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NASA NTRS1992

A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds

We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen the the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the 'spherical' model have features not compatible with data on magnetic clouds.

Farrugia, C. J.↗

NASA NTRS1980

Initial geomagnetic field model from Magsat vector data

Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.

Langel, R. A.↗

NASA NTRS1983

Gas flow through rotameters

Using data available for small rotameters that use spherical floats in gas flow, a linear relationship is derived. It is noted that the relationship provides a good fit for variable volumetric flow, density, and viscosity at constant flow height. With low Reynolds numbers (Re being less than 1), the product of the variable volumetric flow and the viscosity becomes constant; at high Reynolds numbers (Re being greater than 2000), the product of the variable volumetric flow and the square root of the density becomes constant. It is pointed out that the equation given here can be used to obtain an indirect calibration with any gas of known density and viscosity. The constancy of the product of the variable volumetric flow and viscosity at low variable volumetric flows is seen as suggesting the development of simple, inexpensive gas viscometers using rotameter technology.

Levin, H.↗

NASA NTRS1983

10 micron polarimetry of Ceres

Linear polarimetry of Ceres at 10 micron is presented. These data represent the first published polarization measurements of an asteroid in the thermal infrared. It is found that Ceres is polarized at the 0.2-0.6 percent level. This data set is compared with theoretical models of the linear polarization of emitted radiation from a spherical plane. These models are used to derive the pole position and thermal inertia of Ceres. Ceres is best fit with a thermal inertia of 0.0010 + or 0.0003 cal (sq cm K) per square root of second and a pole orientation of beta(p) = 36 deg + or - 5 deg + or -5, lambda(p) = 270 deg + or - 3. It is concluded that 10 micron polarimetry is a potentially powerful technique for remotely sensing the pole orientation and thermal inertia of asteroids.

Johnson, P. E.↗

NASA NTRS1987

Tidal estimation in the Pacific with application to SEASAT altimetry

The techniques for computing the eigenfunctions of the velocity potential (Proudman functions) set out in Sanchez, et al. (1986) in relation to the Atlantic-Indian Oceans are here applied to the Pacific Ocean, using a 6x6 degree grid of 510 points (455 points for the associated stream functions). Normal modes are computed from the first Proudman functions and have natural periods from 43.9h downward. Tidal syntheses are derived from these modes by direct application of the (frictionless) dynamic equations and by least-squares fitting of Proudman functions to the dynamically interpolated tide-gauge data of Schwiderski (1983). The modes contributing the most energy to the principal harmonic tidal constituents are different in the two computations: their natural periods are typically in the range of 9 to 16h for semidiurnal, and 14 to 43h for diurnal tides. The rms of fit for the Proudman functions is, in all cases, better than the corresponding value for the same number of spherical harmonics.

Sanchez, Braulio V.↗

NASA NTRS1974

Optical polarization measurements of the Jupiter atmosphere at 103 deg phase angle

The first measurements have been made of the linear polarization of sunlight scattered by the Jupiter atmosphere at phase angles greater than 12 deg, using the imaging photopolarimeter on Pioneer 10. The data are of high accuracy, in spite of several problems in the instrument. The polarization is positive at 440 nm. There is no direct evidence for spherical particles in the Jupiter clouds. Using a simple model of Rayleigh scattering above a Lambertian cloud layer, a unique fit is found to the observed intensity and polarization at each point on the planet. The resulting Rayleigh optical depths, if they are attributed to molecular scattering alone (i.e., no aerosols above the cloud tops), can be converted into physical altitudes of the cloud tops. The first results suggest that the north tropical zone, parts of the equatorial zone, and the red spot are all elevated regions.

Coffeen, D. L.↗

NASA NTRS2005

Hybrid Systems Diagnosis

This paper reports on an on-going Project to investigate techniques to diagnose complex dynamical systems that are modeled as hybrid systems. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. We cast the diagnosis problem as a model selection problem. To reduce the space of potential models under consideration, we exploit techniques from qualitative reasoning to conjecture an initial set of qualitative candidate diagnoses, which induce a smaller set of models. We refine these diagnoses using parameter estimation and model fitting techniques. As a motivating case study, we have examined the problem of diagnosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.

McIlraith, Sheila↗

NASA NTRS2015

Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage, Management and Transfer

Experimental and numerical results are presented from a new cryogenic fluid slosh program at the Florida Institute of Technology (FIT). Water and cryogenic liquid nitrogen are used in various ground-based tests with an approximately 30 cm diameter spherical tank to characterize damping, slosh mode frequencies, and slosh forces. The experimental results are compared to a computational fluid dynamics (CFD) model for validation. An analytical model is constructed from prior work for comparison. Good agreement is seen between experimental, numerical, and analytical results.

slosh↗

NASA NTRS2015

Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage, Management and Transfer

slosh mode frequencies↗

NASA NTRS2010

Evaluating Descent and Ascent Trajectories Near Non-Spherical Bodies

Spacecraft landing on small bodies pass through regions where conventional gravitation formulations using exterior spherical harmonics are inaccurate. An investigation shows that a formulation using interior solid spherical harmonics might be satisfactory. Interior spherical harmonic expansions are usable inside an imaginary, empty sphere. For this application, such a sphere could be positioned in empty space above the intended landing site and rotating with the body. When the spacecraft is inside this sphere, the interior harmonic expansion would be used instead of the conventional, exterior harmonic expansion. Coefficients can be determined by a least-squares fit to gravitation measurements synthesized from conventional formulations. Due to their unfamiliarity, recurrences for interior, as well as exterior, expansions are derived. Hotine's technique for partial derivatives of exterior spherical harmonics is extended to interior harmonics.

Werner, Robert A.↗

NASA NTRS1995

Improved Bounds on Nonluminous Matter in Solar Orbit

We improve, using a larger set of observations including Voyager 2 Neptune flyby data, previous bounds on the amount of dark matter (DM) trapped in a spherically symmetric distribution about the Sun. We bound DM by noting that such a distribution would increase the effective mass of the Sun as seen by the outer planets and by finding the uncertainty in that effective mass for Uranus and Neptune in fits to the JPL developmental ephemeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephamerides. In addition, we present here the values for Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 Jupiter-ranging normal points (and incorporate these data as well). Our principal result is to limit DM in spherically symmetric distributions in orbit about the Sun interior to Neptune's orbit to less than Earth mass and interior to Uranus's orbit to about 1/6 of Earth's mass.

Anderson, John D.↗

NASA NTRS1979

Development and analysis of a twelfth degree and order gravity model for Mars

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Christensen, E. J.↗

NASA NTRS1995

The effects of redshifts and focusing on the spectrum of an accretion disk in the galactic center black hole candidate Sagittarius A(sup *)

There are firm indications that Sgr A(sup *), a compact, nonthermal radio source at the Galactic center, may be powered by the dissipation of gravitational energy as gas trapped from an ambient wind descends down the potential well, first through a quasi-spherical inflow (extending out to approximately 3 x 10(exp 16) cm) and then through a small accretion disk at less than or approximately = 5-10 Schwarzschild radii. Earlier three-dimensional Bondi-Hoyle numerical simulations have indicated that fluctuations in the accreted specific angular momentum can lead to a variability in the disk flux on a timescale of years. With greatly improved flux measurements at K and H, and the hint of a approximately 10 minute modulation in the IR luminosity, it is crucial to model the disk emission much more precisely than has been attempted thus far. In this Letter we take into account the effects of Doppler and gravitational redshifts, the light-travel time factor, and the light bending near the black hole to determine the measurable spectrum of Sgr A(sup *) in the increasingly important 10(exp 13) Hz less than or approximately = v less than or approximately = 10(exp 16) Hz frequency range. We find that the relativistic disk spectrum is much softer than its Newtonian counterpart, with a predicted UV flux roughly an order of magnitude smaller than had previously been anticipated. In addition, we find that when the physical conditions in the disk are taken to be consistent with the properties of the quasi-spherical infall (specifically, in terms of the accretion rate and disk size), only a slowly spinning or Schwarzschild black hole appears to fit the observations. Our calculations also reveal that the disk flux is much more weakly dependent on the observer's inclination angle than had been suspected on the basis of earlier Newtonian estimates.

Hollywood, J. M.↗

NASA NTRS1981

Voyager 1 assessment of Jupiter's planetary magnetic field

An estimate of Jupiter's planetary magnetic field is obtained from the Voyager 1 observations of the Jovian magnetosphere. An explicit model for the magnetodisc current system is combined with a spherical harmonic model of the planetary field with both sets of parameters determined simultaneously using a nonlinear generalized inverse methodology. The resulting model fits the observations extremely well throughout the analysis interval (r 20 Jovian radii). The Jovian internal field model obtained from the Voyager 1 data is very similar to the octopole Pioneer 11 models. The best fitting magnetodisc lies in the centrifugal equator, 2/3 of the way between the rotational and magnetic equators, as appropriate for centrifugal loading of the magnetosphere by a cold plasma.

Connerney, J. E. P.↗

NASA NTRS1982

Zonal harmonic model of Saturn's magnetic field from Voyager 1 and 2 observations

An analysis of the magnetic field of Saturn is presented which takes into account both the Voyager 1 and 2 vector magnetic field observations. The analysis is based on the traditional spherical harmonic expansion of a scale potential to derive the magnetic field within 8 Saturn radii. A third-order zonal harmonic model fitted to Voyager 1 and 2 observations is found to be capable of predicting the magnetic field characteristics at one encounter based on those observed at another, unlike models including dipole and quadrupole terms only. The third-order model is noted to lead to significantly enhanced polar surface field intensities with respect to dipole models, and probably represents the axisymmetric part of a complex dynamo field.

Connerney, J. E. P.↗

NASA NTRS2001

Impact Test and Simulation of Energy Absorbing Concepts for Earth Entry Vehicles

Nonlinear dynamic finite element simulations have been performed to aid in the design of an energy absorbing concept for a highly reliable passive Earth Entry Vehicle (EEV) that will directly impact the Earth without a parachute. EEV's are designed to return materials from asteroids, comets, or planets for laboratory analysis on Earth. The EEV concept uses an energy absorbing cellular structure designed to contain and limit the acceleration of space exploration samples during Earth impact. The spherical shaped cellular structure is composed of solid hexagonal and pentagonal foam-filled cells with hybrid graphite- epoxy/Kevlar cell walls. Space samples fit inside a smaller sphere at the center of the EEV's cellular structure. Comparisons of analytical predictions using MSC,Dytran with test results obtained from impact tests performed at NASA Langley Research Center were made for three impact velocities ranging from 32 to 40 m/s. Acceleration and deformation results compared well with the test results. These finite element models will be useful for parametric studies of off-nominal impact conditions.

Billings, Marcus D.↗

NASA NTRS1974

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

Suttles, J. T.↗

NASA NTRS2010

GLGM-3: A Degree-ISO Lunar Gravity Model from the Historical Tracking Data of NASA Moon Orbiters

In preparation for the radio science experiment of the Lunar Reconnaissance Orbiter (LRO) mission, we analyzed the available radio tracking data of previous NASA lunar orbiters. Our goal was to use these historical observations in combination with the new low-altitude data to be obtained by LRO. We performed Precision Orbit Determination on trajectory arcs from Lunar Orbiter 1 in 1966 to Lunar Prospector in 1998, using the GEODYN II program developed at NASA Goddard Space Flight Center. We then created a set of normal equations and solved for the coefficients of a spherical harmonics expansion of the lunar gravity potential up to degree and order 150. The GLGM-3 solution obtained with a global Kaula constraint (2.5 x 10(exp -4)/sq l) shows good agreement with model LP150Q from the Jet Propulsion Laboratory, especially over the nearside. The levels of data fit with both gravity models are very similar (Doppler RMS of approx.0.2 and approx. 1-2 mm/s in the nominal and extended phases, respectiVely). Orbit overlaps and uncertainties estimated from the covariance matrix also agree well. GLGM-3 shows better correlation with lunar topography and admittance over the nearside at high degrees of expansion (l > 100), particularly near the poles. We also present three companion solutions, obtained with the same data set but using alternate inversion strategies that modify the power law constraint and expectation of the individual spherical harmonics coefficients. We give a detailed discussion of the performance of this family of gravity field solutions in terms of observation fit, orbit quality, and geophysical consistency.

Mazarico, E.↗