopause moves inward, while at X(sub GSE) = 0 the flank magnetopause moves outward and the flaring angle increases.
Roelof, Edmond C.↗
Multispectral glancing incidence X-ray telescope
A multispectral glancing incidence X-ray telescope is illustrated capable of broadband, high-resolution imaging of solar and stellar X-ray and extreme ultraviolet radiation sources which includes a primary optical system preferably of the Wolter I type having a primary mirror system (20, 22). The primary optical system further includes an optical axis (24) having a primary focus (F1) at which the incoming radiation is focused by the primary mirrors. A plurality of ellipsoidal mirrors (30a, 30b, 30cand 30d) are carried at an inclination to the optical axis behind the primary focus (F1). A rotating carrier (32) is provided on which the ellipsoidal mirrors are carried so that a desired one of the ellipsoidal mirrors may be selectively positioned in front of the incoming radiation beam (26). In the preferred embodiment, each of the ellipsoidal mirrors has an identical concave surface carrying a layered synthetic microstructure coating tailored to reflect a desired wavelength of 1.5 .ANG. or longer. Each of the identical ellipsoidal mirrors has a second focus (F2) at which a detector (16) is carried. Thus the different wavelength image is focused upon the detector irregardless of which mirror is positioned in front of the radiation beam. In this manner, a plurality of low wavelengths in a wavelength band generally less than 30 angstroms can be imaged with a high resolution.
Hoover, Richard B.↗
Thermal Phase Variations of WASP-12b: Defying Predictions
We report Warm Spitzer full-orbit phase observations of WASP-12b at 3.6 and 4.5 micrometers. This extremely inflated hot Jupiter is thought to be overflowing its Roche lobe, undergoing mass loss and accretion onto its host star, and has been claimed to have a C/O ratio in excess of unity. We are able to measure the transit depths, eclipse depths, thermal and ellipsoidal phase variations at both wavelengths. The large-amplitude phase variations, combined with the planet's previously measured dayside spectral energy distribution, are indicative of non-zero Bond albedo and very poor day-night heat redistribution. The transit depths in the mid-infrared-(R(sub p)/R(sub ∗))(sup 2) = 0.0123(3) and 0.0111(3) at 3.6 and 4.5 micrometers, respectively-indicate that the atmospheric opacity is greater at 3.6 than at 4.5 micrometers, in disagreement with model predictions, irrespective of C/O ratio. The secondary eclipse depths are consistent with previous studies: F(sub day)/F(sub ∗) = 0.0038(4) and 0.0039(3) at 3.6 and 4.5 micrometers, respectively. We do not detect ellipsoidal variations at 3.6 micrometers, but our parameter uncertainties-estimated via prayer-bead Monte Carlo-keep this non-detection consistent with model predictions. At 4.5 micrometers, on the other hand, we detect ellipsoidal variations that are much stronger than predicted. If interpreted as a geometric effect due to the planet's elongated shape, these variations imply a 3:2 ratio for the planet's longest:shortest axes and a relatively bright day-night terminator. If we instead presume that the 4.5 micrometer ellipsoidal variations are due to uncorrected systematic noise and we fix the amplitude of the variations to zero, the best-fit 4.5 micrometer transit depth becomes commensurate with the 3.6 micrometer depth, within the uncertainties. The relative transit depths are then consistent with a solar composition and short scale height at the terminator. Assuming zero ellipsoidal variations also yields a much deeper 4.5 micrometer eclipse depth, consistent with a solar composition and modest temperature inversion. We suggest future observations that could distinguish between these two scenarios.
planetary↗
Angular momentum transfer by gravitational torques and the evolution of binary protostars
The efficiency of angular momentum transport by gravitational torques is investigated semianalytically for two idealized models. The first model, a rotating ellipsoid embedded within another ellipsoid, is compared with numerical results for the fission instability of a radpidly-rotating polytrope. The fission instability is aborted by the rapid transfer of angular momentum outward by gravitational torques. The global rates of angular momentum transfer by gravitational torques in rotating gas clouds such as the presolar nebula are shown to be comparable to the rates assumed to be appropriate for transfer by turbulent stresses. The second model is a binary system embedded within a rotating ellipsoid. The binary orbital angular momentum decreases significantly when the phase angle with the ellipsoid is constant; the binary separation may then decrease by a factor of 100 within about an orbital period. For a variable phase angle, little secular loss of orbital angular momentum occurs. Binaries which form in the isothermal regime of the theory of hierarchical fragmentation will not undergo orbital decay, whereas very close binaries composed of nonisothermal fragments may decay and merge into single objects.
Boss, A. P.↗
Spectral infrared hemispherical reflectance measurements for LDEF tray clamps
This paper describes infrared hemispherical reflectance measurements (2-15 microns) that were made on 58 chromic acid anodized tray clamps retrieved from the LDEF spacecraft. These clamps were used for maintaining the experiments in place and were located at various locations about the spacecraft. Changes in reflectance of the tray clamps at these locations were compared with atomic oxygen fluxes at the same locations. A decrease in absorption band depth was seen for the surfaces exposed to space indicating that there was some surface layer erosion. In all of the surfaces measured, little evidence of contamination was observed and none of the samples showed evidence of the brown nicotine stain that was so prominent in other experiments. Total emissivity values were calculated for both exposed and unexposed tray clamp surfaces. Only small differences, usually less than 1 percent, were observed. The spectral reflectances were measured using a hemi-ellipsoidal mirror reflectometer matched with an interferometer spectrometer. The rapid scanning capability of the interferometer allowed the reflectance measurements to be made in a timely fashion. The ellipsoidal mirror has its two foci separated by 2 inches and located on the major axis. A blackbody source was located at one focus while the tray clamp samples were located at the conjugate focus. The blackbody radiation was modulated and then focused by the ellipsoid onto the tray clamps. Radiation reflected from the tray clamp was sampled by the interferometer by viewing through a hole in the ellipsoid. A gold mirror (reflectance approximately 98 percent) was used as the reference surface.
Wood, Bobby E.↗
A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 2: Nonaxisymmetric form
We have previously introduced the parameter alpha as an indicator of stability to m = 2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous (alpha less than or approximately equal to 0.34) and stellar (alpha less than or approximately equal to 0.25) systems. This parameter can be written as alpha = (ft/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total rotational kinetic energy, W is the total gravitational potential energy, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. In this paper, we extend the stability criterion to nonaxisymmetric equilibrium systems by determining empirically the appropriate form of the function f for ellipsoids and elliptical disks and cylinders. We test the validity of this extension of the stability indicator alpha by considering its predictions for previously published, gaseous and stellar, nonaxisymmetric models. The formulation and critical values account accurately for the stability properties of m =2 modes in gaseous Riemann S-type ellipsoids (including the Jacobi and Dedekind ellipsoids) and elliptical Riemann disks as well as in stellar elliptical Freeman disks and cylinders: all these systems are dynamically stable except the stellar elliptical Freeman disks that exhibit a relatively small region of m = 2 dynamical instability. A partial disagreement in the case of stellar Freeman ellipsoids in maximum rotation may be due to the fact that the region of instability has not been previously determined with sufficient accuracy.
Christodoulou, Dimitris M.↗
Map Projection Induced Variations in Locations of Polygon Geofence Edges
This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.
Neeley, Paula↗
Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere
An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.
Weather↗
Estimates of the moon's geometry using lunar orbiter imagery and Apollo laser altimeter data
Selenographic coordinates for about 6000 lunar points identified on the Lunar Orbiter photographs are tabulated and have been combined with those lunar radii derived from the Apollo 15 laser altimeter data. These coordinates were used to derive that triaxial ellipsoid which best fits the moon's irregular surface. Fits were obtaind for different constraints on both the axial orientations and the displacement of the center of the ellipsoid. The semiaxes for the unconstrained ellipsoid were a = 1737.6 km, b = 1735.6 km, and c = 1735.0 km which correspond to a mean radius of about 1736.1 km. These axes were found to be nearly parallel to the moon's principal axes of inertia, and the origin was displaced about 2.0 km from the moon's center of gravity in a direction away from the earth and to the south of the lunar equator.
Jones, R. L.↗
Contributions of satellite-determined gravity results in geodesy
Different forms of the theoretical gravity formula are summarized and methods of standardization of gravity anomalies obtained from satellite gravity and terrestrial gravity data are discussed in the context of three most commonly used reference figures, e.g., International Reference Ellipsoid, Reference Ellipsoid 1967, and Equilibrium Reference Ellipsoid. These methods are important in the comparison and combination of satellite gravity and gravimetric data as well as the integration of surface gravity data, collected with different objectives, in a single reference system. For ready reference, tables for such reductions are computed. Nature of the satellite gravity anomalies is examined to aid the geophysical and geodetic interpretation of these anomalies in terms of the tectonic features of the earth and the structure of the earth's crust and mantle. Computation of the Potsdam correction from satellite-determined geopotential is reviewed. The contribution of the satellite gravity results in decomposing the total observed gravity anomaly into components of geophysical interest is discussed. Recent work on the possible temporal variations in the geogravity field is briefly reviewed.
Khan, M. A.↗
Feasibility study of modern airships, phase 1. Volume 2: Parametric analysis (task 3)
Various types of lighter-than-air vehicles from fully buoyant to semibuoyant hybrids were examined. Geometries were optimized for gross lifting capabilities for ellipsoidal airships, modified delta planform lifting bodies, and a short-haul, heavy-lift vehicle concept. It is indicated that: (1) neutrally buoyant airships employing a conservative update of materials and propulsion technology provide significant improvements in productivity; (2) propulsive lift for VTOL and aerodynamic lift for cruise significantly improve the productivity of low to medium gross weight ellipsoidal airships; and (3) the short-haul, heavy-lift vehicle, consisting of a simple combination of an ellipsoidal airship hull and existing helicopter componentry, provides significant potential for low-cost, near-term applications for ultra-heavy lift missions.
Lancaster, J. W.↗
Triaxial degenerate dwarfs and pulsing X-ray sources
It is shown that triaxial configurations for rotating degenerate dwarfs consisting entirely of fluid are not limited to forms analogous to the Jacobi ellipsoids. Arguments are presented which rule out only the specialized class of uniformly rotating analogs of the Jacobi ellipsoid for some degenerate dwarfs. Several ways of forming triaxial degenerate dwarfs are examined along with the characteristic lifetimes of such objects. Noting that some of the alternative forms may exist in mass-transfer binary systems, consideration is given to the secondaries in Her X-1 and Cen X-3. It is suggested that the secondary in Her X-1 must be close to an analog of a Dedekind ellipsoid, and plausible triaxial white-dwarf configurations are proposed for the secondary in Cen X-3.
Durisen, R. H.↗
Effects of probe shape change on flow phenomena during Jovian entry
The effects of probe shape change on the flow phenomena around a Jovian entry body is investigated. The initial body shapes considered are: 45-degree sphere cone, 35-degree hyperboloid, and 45-degree ellipsoid. The radiating shock-layer flow is assumed to be axisymmetric, inviscid, and in chemical and local thermodynamic equilibrium. The radiative transfer is calculated with an existing nongray radiation model that accounts for molecular band, atomic line, and continuum transitions. The results indicate that the shock-standoff distance, shock temperature and density, wall pressure distribution and radiative heating to the body are influenced significantly because of the probe shape change. The effect of shape change on radiative heating of the afterbody was considerably larger for the sphere cone and ellipsoid than for the hyperboloid. For the peak heating conditions, the net radiative heating to the body was found to be highest for the ellipsoid
Tiwari, S. N.↗