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NASA NTRS1989

Axisymmetric bubble profiles in a slowly rotating helium dewar under low and microgravity environments

The Gravity Probe-B (GP-B) Spacecraft is designed to test the General Theory of Relativity through long-term monitoring the precession of a set of gyros in free-fall around the earth. The potential problems for GP-B Spacecraft design requirements could be due to asymmetry in the static liquid helium distribution, or to perturbations in free surface which is present in the partially-filled liquid helium dewar. In this study, doughnut-shaped helium bubble equilibrium profiles in rotating dewar, under the conditions during the period of GP-B experiment instrument calibration and also during the period of normal operation stages of GP-B Spacecraft, have been numerically calculated. For academic interest, the range of coverage has been extended beyond the conditions assigned by the GP-B Spacecraft experiment.

Hung, R. J.↗

NASA NTRS1993

SCATHA mission termination report

The SCATHA (Spacecraft Charging at High Altitudes) satellite was operated from the Consolidated Space Test Center in Sunnyvale, California from February 1979 to May 1991. It was a spin stabilized vehicle in a highly eccentric orbit that collected data on spacecraft charging. The purpose of such data gathering was to predict and/or model the effects of the Earth's magnetic field on synchronous and near synchronous satellites. During the majority of its lifetime, attitude precession maneuvers were done every 10-15 days to maintain solar panel orientation. Maneuver planning was difficult due to the structural characteristics of SCATHA. It is cylindrically shaped and has seven booms ranging in length from 2 to 50 meters. These precession maneuvers induced predictable nutation that damped out after a few days. Eventually fuel began running low due to these frequent maneuvers. Experiments that had required the spin axis be in the orbit plane had already been turned off or had collected all their data. To increase the vehicle lifetime, the spin axis was moved to ecliptic normal. While this stopped the need for frequent attitude maneuvering (only two per year required now), this movement of the spin axis caused nutation that would not damp out for the remainder of the mission. This phase of the mission, with the ecliptic normal orientation, lasted for approximately three years. Although nutation never damped, data gathering was uninterrupted. In late 1990, when SCATHA's transmitter became seriously degraded, the Air Force decided to turn SCATHA off. This would only be done after the satellite was made 'safe'. The most difficult part of making the vehicle safe was quickly purging the fuel. Several plans were considered. The selected plan was to perform a series of 20 degree attitude precession maneuvers (3 days apart to allow for the worst nutation to damp) until the fuel was depleted. Although this sounded simple, the actual execution proved difficult. This was due to a nearly complete lack of available telemetry data, large undamped motion of the long booms, inadequacies in attitude determination software, and an error in the fuel level calculation software. This paper discusses the various proposed termination plans and execution of the selected one. Attitude determination methodologies, nutation from maneuvers, and effects of the flexible booms on the termination mission are presented and analyzed from a satellite analyst point of view.

Stakkestad, Kjell↗

NASA NTRS1994

Imaging the effect of dipole tilt on magetotail boundaries

Eight years of Interplanetary Monitoring Platform (IMP) 8, four years of International Sun Earth Explorer (ISEE) 2, and one year of IMP 7 magnetometer data have been combined to produce an 'image' of the average magnetic field for a YZ cross section (aberrated GSM) of the magnetotail at a downtail distance of 25 R(sub E). The shape of the neutral sheet and magnetopause boundaries can be observed directly from the images. A fitting function that qualitatively matches the observed boundary shape can then be chosen. This approach improves on previous fits to possible unsuitable functional forms specified independently of the data. In addition, as a refinement of previous studies, we have corrected for varying solar wind dynamic pressure and the effects of tail flaring. We find the magnetopause is displaced above the XY plane with increasing dipole tilt. The neutral sheet is found to curve slightly more than the model of Fairlfield (1980) during times of large dipole tilt and near the flanks appears to differ substantially from the neutral sheet shape given by the analytic model of Voigt (1984), the more recent neutral sheet model of Dandouras (1988) based on the Voigt model, and the semi-empirical model of Tsyganenko (1989).

Hammond, C. Max↗

NASA NTRS1992

Galileo Earth/Moon News Conference

This NASA Kennedy Space Center (KSC) video release (Part 1 of 2) begins with a presentation given by William J. O'Neil (Galileo Project Manager) describing the status and position of the Galileo spacecraft 7 days prior to the Galileo Earth-2 flyby. Slides are presented including diagrams of the Galileo spacecraft trajectory, trajectory correction maneuvers, and the Venus and asteroid flybys. Torrence Johnson (Galileo Project Scientist) follows Mr. O'Neil with an explanation of the Earth/Moon science activities that will be undertaken during the second Galileo/Earth encounter. These activities include remote sensing, magnetospheric and plasma measurements, and images taken directly from Galileo of the Earth and Moon. Dr. Joseph Veverka (Galileo Imaging Team, Cornell University) then gives a brief presentation of the data collected by the first Galileo/Gaspra asteroid flyby. Images sampled from the 57 photographs taken of Gaspra are presented along with discussions of Gaspra's morphology, shape and size, and surface features. These presentations are followed by a question and answer period given for the benefit of scientific journalists whose subjects include overall Galileo spacecraft health, verification of the Gaspra images timeframe, and the condition of certain scientific spacecraft instruments. Part 2 of this video can be retrieved by using Report No. NONP-NASA-VT-2000001078.

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NASA NTRS2000

Exploiting the Temperature Dependence of Magnetic Susceptibility to Control Convection in Fundamental Studies of Solidification Phenomena

It is well known that convection is a dominant mass transport mechanism when materials are solidified on Earth's surface. This convection is caused by gradients in density (and therefore gravitational force) that are brought about by gradients in temperature, composition or both. Diffusion of solute is therefore dwarfed by convection and the study of fundamental parameters, such as dendrite tip shape and growth velocity in the absence of convection is nearly impossible. Significant experimental work has therefore been carried out in orbiting laboratories with the intent of minimizing convection by minimizing gravity. One of the best known experiments of this kind is the Isothermal Dendritic Growth Experiment (IDGE), supported by NASA. Naturally such experiments are costly and one objective of the present investigation is to develop an experimental method whereby convection can be- halted, in solidification and other experiments, on the surface. A second objective is to use the method to minimize convection resulting from the residual accelerations suffered by experiments in microgravity. The method to be used to minimize convection relies on the dependence of the magnetic susceptibility of a fluid on temperature or composition (whichever is driving convection). All materials experience a force when placed in a magnetic field gradient. The direction and magnitude of that force depend on the magnetic susceptibility of the material. Consequently the force will vary if the susceptibility varies with temperature or composition. With a magnetic field gradient in the right direction (typically upward) and of the right magnitude, this variation in the magnetic force can be made to exactly cancel the variation in the gravitational force. Expressed another way, normal buoyancy is exactly countered by a "magnetic buoyancy". To demonstrate the principle, a solution of MnC12 in water has been used. First the variation of the susceptibility of this paramagnetic solution with temperature and concentration was measured. Then a "cell", containing this solution and 50mm long by 15mm high by 155mm wide, was placed in a superconducting magnet at Marshall Space Flight Center. The magnetic field was measured at various positions within the bore of the magnet using a Hall effect probe. In this way, a position was found where the magnetic field gradient was predominantly upward; the magnitude of the gradient could then be adjusted by adjusting the current of the magnet. The ends of the cell consisted of machined copper blocks maintained at controlled temperatures by circulating water from constant temperature baths. The walls of the cell were of rectangular section glass tubing so that the cell contents could be seen. Velocities arising from thermal gradients within the cell were measured by particle image velocimetry (PIV). Particles used for this purpose were silver-coated hollow glass spheres of micrometers diameter and nearly the same density as the solution. A central vertical plane of the cell was illuminated by a laser beam passing through a cylindrical lens. Digital images of the particles were captured on a CCD camera and fed to a computer so that frame-to-frame movements of particles traveling with the fluid were captured. These images were employed to compute velocity maps using commercial PIV software. In a typical experiment the cold end of the cell was maintained at 10C and the warm end at 30 C. With no current in the magnet, i.e.- with natural -convection allowed to occur, the fluid was observed to circulate with an average speed of approximately 0.3 millimeters per second. It was visually apparent that this circulation was diminished as the current was increased. At currents of approximately 20A the flow was halted, to within the precision of the PIV measurements. At yet higher currents the convection was reversed with the hotter solution sinking and the cooler solution rising. At 40A this reversed convection had speeds averaging 0.43 millimeters per second. The measurements of susceptibility and density allow an estimate of the field gradient necessary to halt convection in the experiment. That estimate was 7.8T (squared) per meter and the convection was observed to halt in the magnet at a current giving 7.21T (squared) per meter from the magnetic field measurements. Calculations of the flow have been carried out using the computational fluid dynamics software FLUENT and show good agreement with the measurements.

Seybert, C. D.↗

NASA NTRS2007

Solar Sail Model Validation from Echo Trajectories

The NASA In-Space Propulsion program has been engaged in a project to increase the technology readiness of solar sails. Recently, these efforts came to fruition in the form of several software tools to model solar sail guidance, navigation and control. Furthermore, solar sails are one of five technologies competing for the New Millennium Program Space Technology 9 flight demonstration mission. The historic Echo 1 and Echo 2 balloons were comprised of aluminized Mylar, which is the near-term material of choice for solar sails. Both spacecraft, but particularly Echo 2, were in low Earth orbits with characteristics similar to the proposed Space Technology 9 orbit. Therefore, the Echo balloons are excellent test cases for solar sail model validation. We present the results of studies of Echo trajectories that validate solar sail models of optics, solar radiation pressure, shape and low-thrust orbital dynamics.

Heaton, Andrew F.↗

NASA NTRS1983

Field-aligned ion beams upstream of the earth's bow shock Evidence for a magnetosheath source

High time resolution ISEE-1 and -2 observations of upstream field-aligned ion beams at several crossings of the earth's bow shock indicate that some beams are due to high energy magnetosheath particles leaking through the shock into the upstream region. The distribution immediately downstream of these oblique shocks consists of a 'core' of directly transmitted, slightly heated ions, plus a crescent-shaped, high-velocity distribution, centered roughly on the magnetic field in the direction toward the upstream region, with a fairly well defined low velocity cutoff.

Thomsen, M. F.↗

NASA NTRS1986

Mars lander survey

The requirements, issues, and design options are reviewed for manned Mars landers. Issues such as high 1/d versus low 1/d shape, parking orbit, and use of a small Mars orbit transfer vehicle to move the lander from orbit to orbit are addressed. Plots of lander mass as a function of Isp, destination orbit, and cargo up and down, plots of initial stack mass in low Earth orbit as a function of lander mass and parking orbit, detailed weight statements, and delta V tables for a variety of options are included. Lander options include a range from minimum landers up to a single stage reusable design. Mission options include conjunction and Venus flyby trajectories using all-cryogenic, hybrid, NERVA, and Mars orbit aerobraking propulsion concepts.

William R Stump↗

NASA NTRS1992

Scientific objectives of a Solar Probe mission

The Solar Probe is a mission of exploration and discovery in an uninvestigated region near the sun. The Solar Probe can enhance general understanding of the corona and the solar wind. The first in situ measurements of coronal particles and fields are expected to provide definitive discriminators among many currently proposed models of processes that shape the structure and dynamics of the outer corona and solar wind. In addition, observations of the development of turbulence, nonlinear wave processes, plasma heating, and particle acceleration in the corona can advance these areas of plasma physics in a regime neither duplicated by earth-based laboratories nor by previous space exploration. It also fills the last gap between knowledge of the terrestrial response to solar output as well as provide insight for interpreting observations of general stellar envelopes.

Feldman, W.↗

NASA NTRS1997

Current Collection in a Magnetic Field

It is found that the upper-bound limit for current collection in the case of strong magnetic field from the current is close to that given by the Parker-Murphy formula. This conclusion is consistent with the results obtained in laboratory experiments. This limit weakly depends on the shape of the wire. The adiabatic limit in this case will be easily surpassed due to strong magnetic field gradients near the separatrix. The calculations can be done using the kinetic equation in the drift approximation. Analytical results are obtained for the region where the Earth's magnetic field is dominant. The current collection can be calculated (neglecting scattering) using a particle simulation code. Dr. Singh has agreed to collaborate, allowing the use of his particle code. The code can be adapted for the case when the current magnetic field is strong. The needed dm for these modifications is 3-4 months. The analytical description and essential part of the program is prepared for the calculation of the current in the region where the adiabatic description can be used. This was completed with the collaboration of Drs. Khazanov and Liemohn. A scheme of measuring the end body position is also proposed. The scheme was discussed in the laboratory (with Dr. Stone) and it was concluded that it can be proposed for engineering analysis.

Krivorutsky, E. N.↗

NASA NTRS2004

Lunar and Planetary Science XXXV: Asteroids, Meteors, Comets

Reports included:Long Term Stability of Mars Trojans; Horseshoe Asteroids and Quasi-satellites in Earth-like Orbits; Effect of Roughness on Visible Reflectance Spectra of Planetary Surface; SUBARU Spectroscopy of Asteroid (832) Karin; Determining Time Scale of Space Weathering; Change of Asteroid Reflectance Spectra by Space Weathering: Pulse Laser Irradiation on Meteorite Samples; Reflectance Spectra of CM2 Chondrite Mighei Irradiated with Pulsed Laser and Implications for Low-Albedo Asteroids and Martian Moons; Meteorite Porosities and Densities: A Review of Trends in the Data; Small Craters in the Inner Solar System: Primaries or Secondaries or Both?; Generation of an Ordinary-Chondrite Regolith by Repetitive Impact; Asteroid Modal Mineralogy Using Hapke Mixing Models: Validation with HED Meteorites; Particle Size Effect in X-Ray Fluorescence at a Large Phase Angle: Importance on Elemental Analysis of Asteroid Eros (433); An Investigation into Solar Wind Depletion of Sulfur in Troilite; Photometric Behaviour Dependent on Solar Phase Angle and Physical Characteristics of Binary Near-Earth-Asteroid (65803) 1996 GT; Spectroscopic Observations of Asteroid 4 Vesta from 1.9 to 3.5 micron: Evidence of Hydrated and/or Hydroxylated Minerals; Multi-Wavelength Observations of Asteroid 2100 Ra-Shalom: Visible, Infrared, and Thermal Spectroscopy Results; New Peculiarities of Cometary Outburst Activity; Preliminary Shape Modeling for the Asteroid (25143) Itokawa, AMICA of Hayabusa Mission; Scientific Capability of MINERVA Rover in Hayabusa Asteroid Mission; Characteristics and Current Status of Near Infrared Spectrometer for Hayabusa Mission; Sampling Strategy and Curation Plan of Hayabusa Asteroid Sample Return Mission; Visible/Near-Infrared Spectral Properties of MUSES C Target Asteroid 25143 Itokawa; Calibration of the NEAR XRS Solar Monitor; Modeling Mosaic Degradation of X-Ray Measurements of 433 Eros by NEAR-Shoemaker; Scattered Light Remediation and Recalibration of near Sheomaker s NIS Global Dataaset at 433 Eros; Evaluation of Preparation and Measuring Techniques for Interplanetary Dust Particles for the MIDAS Experiment on Rosetta; Chiron: a Proposed Remote Sensing Prompt Gamma Ray Activation Analysis Instrument for a Nuclear Powered Prometheus Mission;From Present Surveying to Future Prospecting of the Asteroid Belt; Asteroid Physical Properties Probe Microgravity Testing of a Surface Sampling System for Sample Return from Small Solar System Bodies;and Penetrator Coring Apparatus for Cometary Surfaces.

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NASA NTRS2005

[Stellar Occultation Studies of Small Bodies in the Outer Solar System: Accomplishments, Status, and Plans]

Bodies residing in the outer solar system exhibit unique physical processes, and some of the lessons learned from them can be applied to understanding what occurred in the outer solar system during its formation and early evolution. Pluto, the largest known Kuiper Belt object (KBO), and its near twin Triton--an ex-KBO that has been captured by Neptune--have nitrogen atmospheres that are in vapor-pressure equilibrium with surface ice. These atmospheres are most sensitively probed from Earth by the technique of Stellar occultations, which can provide the temperature and pressure profiles of these atmospheres at a spatial resolution of a few kilometers. Recent results from occultations show that the surface pressure of Triton's atmosphere has been increasing and that the shape of the atmosphere deviates from its expected spherical figure. With the occultation technique we can also learn the sizes of smaller bodies that have formed in the outer solar system: Charon, the Centaurs, and KBOs. Our proposed program involves identifying occultation candidates, predicting occultations, observing occultations, analysis of the data, and synthesis of the occultation results with other data. The main goals for our proposed work are to (i) further observe occultations by Triton with the objectives of understanding its pressure changes, distortion, and enigmatic thermal structure (ii) determine whether the abrupt drop in Pluto's stellar occultation light curve is caused by a sharp thermal gradient near its surface or by atmospheric haze, (iii) further observations to characterize the potential collapse of Pluto's atmosphere as it recedes from the sun (information that should be of interest to the Pluto-Kuiper Express), ( iv ) determine Charon's radius more accurately than can be done with the mutual events to derive a better estimate of Charon's density, and ( v ) directly determine the size (and albedo) of Centaurs with the goal of more accurately estimating the sizes of KBOS.

Elliott, James↗

NASA NTRS2008

Spacecraft Materials in the Space Flight Environment: International Space Station - May 2002 to May 2007

The performance of ISS spacecraft materials and systems on prolonged exposure to the low-Earth orbit (LEO) space flight is reported in this paper. In-flight data, flight crew observations, and the results of ground-based test and analysis directly supporting programmatic and operational decision-making are presented. The space flight environments definitions (both natural and induced) used for ISS design, material selection, and verification testing are shown, in most cases, to be more severe than the actual flight environment accounting for the outstanding performance of ISS as a long mission duration spacecraft. No significant ISS material or system failures have been attributed to spacecraft-environments interactions. Nonetheless, ISS materials and systems performance data is contributing to our understanding of spacecraft material interactions in the spaceflight environment so as to reduce cost and risk for future spaceflight projects and programs. Orbital inclination (51.6o) and altitude (nominally near 360 km) determine the set of natural environment factors affecting the functional life of materials and systems on ISS. ISS operates in an electrically conducting environment (the F2 region of Earth s ionosphere) with well-defined fluxes of atomic oxygen, other charged and neutral ionospheric plasma species, solar UV, VUV, and x-ray radiation as well as galactic cosmic rays, trapped radiation, and solar cosmic rays (1-4). The LEO micrometeoroid and orbital debris environment is an especially important determinant of spacecraft design and operations (5, 6). The magnitude of several environmental factors varies dramatically with latitude and longitude as ISS orbits the Earth (1-4). The high latitude orbital environment also exposes ISS to higher fluences of trapped energetic electrons, auroral electrons, solar cosmic rays, and galactic cosmic rays (1-4) than would be the case in lower inclination orbits, largely as a result of the overall shape and magnitude of the geomagnetic field (1-4). As a result, ISS exposure to many environmental factors can vary dramatically along a particular orbital ground track, and from one ground track to the next, during any 24-hour period.

Golden, John↗

NASA NTRS2009

Early History of the Moon: Zircon Perspective

The Moon is believed to have formed from debris produced by a giant impact of a Mars sized body with the Earth (at around 4.51 Ga), forming a primitive body with a thick global layer of melt referred to as the Lunar Magma Ocean (LMO). The crystallization of LMO created internal stratification of the Moon forming main geochemical reservoirs. The surface features on the Moon were shaped by the subsequent collision with several large impactors during a short period of time (3.9-4.0 Ga). This process known as the Late Heavy Bombardment is supported by models of planetary motion, suggesting that rapid migration of giant planets could have triggered a massive delivery of planetesimals from the asteroid belt into the inner Solar System at about 3.9 Ga. Although, general chronology of LMO and LHB is well established using both long lived (U-Pb, Rb-Sr, Sm-147-Nd-143 and Ar-Ar) and extinct (Hf-182-W-182 and 146Sm-142Nd) isotope systems, some of these systems such as Ar-Ar are known to reset easily during secondary thermal overprints. As a result important details in the timing of LMO and LHB remain unresolved. In addition, the relative weakness of these systems under high T conditions can potentially bias the chronological information towards later events in the history of the Moon.

Grange, M.L.↗

NASA NTRS2012

Models Support Energy-Saving Microwave Technologies

During the Apollo Program, astronauts on the Moon encountered a small menace that created big problems: lunar dust. Similar to how tiny bits of Styrofoam behave on Earth adhering to anything they touch lunar dust sticks to spacesuits, spacecraft, tools, and equipment, and is extremely difficult to remove. The clingy nature of the substance is partly due to its electrostatic charge but is also due to its physical characteristics: The sharp, irregularly shaped grains have edges like burrs and feel like abrasive talcum powder to the touch. Not only a nuisance, Moon dust is also a potential health and safety risk. Because it is often laden with ultraviolet radiation and high iron content, it can be detrimental if it gets into the eyes or lungs. In fact, some of the particles are so small that the human body does not even detect them in order to expel them. On the Apollo missions, equipment covered with the dark-colored Moon dust suffered from the absorption of sunlight and tended to overheat. NASA has investigated tools and techniques to manage the sticky stuff, including magnets, vacuums, and shields. In 2009, Kennedy Space Center collaborated with a small business to investigate a method to harden the Moon's surface in a sense, to pave the surface so astronauts and robots could land, drive, and work without disrupting and scattering the material.

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NASA NTRS2016

The Muscles Treasury Survey. I. Motivation and Overview

Ground- and space-based planet searches employing radial velocity techniques and transit photometry have detected thousands of planet-hosting stars in the Milky Way. With so many planets discovered, the next step toward identifying potentially habitable planets is atmospheric characterization. While the Sun-Earth system provides a good framework for understanding the atmospheric chemistry of Earth-like planets around solar-type stars, the observational and theoretical constraints on the atmospheres of rocky planets in the habitable zones (HZs) around low-mass stars (K and M dwarfs) are relatively few. The chemistry of these atmospheres is controlled by the shape and absolute flux of the stellar spectral energy distribution (SED), however, flux distributions of relatively inactive low-mass stars are poorly understood at present. To address this issue, we have executed a panchromatic (X-ray to mid-IR) study of the SEDs of 11 nearby planet-hosting stars, the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) Treasury Survey. The MUSCLES program consists visible observations from Hubble and ground-based observatories. Infrared and astrophysically inaccessible wavelengths (EUV and Lyalpha) are reconstructed using stellar model spectra to fill in gaps in the observational data. In this overview and the companion papers describing the MUSCLES survey, we show that energetic radiation (X-ray and ultraviolet) is present from magnetically active stellar atmospheres at all times for stars as late as M6. The emission line luminosities of C IV and Mg II are strongly correlated with band-integrated luminosities and we present empirical relations that can be used to estimate broadband FUV and XUV (is equivalent to X-ray + EUV) fluxes from individual stellar emission line measurements. We find that while the slope of the SED, FUV/NUV, increases by approximately two orders of magnitude form early K to late M dwarfs (approximately equal 0.01-1), the absolute FUV and XUV flux levels at their corresponding HZ distances are constant to within factors of a few, spanning the range 10-70 erg per (sq cm) s in the HZ. Despite the lack of strong stellar activity indicators in their optical spectra, several of the M dwarfs in our sample show spectacular UV flare emission in their light curves. We present an example with flare/quiescent ultraviolet flux ratios of the order of 100:1 where the transition region energy output during the flare is comparable to the total quiescent luminosity of the star E(sub flare)(UV) approximately 0.3 L(sub *) delta (t) (delta t = 1 s). Finally, we interpret enhanced L(line)/L(sub Bol) ratios for C IV and N V as tentative observational evidence for the interaction of planets with large planetary mass-to-orbital distance ratios (M(sub plan)/A(sub plan)) with the transition regions of their host stars.

Infrared and astrophysically inaccessible waveleng↗

NASA NTRS1975

Electromagnetic fields and torque for a rotating gyroscope with a superconducting shield

In a proposed experiment, a measurement is to be made of the angular precession of a rotating superconducting gyroscope for the purpose of testing different general-relativity theories. For various reasons having to do with the design of the experiment, the superconducting shield surrounding the gyroscope is not spherically symmetric and produces a torque. There are two distinct features of the shield which lead to a torque on the gyroscope. First, its shape is a sphere intersected by a plane. If the angular momentum of the gyroscope is not parallel to the rotational symmetry axis of the shield, there is a torque which is calculated. Second, there are small holes in the spherical portion of the shield. The earth's field can penetrate through these holes and give an additional torque which is also calculated. In the actual experiment, these torques must be accurately known or made very small in order to obtain meaningful results. The present calculation is sufficiently general for application over a wide range of experimental design parameters.

Ebner, C.↗

NASA NTRS1981

Spherical-earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration

Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical earth. The procedure involves representation of the anomalous source as a distribution of equivalent point gravity poles or point magnetic dipoles. The distribution of equivalent point sources is determined directly from the volume limits of the anomalous body. The variable limits of integration for an arbitrarily shaped body are obtained from interpolations performed on a set of body points which approximate the body's surface envelope. The versatility of the method is shown by its ability to treat physical property variations within the source volume as well as variable magnetic fields over the source and observation surface. Examples are provided which illustrate the capabilities of the technique, including a preliminary modeling of potential field signatures for the Mississippi embayment crustal structure at 450 km.

Von Frese, R. R. B.↗