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Differential-integral equation for dissipation function and derivation of conservation relationship connecting reflection, transmission and dissipation functions of finite slab
Electric nonconductor monochromatic thermal radiative biangular reflectance as function of wavelength and surface roughness
Electric nonconductor monochromatic thermal radiative biangular reflectance as function of wavelength and surface roughness
Radar type backscatter from ground to Alouette satellite at HF and 1000 km altitude
Bi-directional reflectance models for describing distribution of reflected energy from rough metallic spacecraft surfaces
Directional reflective coating consisting of cylindrical dielectric fibers oriented perpendicular to absorbing substrate
Jupiter photoelectric spectral scan in UV REPRODUCED as geometric reflectivity vs wavelength, using Aerobee rocket
Jupiter photoelectric spectral scan in UV REPRODUCED as geometric reflectivity vs wavelength, using Aerobee rocket
Reflectance, transmittance and absorptance of muscovite type mica as function of thickness measured, using prism and grating spectrophotometers
Reflectance of pyrolytic graphite and phenolic nylon chars for radiant heat rejection from nonablating heat shield
Reflectance and optical constants of evaporated iridium films measured in vacuum ultraviolet
Optical absorption in triphenylmethylarsonium tetracyanoquinodimethan single crystals noting refractivity, extinction coefficient and reflectance
Various reciprocity relations in duct acoustics have been derived on the basis of the spatial reciprocity principle implied in Green's functions for linear waves. The derivation includes the reciprocity relations between mode conversion coefficients for reflection and transmission in nonuniform ducts, and the relation between the radiation of a mode from an arbitrarily terminated duct and the absorption of an externally incident plane wave by the duct. Such relations are well defined as long as the systems remain linear, regardless of acoustic properties of duct nonuniformities which cause the mode conversions.
Various reciprocity relations in duct acoustics have been derived on the basis of the spatial reciprocity principle implied in Green's functions for linear waves. The derivation includes the reciprocity relations between mode conversion coefficients for reflection and transmission in nonuniform ducts, and the relation between the radiation of a mode from an arbitrarily terminated duct and the absorption of an externally incident plane wave by the duct. Such relations are well defined as long as the systems remain linear, regardless of acoustic properties of duct nonuniformities which cause the mode conversions.
The construction of composition profiles from X-ray intensity bands was investigated. The intensity band-to-composition profile transformation utilizes a solution which can be easily evaluated. The technique can be applied to thin films and thick speciments for which the variation of lattice parameters, linear absorption coefficient, and reflectivity with composition are known. A deconvolution scheme with corrections for the instrumental broadening and ak-alfadoublet is discussed.
The Geostationary Operational Environmental Satellite (GOES)-8 experienced a series of orbital perturbations from autonomous attitude control thrusting before perigee raising maneuvers. These perturbations influenced differential correction orbital state solutions determined by the Goddard Space Flight Center (GSFC) Goddard Trajectory Determination System (GTDS). The maneuvers induced significant variations in the converged state vector for solutions using increasingly longer tracking data spans. These solutions were used for planning perigee maneuvers as well as initial estimates for orbit solutions used to evaluate the effectiveness of the perigee raising maneuvers. This paper discusses models for the incorporation of attitude thrust effects into the orbit determination process. Results from definitive attitude solutions are modeled as impulsive thrusts in orbit determination solutions created for GOES-8 mission support. Due to the attitude orientation of GOES-8, analysis results are presented that attempt to absorb the effects of attitude thrusting by including a solution for the coefficient of reflectivity, C(R). Models to represent the attitude maneuvers are tested against orbit determination solutions generated during real-time support of the GOES-8 mission. The modeling techniques discussed in this investigation offer benefits to the remaining missions in the GOES NEXT series. Similar missions with large autonomous attitude control thrusting, such as the Solar and Heliospheric Observatory (SOHO) spacecraft and the INTELSAT series, may also benefit from these results.
In writing the integral equations for the median mass diameter and number concentration, or comparable parameters of the raindrop size distribution, it is apparent that the forms of the equations for dual-polarization and dual-wavelength radar data are identical when attenuation effects are included. The differential backscattering and extinction coefficients appear in both sets of equations: for the dual-polarization equations, the differences are taken with respect to polarization at a fixed frequency while for the dual-wavelength equations, the differences are taken with respect to frequency at a fixed polarization. An alternative to the integral equation formulation is that based on the k-Z (attenuation coefficient-radar reflectivity factor) parameterization. This-technique was originally developed for attenuating single-wavelength radars, a variation of which has been applied to the TRMM Precipitation Radar data (PR). Extensions of this method have also been applied to dual-polarization data. In fact, it is not difficult to show that nearly identical equations are applicable as well to dualwavelength radar data. In this case, the equations for median mass diameter and number concentration take the form of coupled, but non-integral equations. Differences between this and the integral equation formulation are a consequence of the different ways in which attenuation correction is performed under the two formulations. For both techniques, the equations can be solved either forward from the radar outward or backward from the final range gate toward the radar. Although the forward-going solutions tend to be unstable as the attenuation out to the range of interest becomes large in some sense, an independent estimate of path attenuation is not required. This is analogous to the case of an attenuating single-wavelength radar where the forward solution to the Hitschfeld-Bordan equation becomes unstable as the attenuation increases. To circumvent this problem, the equations can be expressed in the form of a final-value problem so that the recursion begins at the far range gate and proceeds inward towards the radar. Solving the problem in this way traditionally requires estimates of path attenuation to the final gate: in the case of orthogonal linear polarizations, the attenuations at horizontal and vertical polarizations (same frequency) are required while in the dual-wavelength case, attenuations at the two frequencies (same polarization) are required.
Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.