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Gravity anomalies and linear transforms over rotating spheres treated as random process with spectrum analysis and applications for geodesy
Analysis of the Dyson Sphere, an extremely advanced civilization's hypothetical construct entirely surrounding a star, shows that new stress inward to the star increases to maxima at the poles if the sphere is rotating. This is because the centrifugal force in the rotating frame of reference vanishes at zero rotational radius, which occurs at the poles. There is less of the centrifugal force at high latitudes than low to offset the star's gravity. A form is derived for a thin, rigid, rotating shell, surrounding a large pointlike mass and/or charge, which will experience the least possible net stress at every point upon it - a shape on which every point not on the shell's equator is as near as possible to being in orbit. In orbit, whose plane passes through the primary body's center of mass or of charge, F(grav), or Fg, is exactly opposite in direction to F(centrif), or Fc, and is equal in amount. At all points not on the equator, Fc will not entirely offset Fg, because of Fg's vector decomposition. However, both forces are always constrained to be equal in absolute amount everywhere on the shell, equator included. The derived shape, given by the figure of revolution around the x-axis of x = square root (y-1-72), will prove useful in large-scale space construction. Also, various engineering problems are discussed.
A proposed instrument for measuring a static electric field would be based partly on a conventional rotating-split-cylinder or rotating-split-sphere electric-field mill. However, the design of the proposed instrument would overcome the difficulty, encountered in conventional rotational field mills, of transferring measurement signals and power via either electrical or fiber-optic rotary couplings that must be aligned and installed in conjunction with rotary bearings. Instead of being made to rotate in one direction at a steady speed as in a conventional rotational field mill, a split-cylinder or split-sphere electrode assembly in the proposed instrument would be set into rotational vibration like that of a metronome. The rotational vibration, synchronized with appropriate rapid electronic switching of electrical connections between electric-current-measuring circuitry and the split-cylinder or split-sphere electrodes, would result in an electrical measurement effect equivalent to that of a conventional rotational field mill. A version of the proposed instrument is described.
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.
Flow field around and drag on sphere rising axially through rotating viscous fluid
The behavior of a single gas bubble inside a rotating liquid-filled sphere has been investigated analytically and experimentally as part of ground-based investigations aimed at aiding in the design and interpretation of Shuttle experiments. In the analysis, a quasi-static description of the motion of a bubble was developed in the limit of small values of the Taylor number. A series of rotation experiments using air bubbles and silicone oils were designed to match the conditions specified in the analysis, i.e., the bubble size, sphere rotation rate, and liquid kinematic viscosity were chosen such that the Taylor number was much less than unity. The analytical description predicts the bubble velocity and its asymptotic location. It is shown that the asymptotic position is removed from the axis of rotation.
NASA’s Multi-Angle Imager for Aerosols (MAIA) mission, under development at the Jet Propulsion Laboratory, is designed to study the adverse health effects of different types of particulate air pollution. Planned for launch in 2023 for a 3-year mission, the MAIA satellite instrument will focus on a selected set of metropolitan target areas, where air quality monitors and health data are available. Aerosol concentration and speciation are inferred from multi-angle measurements of backscattered sunlight in 14 spectral bands from 350-2200 nm, with bands near 442, 645 and 1040 nm measuring the degree (DoLP) and angle of linear polarization (AoLP) in addition to radiance. The pushbroom camera has a ~240-km cross-track field of view with a nadir resolution of ~200 m, and is mounted onto a biaxial gimbal to provide along-track view angles within ±60°, to extend the field of regard to ±48°, and to view the instrument’s onboard calibrator (OBC) and dark target. The OBC consists of a sunlit transmissive diffuser, followed by 12 polarizers at different orientations. MAIA’s polarimetry is implemented using miniature wire grid polarizers on the focal plane array, and dual photoelastic modulators (PEMs) and achromatic quarter-wave plates to rapidly rotate the polarization. The resulting ~26-Hz intensity modulation encodes the linearly polarized and total radiance in each pixel, leaving the DoLP and AoLP insensitive to gain calibration. We report on the polarimetric calibration of the MAIA camera using a vacuum-compatible polarization state generator, consisting of a 1600W Xenon lamp, 12-inch integrating sphere, and rotating high-extinction polarizer. Mueller-matrix-based calibration coefficients for each detector pixel are derived from measurements at multiple polarizer angles, and are used to correct the measurements for instrumental polarization aberrations. Prior to flight, the calibrated MAIA camera is panned across the OBC to characterize its output, using uniform illumination with an irradiance similar to the Sun.
Abstract not provided.
Rotational, precessional and nutational motion of body entering Mars atmosphere in vertical and oblique directions
Aerodynamic torque on spinning spherical satellite
A new technique is reported for calculating the entire flow field on spherically blunted cones at high angles of attack and high laminar Reynolds numbers. An approximate system of parabolic equations obtained from the steady Navier-Stokes equations by assuming the viscous, streamwise derivative terms are small compared to the viscous normal and circumferential derivatives is the basis of the calculations. These equations are valid for both the inviscid and viscous regions, including the circumferential separation zone that develops on the leeward side at high angles of attack. Two different methods are used to obtain the initial conditions for these equations at the sphere cone tangency plane. For small nose Reynolds numbers, an axisymmetric merged layer solution around a sphere is rotated to provide a three-dimensional initial plane of data. For large nose Reynolds numbers, the nose region is solved using an inviscid, three dimensional time dependent solution combined with a boundary layer solution for the viscous flow. The computed flowfield including the leeward separation region is described and compared with data for a 7 deg half angle cone at 10 deg angle of attack, and a blunt 15 deg half angle cone at 15 deg angle of attack.
Completed and ongoing research activities are discussed briefly, including a three-dimensional, linear stability analysis of the baroclinic Hadley cell and a numerical model of the baroclinic flow between two rotating concentric spheres. This model simulates axisymmetric flow in the Atmospheric General Circulation Experiment configuration. A computer code designed to solve the strongly nonlinear stability problem for the Eady basic state is mentioned.
Emission (2 cm) from 15 Eunomia was detected on March 27, 1983, using the VLA. At this time, 15 Eunomia was 2.0 AU distant from earth. A flux density of 687 + or - 70 micro-Jy was measured at 14.96 GHz (50-MHz bandwidth). If 246 km is adopted for the diameter, a disk temperature of 184 + or - 20 K results. This is consistent with a rapidly rotating, black sphere with 15 Eunomia's diameter and distance (171 K).
In the theory of hydrostatic quasi-geostrophic flow in the Earth's atmosphere the principal results do not depend on the eddy viscosity. This contrasts with published theories of convection in deep rotating fluid spheres, where the wavelength of the fastest growing disturbance varies as E sup 1/3, where E, the Ekman number, is proportional to the eddy viscosity. A new theory of quasi-columnar motions in stably stratified fluid spheres attempts to capture the luck of the meteorologists. The theory allows one to investigate the stability of barotropic and baroclinic zonal flows that extend into the planetary interior. It is hypothesized that the internal heat Jupiter and Saturn comes out not radially but on sloping surfaces defined by the internal entropy distribution. To test the hypothesis one searches for basic states in which the wavelength of the fastest-growing disturbance remains finite as E tends to zero, and is which the heat flux vector is radially outward and poleward.
The migration of bubbles or drops in a rotating liquid-filled sphere was observed under a variety of experimental conditions, and the trajectory, final equilibrium position, and shape were compared with results of analysis. It was found that small migrating bubbles or drops were spherical and, under the quasi-steady conditions employed, behaved in a predictable manner. Large migrating bubbles were nonspherical yet still behaved predictably except when close to the sphere wall. At low rotation rates, the final equilibrium position was offset from the rotation axis and stationary in the rotating liquid relative to a laboratory (inertial) reference frame. One of the bubble migration experiments was accomplished in the near-free-fall environment provided by the NASA KC-135 flight program. At higher rotation rates and under zero gravity conditions where the rotation axis is the final equilibrium position, the shape was reasonably predictable.
Proposed built-in sunshade enables large-aperture reflecting telescope to view laser transmitter apparently close to Sun, without adding excessive size or mass to telescope. Telescope looks through sunshade from behind and below. Tops of hexagonal tubes trimmed to spherical shape corresponding to sphere of rotation of telescope. Sunshade supports secondary reflector. Discerns signals from sources only 12 degrees from line of sight to Sun. Sunshade equipped with internal vanes running lengths of tubes receives signals from sources within 6 degree or even 3 degree of apparent position of Sun.
A new technique to simulate Taylor vortices in a spherical gap between a rotating inner sphere and a stationary outer one has been developed and tested. Paths leading to zero-, one-, and two-vortex flows are designed heuristically. Fictitious symmetric boundaries near the equator are imposed, and the choice of the location of the fictitious boundaries is determined by either one- or two-vortex flow being stimulated. The imposition of one or two fictitious boundaries during the initial calculation generates the state suitable for one-or two-vortex flow to exist. After removing the fictitious boundaries, the flow settles down into its own attractor. Using this method, the three steady flow modes can be simulated by using a half domain. The technique can converge to desired flows very fast, and its results show excellent agreement with experimental ones.