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NASA NTRS1977

Photometry of the Gallilean satellites

The dependence of the magnitudes and colors on both solar and orbital phase angles is derived from photometric observations of the Gallilean satellites. The rotational variations are best defined by the most recent observations; as a consequence of the complex albedo distributions on the satellites, the light curves cannot be represented by simple analytic expressions. The recent data also establish the mean magnitudes on the V photometric system to within + or - 0.02 magnitude and permit accurate geometric albedos to be derived. The dependence of magnitude on solar phase angle, and particularly at very small phase angles, is best shown by the extensive observations from 1926 and 1927. The determined rotational curves are used to reduce these data and express the phase effect in terms of a linear curve for phase angles greater than 6 deg and a quadratic curve for smaller angles. The phase dependence of these satellites is compared with that observed for other small bodies in the solar system; particularly interesting are the anomalously large phase coefficient and opposition effect of Io.

Morrison, D.↗

NASA NTRS1975

A determination of the composition of the Venus clouds from aircraft observations in the near infrared

Summary of the evidence showing that the first optical depth of the Venus cloud layer is composed of a water solution of sulfuric acid, including earlier aircraft observations of Venus' reflectivity in the region from 1 to 4 microns obtained at a phase angle of 120 deg. Analyses of these aircraft results indicated that of all the proposed cloud candidates only a sulfuric acid solution with a concentration of 75% or more H2SO4 by weight was consistent with the observed 3-micron cloud feature. Aircraft observations of Venus are presented which were obtained in the same spectral region at a phase angle of 40 deg and in the region from 3 to 6 microns at a phase angle of 136 deg. Comparing the two sets of observations in the region from 1 to 4 microns, a striking phase effect is found: the reflectivity is much lower in the 3-micron region and there is a much more marked decline between 1.3 and 2.5 microns for the data obtained at the smaller phase angle. The observations made at the 40-deg phase angle are consistent with the theoretical behavior of a sulfuric acid cloud and imply that the sulfuric acid is present to at least many tens of optical depth below the cloud tops. Arguments concerning the concentration of the solution are reviewed, and it is concluded that the best current estimate is about 85% H2SO4 by weight.

Pollack, J. B.↗

NASA NTRS2022

Interstellar Object Encounter Trade Space Exploration

2017 and 2019 saw the discovery of the first twointerstellar objects (ISO) in the solar system, 1I ‘Oumuamuaand 2I Borisov, but left scientists with more questions thananswers as to the objects’ origins. To fully resolve these openquestions, scientists need a closer look at an interstellar objectvia a dedicated spacecraft and close approach. However, ISOspose unique engineering challenges for close encounters becauseof their extremely high relative velocity, unfavorable approachgeometry, and limited alert time; ISOs often are only discovereda few months before a spacecraft would need to launch toencounter it.Typical encounters with small bodies have occurred at relativevelocities on the order of 10 km/s with approach phase below90 deg (at least half-lit). Except for the Halley Armada in the80s, the most extreme flybys have been of comet Borrelly ata relative velocity of 16.6 km/s (but only a phase angle of 65deg) and Annefrank at a phase angle of 150 deg (but a relativevelocity of only 7.2 km/s). Furthermore, planetary missionsgenerally target bodies whose ephemerides are well constrainedbecause of many years of Earth based observations. On theother hand, ISOs typically have relative velocities of 30-90 km/s,phase angles biased towards over 90 deg, and larger positionuncertainties because of shorter ground-based observationalarcs, and thus represent much more difficult targets.Our team has been developing the flight system architecturesand technologies necessary to enable future reconnaissance ofan interstellar object by flyby, potentially including an impactor.This endeavor seeks to catalyze planetary exploration and itsintersection with exo-planet science. We establish encounterguidance, navigation, and control requirements within the tradespace of trajectories to a synthetic ISO population. Flightsystem constraints, Earth departure capabilities, and ability fora mission team to quickly respond to an inbound target limitthe accessible space for a future mission. This trade spaceanalysis reveals enabling mission architectures, and providesrecommendations for supporting investment to enable an ISOmission in the next decade.

Farnocchia, Davide↗

NASA NTRS1988

The near-infrared polarization and color of Comet Halley: What can we learn about the grains

The near infrared polarization and JHK colors of light scattered by dust grains in comet Halley were measured over a wide range in phase angle and heliocentric distance. Colors were redder than solar with no statistically significant variation with phase angle, heliocentric distance, or pre- and post-perihelion. This suggests that the grain population did not change drastically over time and that the data may be combined and modeled. However, short term variations in visible polarization and dust albedo were seen in Halley. Also, near infrared colors became systematically bluer after the observations were completed. The near infrared colors of Halley fall in the range of those of other comets. The near infrared polarization is similar to the visible polarization of Halley and other comets in showing a negative branch at small phase angles and an approximately linear rise toward positive values at larger phase angles. Mie theory calculations and a size distribution based on spacecraft data were used to model the near infrared polarization and color of comet Halley. Numerous lines of evidence point to the presence of dark, absorbing, probably carbonaceous materials in comets.

Brooke, Timothy Y.↗

NASA NTRS1980

Influence of mistuning on blade torsional flutter

An analytical technique for the prediction of fan blade flutter was evaluated by utilizing first stage fan flutter data from tests on an advanced high performance engine. The formulation includes both aerodynamic and mechanical coupling among all the blades of the assembly. Mistuning is accounted for in the analysis so that individual blade inertias, frequencies, or damping can be considered. Airfoil stability was predicted by calculating a flutter determinant, the eigenvalues of which indicate the extent of susceptibility to flutter. When blade to blade differences in frequencies are considered, a stable system is predicted for the test points examined. For a tuned system, it was found that torsional flutter can be predicted at a limited number of interblade phase angles. Examination of these phase angles indicated that they were "close" to the condition of acoustic resonance. For the range of Mach numbers and reduced frequencies considered, the so called subcritical flutter cannot be predicted. The essential influence of mechanical coupling among the blades is to change the frequencies of the system with little or no change in damping; however, aerodynamic coupling together with mechanical coupling could change not only frequencies, but also damping in the system, with a trend toward instability.

Srinivasan, A. V.↗

NASA NTRS1981

Effects of mistuning on blade torsional flutter

An analytical model for the prediction of fan blade flutter is presented and evaluated using data from NASA tests on an advanced high performance engine. For the cascade conditions appropriate to the test points studied, the aerodynamic theory cannot predict subcritical flutter. Under the assumptions of a tuned assembly, the imaginary part of the aerodynamic coefficients does indicate flutter for a limited number of interblade phase angles, but these interblade phase angles are close to those at which the acoustic resonance is predicted. Upon using the individual blade frequencies and solving the mistuned system with aerodynamic coupling only, the results show a stable system. Eigenvectors calculated for the mistuned system demonstrate the presence of several harmonics in each mistuned mode. Inclusion of both mechanical and aerodynamic coupling in the solution of the eigenproblem influences not only the frequencies but also damping in the system with a trend toward stability.

Srinivasan, A. V.↗

NASA NTRS1977

The photometry of flat, basaltic surfaces

A photometer was developed and successfully operated to obtain photometric measurements on several flat, particulate surfaces of basalt for coplanar scattering geometries. The test materials were two size ranges each of two different basalts with significantly different albedos. The measurements include a range of phase angles from 30 to 80 degrees and were obtained by varying the angles of incidence and emission such that the phase angle remained constant. The data were used elsewhere in the verification of the Meador-Weaver photometric function and are presented here in the form of Minnaert plots. In this form the data offered the first support for the accuracy of the Meador-Weaver photometric function because of a deviation of the data from a straight line trend at larger departures from the mirror point geometry. This trend is predicted by the Meador-Weaver function but not by the Minnaert function. The failure of photometric data to support the Minnaert function was not evident in earlier measurements because of the restriction of planetary data to small departures from the mirror point geometry and to small values of the phase angle.

Weaver, W. R.↗

NASA NTRS2020

Improved Lunar Irradiance Model Using Multiyear MODIS Lunar Observations

The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on board the Terra and Aqua spacecrafts were launched on December 18, 1999, and May 4, 2002, respectively. One of the features of the MODIS instruments is the ability to perform observations of the lunar surface from its space view (SV) port. This event is scheduled approximately once a month via a spacecraft roll maneuver, which enables the lunar phase to be confined to within 1° for each instrument. The Moon is considered to be an extremely stable reference to monitor the long-term radiometric stability of the reflective solar bands (RSB). Each MODIS instrument can also view the Moon for about four months in a year without a roll maneuver. This is caused by the intrusion of the Moon in the SV. The lunar phase angles of these unscheduled lunar observations are distributed over a wide range varying from approximately 50° to 80° for Terra MODIS and from about -80° to -50° for Aqua MODIS, where the positive phase angle refers to a waning Moon, while the negative phase angle corresponds to a waxing Moon. Together, the scheduled and unscheduled lunar observations are used to monitor the long-term radiometric stability of the RSB. Of the several challenges involved in the modeling of the lunar optical properties, such as its absolute brightness, a number of optical and view geometry effects need to be considered. These effects are much easier to characterize for the scheduled observations due to confinement of the lunar phase angles compared to those for the unscheduled intrusions of the Moon in the SV. Nevertheless, it is still a challenge to remove the view geometry effect in the calibration coefficients derived from the scheduled lunar observations and even more challenging for the unscheduled lunar intrusions. In this work, the lunar absolute irradiance is modeled using known attributes and from the lunar observations by the two MODIS instruments from the time period between the years 2005 and 2012.

Calibration↗

NASA NTRS1993

Lunar phase function effects on spectral ratios used for resource assessment

Groundbased telescopic CCD images of 36 selected locations on the moon were obtained in five 'standard' bandpasses at 12 phase angles ranging from -78 deg to +75 deg to measure phase function effects on the ratio values used to quantify the abundance of TiO2 and qualitatively indicate soil maturity. Consistent with previous studies, we find that the moon is 'bluer' at small phase angles, but that the effect on the ratio values for TiO2 abundance for the phase angles of our data is on the order of the measurement uncertainties throughout the range of abundances found in the mare. The effect is more significant as seen from orbiting spacecraft over a range of selenographic latitude. Spectral ratio images (400/560 and 400/730 nm) were used to map the abundance of TiO2 using the empirical relation found by Charlette et al from analysis of returned lunar soils. Additionally, the 950/560 and 950/730 nm image ratios were used to define the regions of mature mare soil in which the relation is valid. Although the phase function dependence on wavelength was investigated and quantified for small areas and the integrated disc, the effect specifically on TiO2 mapping was not rigorously determined. For consistency and convenience in observing the whole lunar front side, our mapping utilized images taken -15 deg less than alpha less than 15 deg when the moon was fully illuminated from earth; however, this includes the strong opposition peak.

Larson, S. M.↗

NASA NTRS1987

Io: Comparison of photometric scans produced by the Minnaert and Hapke functions

Experience has shown that the empirical Minnaert function is a very useful approximation to real photometric behavior near opposition (phase angle = 0), but that in general it cannot accurately model photometric scans across the face of even a homogeneous planet at higher phase angles. Given recent work on fitting the rigorous Hapke function to Voyager data for Io, we can test to what degree the Minnaert function breaks down in the case of Ionian materials by comparing photometric scans produced by the two approaches. At phase angles 2, 20, 30, 60, and 90 deg, we have computed scans of the reflectance along the photometric equator and mirror meridian that would be expected for a homogeneous planet whose surface obeys Hapke's law. The values used for the Hapke parameters omega(0), h, g, and bar-theta were derived for Io by Simonelli and Veverka in both the Voyager narrow angle camera violet filter and orange filter. Each calculated Hapke scan is compared with the corresponding scan predicted by Minnaert's law for various values of the Minnaert limb-darkening parameter k. For a Minnaert scan at a particular k, the value of the reflectance parameter B(0) is arbitrarily chosen so that the Minnaert and Hapke scans coincide at the so-called specular point (the point where the photometric equator and mirror meridian intersect). The violet filter photometric scans that result from this process are shown. Results indicate that the empirical Minnaert function, while not a perfect model of real photometric behavior, does provide a very useful parameterization of limb darkening at phase angles out to 90 deg, and is especially useful near opposition.

Simonelli, Damon P.↗

NASA NTRS2021

Unscheduled Lunar Observations for Radiometric Characterization of VIIRS Reflective Solar Bands

Regularly scheduled lunar observations are a major component of the on-orbit calibration of the Suomi National Polar-Orbiting Partnership (SNPP) Visible Infrared Imaging Radiometer Suite (VIIRS) reflective solar bands (RSB). With a few exceptions, these scheduled lunar observations have been performed with the same phase angles ranging from -51.5° to -50.5°. In addition to these observations that require a roll maneuver, the VIIRS instruments also view the Moon via its space-view port without a roll maneuver, covering a wide range of phase angles. In this paper, we present techniques used to derive the radiometric gain for the VIIRS RSB using unscheduled lunar observations that are made over a range of phase angles. An empirical correction to account for residual phase angle dependencies is derived from on-orbit SNPP VIIRS unscheduled lunar events and is successfully applied to estimate the radiometric gain that shows good agreement with the gains derived from the scheduled lunar events as well as those derived from the solar diffuser. In addition to the follow-on VIIRS instrument on the NOAA-20 satellite, three more VIIRS instruments are scheduled to be launched in the next decade. The methodologies developed in this work are expected to be applied to unscheduled lunar events from other VIIRS instruments to support their on-orbit RSB calibration.

VIIRS↗

NASA NTRS1989

Multiple coherent mode interaction in a developing round jet

The integral energy method has been used in order to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear layer momentum thickness, the wave mode kinetic energy and the wave mode phase angle. It is shown that the nonlinear interaction between wave modes is dependent on the wave mode phase angles. The initial wave mode phase angles as well as the initial energy densities play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.

Lee, S. S.↗

NASA NTRS1992

Surface photometric properties and albedo changes in the central equatorial region of Mars

Comparison of the Viking Orbiter 2 Approach mosaic taken 11 Mars months later provides qualitative information on the photometric properties of the martian albedo features, and the distribution of dust and sand deposits responsible for the atmosphere near the northern summer solstice. The approach mosaic was taken at L (sub s) 106 degrees (early N. summer), phase angle 106 degrees; and airmasses varying from 4.6 at 30 degrees N to 3.3 near 10 degrees S. The apoapsis mosaic was taken in four sequences between L (sub s) 72 degrees and 76 degrees (late N. spring), near phase angles of 47 degrees, and at airmasses near 2.5. Systematic differences in the photometric decalibrations used to generate these mosaics may induce multiplicative errors of 5-10 percent of the observed albedos in comparisons of the mosaics, but they are probably nearer 3 percent of the albedos. In the study area (30 degrees N to 20 degrees S, 57 degrees E to 75 degrees W), scene-average approach Minnaert albedos were about 10 percent greater than apoapsis albedos and slightly less 'red'. The preferred explanation for the observed approach-apoapsis albedo difference is that both Arabia and Meridiani materials are smoother on millimeter and larger scales than other units in the study area. This is in good agreement with preliminary conclusions of Thorpe and (for dark intracrater Meridiani splotches) Regner et al. This is also consistent with reasonable models of these surfaces. 'Dark Blue' Meridiani surfaces are interpreted as consisting of sand dunes and sand sheets, which would be expected to have macroscopically smooth, nonshadowing surfaces. Viking Lander images of the surfaces at both landing sites show that smooth drift area's brightnesses are close to those of adjacent rough soil areas at low phase angles, but drifts become much brighter than rough soils when looking up-sun at high phase angles. Smooth patches of duricrust at both landing sites, interpreted by Strickland as eolian deposits (regardless of how they became salt enriched and cemented), also show this behavior.

Strickland, Edwin L., III↗

NASA NTRS1979

The Mars opposition effect at 20 deg N. latitude and 20 deg W. longitude

Low phase angle observations in the Chryse-Acidalia region have been obtained by the Viking Orbiter 1 spacecraft under clearer atmospheric conditions than reported earlier. A variety of surface features were recorded, e.g., crater streaks, dark and bright patches. Several findings for this scene include: an abrupt brightness increase (10%) was found at phase angles less than 3 deg, an effect dependent on surface albedo and possibly particle distribution; a slight weakening of reflectance surge with decreasing wavelengths; a larger opposition effect for features of high albedo was recorded; and a greater reddening with increased phase angle took place for low albedo regions. Both reflectance and contrast values are provided at three wavelengths as a function of phase angle from 0.15 to 20 deg.

Thorpe, T. E.↗

NASA NTRS2000

Sensitivity of a Wave Structure to Initial Conditions

Microgravity experiments aimed at quantifying effects of gentler via controlled sinusoidal forcing transmitted on the interface between two miscible liquids have shown the evolution of a quasi -stationary four-mode wave structure oriented vertically. The sensitivity of the wave structure to phase angle variation is investigated computationally. We show that a slight variation of the phase angle is sufficient to cause a bifurcation to a two-mode structure. The dependence of phase angle on wave structure is attributed to sensitivity on initial conditions due to the strong nonlinearity of the coupled field equations for the parametric space of interest.

Duval, Walter M. B.↗

NASA NTRS1988

Investigation of oscillating cascade aerodynamics by an experimental influence coefficient technique

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the torsion mode unsteady aerodynamics of a biconvex airfoil cascade at realistic values of the reduced frequency for all interblade phase angles at a specified mean flow condition. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized in which only one airfoil in the cascade is oscillated at a time and the resulting airfoil surface unsteady pressure distribution measured on one dynamically instrumented airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at a specified interblade phase angle are then determined through a vector summation of these data. These influence coefficient determined oscillation cascade data are correlated with data obtained in this cascade with all airfoils oscillating at several interblade phase angle values. The influence coefficients are then utilized to determine the unsteady aerodynamics of the cascade for all interblade phase angles, with these unique data subsequently correlated with predictions from a linearized unsteady cascade model.

Buffum, Daniel H.↗

NASA NTRS1988

Investigation of oscillating cascade aerodynamics by an experimental influence coefficient technique

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the torsion mode unsteady aerodynamics of a biconvex airfoil cascade at realistic values of the reduced frequency for all interblade phase angles at a specified mean flow condition. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized in which only one airfoil in the cascade is oscillated at a time and the resulting airfoil surface unsteady pressure distribution measured on one dynamically instrumented airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at a specified interblade phase angle are then determined through a vector summation of these data. These influence coefficient determined oscillating cascade data are correlated with data obtained in this cascade with all airfoils oscillating at several interblade phase angle values. The influence coefficients are then utilized to determine the unsteady aerodynamics of the cascade for all interblade phase angles, with these unique data subsequently correlated with predictions from a linearized unsteady cascade model.

Buffum, Daniel H.↗

NASA NTRS2007

Optimal Electrodynamic Tether Phasing Maneuvers

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

Bitzer, Matthew S.↗