Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Spherical harmonic method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Patched Local Lunar Gravity Solutions using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into twelve regions and two polar caps, with a resolution of 0.15˚ x 0.15˚ (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Sander Goossens↗
NASA NTRS1998

Modelling and Estimation of Dynamic Ocean Topography Within Global Geopotential Solutions

In this poster, we will present a report on the ongoing investigation "Improved Gravitational and Dynamic Height Models Through the use of Oceanographic Data." we have used a two year mean (1993-1994) of the Dynamic ocean Topography (DOT) field implied by the Semtner and Chervin POCM_4B model, and developed normal equations in surface spherical harmonics to degree and order 30. These normal equations, were combined with normal equations derived from TOPEX and ERS-1 altimeter data over the same time period. Combination solutions (based on satellite tracking data, altimeter data, surface gravity data and OCM data) were were developed Test solutions were obtained estimating the DOT field to 2Ox2O and 3ox3O. These solutions were tested with independent DOT values computed over 38 WOCE hydrographic sections, which contained a total of 3072 stations and represented 216000 km of travelled lines. The weighted standard deviation of the differences between the DOT obtained from the hydrographic data and and the field estimated from the joint combination solutions was computed for each of the test models, the weighted standard deviation for the baseline combination solution excluding the POCM4_B data was 9.7 cm for a DOT solution to 30x30, where introducing the POCM4_B data into the combination model reduced the standard deviation to 9.2 cm, indicating the the introduction of oceanographic information benefits the solution for the dynamic ocean topography. We will discuss the weighting schemes applied and the method of solution. Another aspect of our investigation involves testing alternate parametric representations of the dynamic height field. We looked at the alternative representations in terms of the Proudman functions (PF), and compared these to the use of spherical harmonics (SH) to represent the dynamic ocean topography, using once again the 1993 and 1994 output of the POCM4_B OCM as the reference model. A significant advantage of PF's over SH's is that the former require no "fill-in" values over areas where the DOT is undefined. We show that the PF and SH results using equal number of parameters agree quite well in overall content. In addition, PFs appear better suited for representation of high frequency signals close to the signal boundary. The development of the PF solutions for the DOT will be described and the statistics of the comparisons will be presented.

Lemoine, Frank G.↗
NASA NTRS1976

Automatic noise limiter-blanker

A blanker system that may be used with audio noise limiters or automatic noise limiters was described. The system employs a pair of silicon diodes and two RC filters connected across the feedback impedance of an operational amplifier so as to counteract impulse noise interference caused by local spherics activity or 60 Hz harmonics radiated from ac motor control systems. The following information is given: circuit diagram and description, operating details, evaluation, discussion of other noise blanking methods.

Burhans, R. W.↗
NASA NTRS1989

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, F. J.↗
NASA NTRS2006

Repeat Ground Track Lunar Orbits in the Full-Potential Plus Third-Body Problem

A high degree and order Lunar gravitational field is superimposed on the Earth-Moon Restricted Three Body model to capture the dominating forces on a spacecraft in the vicinity of the Moon. For the synchronously rotating Moon, periodic orbits in this model map repeat ground tracks and represent higher order solutions to the frozen orbit problem. The near-circular, stable or near-stable solutions are found over a wide range of defining characteristics making them suitable for long-lifetime parking applications such as science orbits, crew exploration vehicle parking orbits, and global coverage constellation orbits. A full ephemeris is considered for selected orbits to evaluate the validity of the time-invariant, simplified model. Of the most promising results are the low-altitude families of near-circular, inclined orbits that maintain long-term stability despite the highly non-spherical Lunar gravity. The method is systematic and enables rapid design and analysis of long-life orbits around any tidally-locked celestial body with an arbitrarily high degree and order spherical harmonic gravity field. .

periodic↗
NASA NTRS1976

Structure of the atmosphere of Jupiter from Pioneer 10 and 11 radio occultation measurements

A technique for incorporating effects of the oblateness of Jupiter's atmosphere into the data analysis procedure for radio-occultation measurements is described which makes use of a spherical harmonic representation of the gravity field to compute the shape of the planet. With this technique, the center of refraction is located by the radius of curvature and the normal direction at the closest approach point of the ray. The present technique, a subsequent approximation involving the use of a constant center of refraction, and the Abel integral transform inversion method for spherical planets are applied to Pioneer 10 and 11 data. All the intermediate results obtained show a temperature inversion between 10 and 100 mb, with temperatures from 130 to 170 K at 10 mb and from 80 to 120 K at 100 mb. Comparison of the radio-occultation profiles with radiative-convective equilibrium models and the temperature profile based on Pioneer 10 IR radiometer data indicates good agreement between the models and the occultation results.

Kliore, A. J.↗
NASA NTRS1992

Incorporation of a priori gravity field information in satellite orbit determination using bin parameters

A method to determine satellite orbits using tracking data and a priori gravitational field is described. The a priori constraint on the orbit dynamics is determined by the covariance matrix of the spherical harmonic coefficients for the gravity model, so that the optimal combination of the measurements and gravitational field is achieved. A set of bin parameters is introduced to represent the perturbation of the gravitational field on the position of the satellite orbit. The covariance matrix of a conventional gravity model is transformed into that for the bin parameters by the variational partial derivatives. The covariance matrices of the bin parameters and the epoch state are combined to form the covariance matrix of the satellite positions at the measurement times. The combined matrix is used as the a priori information to estimate the satellite positions with measurements.

Wu, Jiun-Tsong↗
NASA NTRS2012

Improved Maneuver Reconstructions for the GRAIL Orbiters

Maneuver reconstructions for the Gravity Recovery and Interior Laboratory (GRAIL) A and B lunar orbiters were improved through updates to the orbit determination filter and dynamic models. Consistent reconstructions of the 27 GRAIL A and B maneuvers from the Trans-Lunar Cruise phase in the fall of 2011 through the Transition to Science Formation phase in February 2012 were performed. Standard methods of orbit determination were applied incorporating the latest dynamic models and filter strategies developed by the GRAIL Navigation and Science Teams, including a high resolution, 420 x 420 degree and order lunar spherical harmonic gravity field model. For Trans-Lunar Cruise for GRAIL-A (TLC-A), all maneuvers executed with delta V errors below 5.50 +/- 0.50 mm/s and pointing errors below 0.25 degrees. GRAIL-A lunar orbit maneuvers had delta V errors below 30.0 mm/s and pointing errors below 0.51 degrees. For TLC-B, all maneuvers executed with delta V errors below 8.60 +/- 1.41 mm/s and pointing errors below 0.300 degrees. GRAIL-B maneuvers in lunar orbit executed with maximum delta V errors of 25.0 mm/s and pointing error of 0.43 degrees. These maneuver reconstructions will enable the GRAIL Navigation Team to better characterize the main engine performance of each spacecraft. This will help the Navigation Team to navigate low (greater than 8 km) altitude orbits during the extended mission phase in the fall of 2012.

lunar mapping↗
NASA NTRS1983

Variational global analysis of satellite temperature soundings

A variational spherical harmonic analysis is developed for the production of global geopotential height and geostropic wind fields from the TIROS-N spacecraft's temperature sounding profiles. This scheme is based on Tykhonov's (1964) regularization method, and the smoothing parameter is determined by cross validation. The scheme is noted to be stable and computationally efficient, and it does not depend on a priori information. Its applications to three-dimensional temperature retrievals and to four-dimensional spectral analyses are illustrated.

Halem, M.↗
NASA NTRS1985

Second-order Compton-Getting effect on arbitrary intensity distribution

Theoretical studies of energetic particles in space are often referred to a special frame of reference. To compare theory with experiment, one has to transform the particle distribution from the special frame to the observer's frame, or vice versa. Various methods have been derived to obtain the directional distribution in the comoving frame from the directional fluxes measured on a spacecraft. These methods have become progressively complicated as increasingly detailed directional particle data become available. A set of 2nd order correct formulae for the transformation of an arbitrary differential intensity distribution, expressed as a series of spherical harmonics, between any two frames in constant relative motion is presented. These formulae greatly simplify the complicated procedures currently in use for the determination of the differential intensity distribution in a comoving frame.

Ng, C. K.↗
NASA NTRS1987

Equipotential transformation of multipole systems to dipole systems

The vector sum of fields produced by a set of magnetic dipoles with different magnetic moments that are both tilted from the planetary spin axis and offset from the planetary center by different amounts can be used to completely represent a planetary magnetic field in the conventional form of spherical harmonic expansion. The scalar equipotential transformation analytically results in 24 equations that may subsequently be solved for the 24 adjustable parameters in dipole systems with the predetermined main dipole. Attention is given to this method's application to the Jovian magnetic field.

Wang, W. X.↗
NASA NTRS2012

Prediction of BVI Noise for an Active Twist Rotor Using a Loosely Coupled CFD/CSD Method and Comparison to Experimental Data

Numerical predictions of the acoustic characteristics of an Active Twist Rotor (ATR), using two methods to compute the rotor blade aerodynamics and elastic blade motion are compared to experimental data from a wind tunnel test in the NASA Langley Transonic Dynamics Tunnel (TDT) in 2000. The first method, a loosely coupled iterative method, utilizes the Computational Fluid Dynamics (CFD) code OVERFLOW 2 and the Computational Structural Dynamics (CSD) code CAMRAD II. The second method utilizes the CAMRAD II free-wake model only. The harmonic active-twist control to the main rotor blade system is identified with three parameters - harmonic actuation frequency, actuation amplitude, and control phase angle. The resulting aerodynamics and blade motion data from the two methods are then used in the acoustics code PSU-WOPWOP to predict acoustic pressure on a spherical array of equally spaced observers surrounding the rotor. This spherical distribution of pressure is used to compute the sound power level representing baseline and actuated conditions. Sound power levels for three categories of noise are defined as - blade-vortex interaction sound power level (BVIPWL), low frequency sound power level (LFPWL), and overall sound power level, OAPWL. Comparisons with measured data indicate the CFD/CSD analysis successfully captures the trends in sound power levels and the effects of active-twist control at advance ratios of 0.14 and 0.17. The free-wake model predictions show inconsistent sound power levels relative to the trends in the experimental and CFD data. This paper presents the first ever comparison between CFD/CSD acoustic predictions for an active-twist rotor and experimental measurements.

Fogarty, David E.↗
NASA NTRS1975

Downward continuation of gravity information from satellite to satellite tracking or satellite gradiometry in local areas

Integral formulas in the parameter domain are used instead of a representation by spherical harmonics. The neglected regions will cause a truncation error. The application of the discrete form of the integral equations connecting the satellite observations with surface gravity anomalies is discussed in comparison with the least squares prediction method. One critical point of downward continuation is the proper choice of the boundary surface. Practical feasibilities are in conflict with theoretical considerations. The properties of different approaches for this question are analyzed.

Rummel, R.↗
NASA NTRS1979

The magnetic field of Mercury

Data from Mariner 10 observations of Mercury indicate that there exists an intrinsic magnetic field of the planet, sufficiently strong at present to deflect the solar wind flow around the planet and to form a detached bow shock wave in the super Alfvenic solar wind. Four methods used to analyze the magnetic field data and derive quantitative values for the description of the planetary field include (1) comparison of bow shock and magnetopause relative positions at Mercury to those at Earth; (2) direct spherical harmonic analysis of the data; (3) modeling of the magnetosphere by an image dipole and infinite 2-D current sheet in addition to the planetary field; and (4) scaling of a mathematical model for the terrestrial magnetosphere. The results obtained yield dipole moments ranging from 2.4 to 5.1x10 to the 22d power, with the lower values associated cw cm with certain models using partial quadrupole and octupole terms to improve the least squares fitting of models to observations.

Ness, N. F.↗
NASA NTRS1980

Protostellar formation in rotating interstellar clouds. I - Numerical methods and tests

Attention is given to numerical methods and tests of a series of gravitational hydrodynamics computer codes constructed in order to numerically follow the dynamic collapse of spherically symmetric (1-D), axisymmetric (2-D), and non-axisymmetric (3-D) isothermal interstellar clouds. A spherical harmonic expansion is used to solve the Poisson equation for the gravitational potential. It is shown that the use of explicit donor-cell hydrodynamics on a moving spherical coordinate grid ensures mass and momentum conservation and allows the grid to follow the collapse of the fluid. Finally, the performance of the codes is examined.

Boss, A. P.↗
NASA NTRS1983

On determining the large-scale ocean circulation from satellite altimetry

It is contended that a spherical harmonic expansion of the difference between the altimeter-derived mean sea surface and the geoid estimate should reveal the large-scale circulation of the ocean surface layer when the low-degree terms are examined. Methods based on this principle are proposed and partially demonstrated over the Pacific Ocean with the aid of the mean sea surface derived from the Seasat altimeter and the Goddard Earth Model 9 earth gravity model. The preliminary results reveal a well-defined clockwise gyre in the North Pacific and a much less well defined counterclockwise gyre in the South Pacific. When the dynamic topography thus obtained is compared with Wyrtki's (1975) dynamic topography derived from hydrographic data, the agreement is found to be within the limit of geoid uncertainties and satellite orbital errors.

Tai, C.-K.↗
NASA NTRS1993

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Hahne, G. E.↗
NASA NTRS1989

Radial deformation of the earth by oceanic tidal loading

A high-degree spherical harmonic series is used to compute the radial deformation of the Earth by oceanic tidal loading. By exploiting fast numerical transforms, this approach is found to be much more efficient, but no less accurate, than the traditional Green's function approach. The method is used to derive an atlas of load tide maps for 10 constitutents of the NSWC ocean tide model.

Ray, R. D.↗