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At least 91 records · Page 5

The oblateness of Uranus at the 1-microbar level

Atmospheric occultation half-light times and scale heights, together with updated ring-orbit model parameters, are presently used to ascertain the planetary limb shape and thereby derive the radius and oblateness of Uranus at the 1-microbar level from stellar occultation observations obtained on March 10, 1977, and March 23, 1983. Assuming that the planet is in hydrostatic equilibrium, the inferred rotation period is 17.7 + or - 0.6 hr in the -30 to +26 deg latitude range of these observations. These results are noted to be consistent with those based by Lindal et al. (1987) on Voyager 2 observations, where the period at 5 deg latitude is of the order of 18.0 + or - 0.3 hr.

Baron, Richard L.

Dynamical instabilities in axisymmetric stellar systems. I - Oblate E6 models

The stability of a set of models based on isothermal oblate E6 elliptical galaxies is studied using N-body techniques. The only stable models are those that are near the isotropic model and have nearly equal number of stars in retrograde and prograde orbits. Fast rotators are unstable to modes that appear to be analogous to the classical streaming instability seen in many disk systems. Systems with a large velocity dispersion in the direction of the cylindrical radius are unstable to modes that appear to be similar to the radial orbit instability observed in some spherical systems. However, evidence is presented that these two instabilities may be related, and an instability criterion that applies to both is constructed.

Levison, Harold F.

The settling of warped disks in oblate dark halos

When a galaxy forms, the disk may initially be tilted with respect to a flattened dark halo. The misalignment between the disk and the halo is a common explanation for galactic disk warps, since in this state disks have precessing bending modes which resemble real warps. The gravitational response of the halo has often been ignored, and its strength and effect on possible bending modes is unknown. We therefore calculate the response of an oblate halo to a precessing inclined exponential disk using a variety of techniques. We construct models with a rigid exponential disk precessing in a particle halo, a particle disk precessing inside a static bulge/halo potential, and a self-consistent model with a particle disk, bulge, and halo. When the disk: halo mass ratio is small (approximately 10%) within 5 exponential scale radii, the disk settles to the equatorial plane of the halo within five orbital times. When the disk and halo mass are comparable, the halo rapidly aligns with the disk within a few orbital times, while the disk inclination drops. The rapid response of the halo to an inclined precessing disk suggests that the warps seen in galactic disks are not due to a misalignment between the disk and the inner halo. If a galaxy forms inclined to the principal plane of a dark halo, either the disk will settle to a pricipal plane or the inner halo will twist to align with the disk. The outer halo will remain misaligned for a much longer time and therefore may still exert a torque. Warped bending modes may still exist if the misalignment of the outer halo persists for a Hubble time.

Dubinski, John

An Experimental Investigation of the Damping of Liquid Oscillations in an Oblate Spheroidal Tank With and Without Baffles

An experimental investigation was conducted to determine the damping of the fundamental antisymmetric mode of oscillation of liquids contained in an oblate spheroidal tank. The decay of the fundamental mode was studied for a range of liquid depths in tanks with and without baffles. In the investigation of baffle effects, ring and cruciform baffles of various sizes were fixed at different locations within the tank. Data presented show the variation of the damping factor with tank fullness and with baffle type, width, location, and orientation as well as the effects of the amplitude of the liquid oscillations and of small variations in the liquid kinematic viscosity on the damping factor. The results of the investigation indicate that the addition of ring baffles to the tank results in an increase in the available effective damping when the baffle plane is in a region near the equilibrium liquid surface, and that cruciform baffles are effective in the damping of the fundamental mode in the near-empty tank. No apparent changes in damping for the tanks having ring baffles were observed as the kinematic viscosity of the liquid was varied over a small range.

Stephens, David G.

Time of Arrival Retrievals on an Oblate Spheroidal Earth

The current National Lightning Detection Network (NLDN) retrieval algorithm is based on a chi sq minimization. This numerical approach finds the lightning ground strike location on an ellipsoidal Earth that optimally agrees with multiple station time of arrival (TOA) measurements and, if available, magnetic bearing data. In addition, an analytic solution for determining lightning ground strike locations on a spherical Earth using only TOA data has been recently introduced. In the current work, a quasi-analytic approach is suggested for determining lightning ground strike locations on an oblate spheroidal Earth by perturbing the spherical model results proposed by Koshak. Latitude, longitude, time, and the associated perturbed quantities are related through terms in a Taylor series. The correction terms may be considered collectively as a vector which may be calculated by an overconstrained inversion. Expressions for the derivatives contained in the Taylor series are given in terms of elliptic integrals.

Solakiewicz, Richard J.

Time-of-Arrival Lightning Location Retrieval Using an Oblate Spheroidal Earth Model

The problem of retrieving lightning ground strike location on an oblate spheroidal Earth using a network of 4 or more time-of-arrival sensors is considered. A recently developed analytic method for obtaining such retrievals on a spherical Earth surface is perturbed resulting in an iterative procedure to get correction terms. The perturbation procedure consists of applying a vector Newton's method to eqs. relating the distances from the lightning location to each sensor along a geodesic and the times of arrival of the wave produced by the lightning source at each sensor.

Solakiewicz, Richard

Improved Earth Oblateness Rate Reveals Increased Ice Sheet Losses and Mass-Driven Sea Level Rise

Satellite laser ranging (SLR) observations are routinely applied toward the estimation of dynamic oblateness, C(sub 20), which is the largest globally integrated component of Earth's time-variable gravity field. Since 2002, GRACE and GRACE Follow-On have revolutionized the recovery of higher spatial resolution features of global time-variable gravity, with SLR continuing to provide the most reliable estimates of C (sub 20).We quantify the effect of various SLR processing strategies on estimating C(sub 20) and demonstrate better signal recovery with the inclusion of GRACE-derived low-degree gravity information in the forward model. This improved SLR product modifies the Antarctic and Greenland Ice Sheet mass trends by -15.4 and -3.5 Gt/year, respectively, as compared to CSR TN11, and improves global mean sea level budget closure by modifying sea level rise by +0.08 mm/year. We recommend that this new C(sub 20) product be applied to RL06 GRACE data products for enhanced accuracy and scientific interpretation.

Loomis, B. D.

Scattering By Relatively Small Oblate Spheroidal Drops of Water in the Rainbow Region: T-Matrix Results and Geometric Interpretation

Late in 1999 Michael Mishchenko carried out T-matrix calculations of light scattered by oblate spheroidal drops of water at Marston's request. The purpose of the investigation was to determine if the caustic features, known by that time to be visible in the far-field scattering near the primary rainbow region for horizontally illuminated relatively large drops, would also be present in T-matrix calculations of the scattering by small drops. The axis of rotational symmetry of the drop was taken to be vertical, and the illumination was taken to be horizontal. Scattering into the relevant angular region was evaluated for drop aspect ratios D/H = 1, 1.23, 1.311, and 1.37 where D denotes the equatorial diameter and H the vertical diameter. The results are limited to polarized monochromatic illumination with ka = 140 where a = D/2 and k = 2π/λ with λ being the wavelength of the illumination. As expected from geometrical analysis, a horizontal “V” shaped caustic is visible for D/H = 1.311. The T-matrix results, gray-tone intensity displays provided by Mishchenko, remain instructive.

Scattering by spheroids

Noncoplanar minimum delta V two-impulse and three-impulse orbital transfer from a regressing oblate earth assembly parking ellipse onto a flyby trans-Mars asymptotic velocity vector.

Comparison of two-impulse and three-impulse orbital transfer, using data from a 63-case numerical study. For each case investigated for which coplanarity of the regressing assembly parking ellipse was attained with the target asymptotic velocity vector, a two-impulse maneuver (or a one-impulse equivalent) was found for which the velocity expenditure was within 1% of a reference absolute minimum lower bound. Therefore, for the coplanar cases, use of a minimum delta-V three-impulse maneuver afforded scant improvement in velocity penalty. However, as the noncoplanarity of the parking ellipse and the target asymptotic velocity vector increased, there was a significant increase in the superiority of minimum delta-V three-impulse maneuvers for slowing the growth of velocity expenditure. It is concluded that a multiple-impulse maneuver should be contemplated if nonnominal launch conditions could occur.

Bean, W. C.

An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

Mueller, A. C.

Graphical measurement of Saturn's oblateness and the radius of the Encke gap

The geometric distortions attendant to spin-scan imaging were extraordinarily manifest in the Pioneer encounter with Saturn. By overlapping graphical predictions of these distortions with raster scans of the raw intensity data, both displayed to the same scale on a Versatec printer-plotter, it is possible to determine the precise geometry of a data-taking sequence. The predictions are quite sensitive to the assumed dimensions of Saturn and its rings. It is accordingly concluded that the ratio of polar to equatorial radius is 0.91 and that the Encke gap is 133,500 km from Saturn's center.

Burke, J. J.