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At least 325 records · Page 18

Interferometric Characterization of the Earth's Atmosphere from Lagrange Point 2

Part of the NASA plans for future Earth Science missions calls for observations using novel vantage points that can produce science products otherwise unobtainable. Observations of the Earth from the Lagrange-2 point, L-2, (1.5 million km behind the Earth on the Earth-Sun line) affords a unique vantage point for atmospheric science. Spectral observation of the Earth's atmosphere using solar occultation techniques in the near infrared (1 to 4 microns) provides one of the most accurate methods of passively sensing attitude profiles of the major species (CO2, O3, O2, CH4, H2O N2O). While traditional polar orbiting occultation measurements can obtain about 14 measurements per day (2 per orbit), solar occultation observations from the Lagrange-2 point will yield hourly profile measurements at all latitudes. The expected spatial resolution is 2 km in altitude, 0.5 degrees in latitude, and 2 degrees in longitude. The result from 24 hours of observations will be a three-dimensional map of atmospheric composition. To accomplish this task from L-2 requires the development of a large moderate spectral resolution instrument whose entrance aperture is about 10 meters. Use of a standard telescope design with a 10-meter circular mirror or a 10-meter strip mirror would be prohibitively expensive and excessively massive. Instead, we are proposing the development of a 10-meter linear interferometer coupled to a Fourier transform imaging spectrometer. The result will be a highly efficient design with sufficient sensitivity, while having both spatial and spectral resolution to produce the desired results. Preliminary calculations show that seven species (CO2, O3, O2, CH4, H2O N2O) have clearly separated spectral features in the I to 4 microns range with sufficient absorption to produce profile information from near the Earth's surface to the middle stratosphere. For CO2 the estimated sensitivity to change is 0.33% or 1 part in 330. This should be sufficient to detect changes that are significant for the carbon cycle studies. Initial instrument design studies are underway to determine the optimum optical design for the interferometer-spectrometer as well as the necessary highly stable mechanical designs. Separate design studies are being conducted for the spacecraft. shuttle launch facility, low-light solar power design, thermal control, and unique navigation requirements to reach and maintain the tight halo orbit about L-2.

Herman, Jay R.↗

Triana Safehold: A New Gyroless, Sun-Pointing Attitude Controller

Triana is a single-string spacecraft to be placed in a halo orbit about the sun-earth Ll Lagrangian point. The Attitude Control Subsystem (ACS) hardware includes four reaction wheels, ten thrusters, six coarse sun sensors, a star tracker, and a three-axis Inertial Measuring Unit (IMU). The ACS Safehold design features a gyroless sun-pointing control scheme using only sun sensors and wheels. With this minimum hardware approach, Safehold increases mission reliability in the event of a gyroscope anomaly. In place of the gyroscope rate measurements, Triana Safehold uses wheel tachometers to help provide a scaled estimation of the spacecraft body rate about the sun vector. Since Triana nominally performs momentum management every three months, its accumulated system momentum can reach a significant fraction of the wheel capacity. It is therefore a requirement for Safehold to maintain a sun-pointing attitude even when the spacecraft system momentum is reasonably large. The tachometer sun-line rate estimation enables the controller to bring the spacecraft close to its desired sun-pointing attitude even with reasonably high system momentum and wheel drags. This paper presents the design rationale behind this gyroless controller, stability analysis, and some time-domain simulation results showing performances with various initial conditions. Finally, suggestions for future improvements are briefly discussed.

Chen, J.↗

Theoretical Analysis of Thermodynamic Measurements near a Liquid-Gas Critical Point

Over the years, many ground-based studies have been performed near liquid-gas critical points to elucidate the expected divergences in thermodynamic quantities. The unambiguous interpretation of these studies very near the critical point is hindered by a gravity-induced density stratification. However, these ground-based measurements can give insight into the crossover behavior between the asymptotic critical region near the transition and the mean field region farther away. We have completed a detailed analysis of heat capacity, susceptibility and coexistence curve measurements near the He-3 liquid-gas critical point using the minimal-subtraction renormalization (MSR) scheme within the phi(exp 4) model. This MSR scheme, using only two adjustable parameters, provides a reasonable global fit to all of these experimental measurements in the gravity-free region out to a reduced temperature of |t| approx. 2x10(exp -2). Recently this approach has also been applied to the earlier microgravity measurements of Haupt and Straub in SF(sub 6) with surprising results. The conclusions drawn from the MSR analyses will be presented. Measurements in the gravity-affected region closer to the He-3 critical point have also been analyzed using the recent crossover parametric model (CPM) of the equation-of-state. The results of fitting heat capacity measurements to the CPM model along the He-3 critical isochore in the gravity-affected region will also be presented.

Barmatz, M.↗

High gain antenna pointing on the Mars Exploration Rovers

This paper describes the algorithm used to point the high gain antennae on NASA/JPL's Mars Exploration Rovers. The gimballed antennae must track the Earth as it moves across the Martian sky during communication sessions. The algorithm accounts for (1) gimbal range limitations, (2) obstructions both on the rover and in the surrounding environment, (3) kinematic singularities in the gimbal design, and (4) up to two joint-space solutions for a given pointing direction. The algorithm computes the intercept-times for each of the occlusions and chooses the jointspace solution that provides the longest track time before encountering an occlusion. Upon encountering an occlusion, the pointing algorithm automatically switches to the other joint-space solution if it is not also occluded. The algorithm has successfully provided flop-free pointing for both rovers throughout the mission.

motion planning↗

Radio Point Sources Toward Galaxy Clusters at 30 GHz

Extra-galactic point sources are a significant contaminant in cosmic microwave background and Sunyaev-Zel'dovich effect experiments. Deep interferometric observations with the BIMA and OVRO arrays are used to characterize the spatial, spectral, and flux distributions of radio point sources toward galaxy clusters at 28.5 GHz. We compute counts of mJy point source fluxes from 90 fields centered on known massive galaxy clusters and 8 non-cluster fields. Counts in the non-cluster fields are consistent with extrapolations from the results of other surveys. We also compute counts towards clusters as a function of luminosity in three redshift bins out to z = 1.0 and see no clear evidence for evolution with redshift. We compute spectral indices of mJy sources in cluster fields between 1.4 and 28.5 GHz. The distribution is skewed, with a median spectral index of 0.76 and 25th and 75th percentiles of 0.55 and 0.95, respectively. This is steeper than the spectral indices of brighter field point sources measured by other surveys.

Coble, K.↗

Apparatus and method using a holographic optical element for converting a spectral distribution to image points

A holographic optical element transforms a spectral distribution of light to image points. The element comprises areas, each of which acts as a separate lens to image the light incident in its area to an image point. Each area contains the recorded hologram of a point source object. The image points can be made to lie in a line in the same focal plane so as to align with a linear array detector. A version of the element has been developed that has concentric equal areas to match the circular fringe pattern of a Fabry-Perot interferometer. The element has high transmission efficiency, and when coupled with high quantum efficiency solid state detectors, provides an efficient photon-collecting detection system. The element may be used as part of the detection system in a direct detection Doppler lidar system or multiple field of view lidar system.

McGill, Matthew J.↗

Pointing compensation system for spacecraft instruments

A closed loop system reduces pointing errors in one or more spacecraft instruments. Associated with each instrument is a electronics package (3) for commanding motion in that instrument and a pointing control system (5) for imparting motion in that instrument in response to a command (4) from the commanding package (3). Spacecraft motion compensation logic (25) compensates for instrument pointing errors caused by instrument-motion-induced spacecraft motion. Any finite number of instruments can be so compensated, by providing each pointing control system (5) and each commanding package (3), for the instruments desired to be compensated, with a link to the spacecraft motion compensation logic (25). The spacecraft motion compensation logic (25) is an electronic manifestation of the algebraic negative of a model of the dynamics of motion of the spacecraft. An example of a suitable model, and computer-simulated results, are presented.

Plescia, Carl T.↗

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗

A General Closed-Form Solution for the Lunar Reconnaissance Orbiter (LRO) Antenna Pointing System

The National Aeronautics and Space Administration s (NASA) Lunar Reconnaissance Orbiter (LRO) launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle into a direct insertion trajectory to the Moon LRO, designed, built, and operated by the NASA Goddard Space Flight Center in Greenbelt, MD, is gathering crucial data on the lunar environment that will help astronauts prepare for long-duration lunar expeditions. During the mission s nominal life of one year its six instruments and one technology demonstrator will find safe landing site, locate potential resources, characterize the radiation environment and test new technology. To date, LRO has been operating well within the bounds of its requirements and has been collecting excellent science data images taken from the LRO Camera Narrow Angle Camera (LROC NAC) of the Apollo landing sites have appeared on cable news networks. A significant amount of information on LRO s science instruments is provided at the LRO mission webpage. LRO s Attitude Control System (ACS), in addition to controlling the orientation of the spacecraft is also responsible for pointing the High Gain Antenna (HGA). A dual-axis (or double-gimbaled) antenna, deployed on a meter-long boom, is required to point at a selected Earth ground station. Due to signal loss over the distance from the Moon to Earth, pointing precision for the antenna system is very tight. Since the HGA has to be deployed in spaceflight, its exact geometry relative to the spacecraft body is uncertain. In addition, thermal distortions and mechanical errors/tolerances must be characterized and removed to realize the greatest gain from the antenna system. These reasons necessitate the need for an in-flight calibration. Once in orbit around the moon, a series of attitude maneuvers was conducted to provide data needed to determine optimal parameters to load onboard, which would account for the environmental and mechanical errors at any antenna orientation. The nominal geometry for the HGA involves an outer gimbal axis that is exactly perpendicular to the inner gimbal axis, and a target direction that is exactly perpendicular to the outer gimbal axis. For this nominal geometry, closed-form solutions of the desired gimbal angles are simple to get for a desired target direction specified in the spacecraft body fame. If the gimbal axes and the antenna boresight are slightly misaligned, the nominal closed-form solution is not sufficiently accurate for computing the gimbal angles needed to point at a target. In this situation, either a general closed-form solution has to be developed for a mechanism with general geometries, or a correction scheme has to be applied to the nominal closed-form solutions. The latter has been adopted for Solar Dynamics Observatory (SDO) as can be seen in Reference 1, and the former has been used for LRO. The advantage of the general closed-form solution is the use of a small number of parameters for the correction of nominal solutions, especially in the regions near singularities. Singularities here refer to cases when the nominal closed-form solutions have two or more solutions. Algorithm complexity, however, is the disadvantage of the general closed-form solution.

Shah, Neerav↗

Automatic Identification of Solar X-Ray Bright Points in Hinode X-Ray Data

We have automated a method that is used to find point sources in Chandra X-ray telescope data, to identify solar bright points in Hinode X-ray data. This tool, called lextrct, first identifies candidate sources that are brighter than the surrounding background. The algorithm also allows selected pixels to be excluded from the source-finding, thus allowing saturated pixels (from flares and/or active regions) to be ignored. We then use lextrct to fit the sources to two-dimensional, elliptical Gaussians. The size and orientation give an approximation of the shape of the bright points. We are in the process of analyzing observations through the Al_poly filter with a four-second exposure time, to obtain a catalogue of bright points, which will include their sizes, lifetimes, intensities, and position on the solar disk

Adams, M. L.↗

Portable Dew Point Mass Spectrometry System for Real-Time Gas and Moisture Analysis

A portable instrument incorporates both mass spectrometry and dew point measurement to provide real-time, quantitative gas measurements of helium, nitrogen, oxygen, argon, and carbon dioxide, along with real-time, quantitative moisture analysis. The Portable Dew Point Mass Spectrometry (PDP-MS) system comprises a single quadrupole mass spectrometer and a high vacuum system consisting of a turbopump and a diaphragm-backing pump. A capacitive membrane dew point sensor was placed upstream of the MS, but still within the pressure-flow control pneumatic region. Pressure-flow control was achieved with an upstream precision metering valve, a capacitance diaphragm gauge, and a downstream mass flow controller. User configurable LabVIEW software was developed to provide real-time concentration data for the MS, dew point monitor, and sample delivery system pressure control, pressure and flow monitoring, and recording. The system has been designed to include in situ, NIST-traceable calibration. Certain sample tubing retains sufficient water that even if the sample is dry, the sample tube will desorb water to an amount resulting in moisture concentration errors up to 500 ppm for as long as 10 minutes. It was determined that Bev-A-Line IV was the best sample line to use. As a result of this issue, it is prudent to add a high-level humidity sensor to PDP-MS so such events can be prevented in the future.

Arkin, C.↗

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗

Using Spare Logic Resources To Create Dynamic Test Points

A technique has been devised to enable creation of a dynamic set of test points in an embedded digital electronic system. As a result, electronics contained in an application specific circuit [e.g., gate array, field programmable gate array (FPGA)] can be internally probed, even when contained in a closed housing during all phases of test. In the present technique, the test points are not fixed and limited to a small number; the number of test points can vastly exceed the number of buffers or pins, resulting in a compact footprint. Test points are selected by means of spare logic resources within the ASIC(s) and/or FPGA(s). A register is programmed with a command, which is used to select the signals that are sent off-chip and out of the housing for monitoring by test engineers and external test equipment. The register can be commanded by any suitable means: for example, it could be commanded through a command port that would normally be used in the operation of the system. In the original application of the technique, commanding of the register is performed via a MIL-STD-1553B communication subsystem.

Katz, Richard↗

Analysis of Screen Channel LAD Bubble Point Tests in Liquid Oxygen at Elevated Temperature

The purpose of this paper is to examine the key parameters that affect the bubble point pressure for screen channel Liquid Acquisition Devices in cryogenic liquid oxygen at elevated pressures and temperatures. An in depth analysis of the effect of varying temperature, pressure, and pressurization gas on bubble point is presented. Testing of a 200 x 1400 and 325 x 2300 Dutch Twill screen sample was conducted in the Cryogenics Components Lab 7 facility at the NASA Glenn Research Center in Cleveland, Ohio. Test conditions ranged from 92 to 130K and 0.138 - 1.79 MPa. Bubble point is shown to be a strong function of temperature with a secondary dependence on pressure. The pressure dependence is believed to be a function of the amount of evaporation and condensation occurring at the screen. Good agreement exists between data and theory for normally saturated liquid but the model generally under predicts the bubble point in subcooled liquid. Better correlation with the data is obtained by using the liquid temperature at the screen to determine surface tension of the fluid, as opposed to the bulk liquid temperature.

Hartwig, Jason↗

Micro-Fresnel Zone Plate Optical Devices Using Densely Accumulated Ray Points

An embodiment generally relates to an optical device suitable for use with an optical medium for the storage and retrieval of data. The optical device includes an illumination means for providing a beam of optical radiation of wavelength .lamda. and an optical path that the beam of optical radiation follows. The optical device also includes a diffractive optical element defined by a plurality of annular sections. The plurality of annular sections having a first material alternately disposed with a plurality of annular sections comprising a second material. The diffractive optical element generates a plurality of focal points and densely accumulated ray points with phase contrast phenomena and the optical medium is positioned at a selected focal point or ray point of the diffractive optical element.

Choi, Sang H.↗

Development of an Open Rotor Cycle Model in NPSS Using a Multi-Design Point Approach

NASA's Environmentally Responsible Aviation Project and Subsonic Fixed Wing Project are focused on developing concepts and technologies which may enable dramatic reductions to the environmental impact of future generation subsonic aircraft (Refs. 1 and 2). The open rotor concept (also referred to as the Unducted Fan or advanced turboprop) may allow the achievement of this objective by reducing engine emissions and fuel consumption. To evaluate its potential impact, an open rotor cycle modeling capability is needed. This paper presents the initial development of an open rotor cycle model in the Numerical Propulsion System Simulation (NPSS) computer program which can then be used to evaluate the potential benefit of this engine. The development of this open rotor model necessitated addressing two modeling needs within NPSS. First, a method for evaluating the performance of counter-rotating propellers was needed. Therefore, a new counter-rotating propeller NPSS component was created. This component uses propeller performance maps developed from historic counter-rotating propeller experiments to determine the thrust delivered and power required. Second, several methods for modeling a counter-rotating power turbine within NPSS were explored. These techniques used several combinations of turbine components within NPSS to provide the necessary power to the propellers. Ultimately, a single turbine component with a conventional turbine map was selected. Using these modeling enhancements, an open rotor cycle model was developed in NPSS using a multi-design point approach. The multi-design point (MDP) approach improves the engine cycle analysis process by making it easier to properly size the engine to meet a variety of thrust targets throughout the flight envelope. A number of design points are considered including an aerodynamic design point, sea-level static, takeoff and top of climb. The development of this MDP model was also enabled by the selection of a simple power management scheme which schedules propeller blade angles with the freestream Mach number. Finally, sample open rotor performance results and areas for further model improvements are presented.

Hendricks, Eric S.↗

Method for Measuring Collimator-Pointing Sensitivity to Temperature Changes

For a variety of applications, it is important to measure the sensitivity of the pointing of a beam emerging from a collimator, as a function of temperature changes. A straightforward method for carrying out this measurement is based on using interferometry for monitoring the changes in beam pointing, which presents its own problems. The added temperature dependence and complexity issues relating to using an interferometer are addressed by not using an interferometer in the first place. Instead, the collimator is made part of an arrangement that uses a minimum number of low-cost, off-the-shelf materials and by using a quad diode to measure changes in beam pointing. In order to minimize the influence of the test arrangement on the outcome of the measurement, several steps are taken. The collimator assembly is placed on top of a vertical, 1-m-long, fused silica tube. The quad diode is bonded to a fused silica bar, which, in turn, is bonded to the lower end of the fused silica tube. The lower end of the tube rests on a self-aligning support piece, while the upper end of the tube is kept against two rounded setscrew tips, using a soft rubber string. This ensures that very little stress is applied to the tube as the support structure changes dimensions due to thermal expansion. Light is delivered to the collimator through a bare fiber in order to minimize variable bending torque caused by a randomly relaxing, rigid fiber jacket. In order to separate the effect of temperature on the collimator assembly from the effect temperature has on the rest of the setup, multiple measurements are taken with the collimator assembly rotated from measurement to measurement. Laboratory testing, with 1-m spacing between the collimator and the quad diode, has shown that the sensitivity of the arrangement is better than 100 nm rms, over time spans of at least one hour, if the beam path is protected from atmospheric turbulence by a tube. The equivalent sensitivity to detecting changes in pointing angle is 100 nanoradians.

Abramovici, Alex↗

An Error Analysis of the Phased Array Antenna Pointing Algorithm for STARS Flight Demonstration No. 2

STARS is a multicenter NASA project to determine the feasibility of using space-based assets, such as the Tracking and Data Relay Satellite System (TDRSS) and Global Positioning System (GPS), to increase flexibility (e.g. increase the number of possible launch locations and manage simultaneous operations) and to reduce operational costs by decreasing the need for ground-based range assets and infrastructure. The STARS project includes two major systems: the Range Safety and Range User systems. The latter system uses broadband communications (125 kbps to 500 kbps) for voice, video, and vehicle/payload data. Flight Demonstration #1 revealed the need to increase the data rate of the Range User system. During Flight Demo #2, a Ku-band antenna will generate a higher data rate and will be designed with an embedded pointing algorithm to guarantee that the antenna is pointed directly at TDRS. This algorithm will utilize the onboard position and attitude data to point the antenna to TDRS within a 2-degree full-angle beamwidth. This report investigates how errors in aircraft position and attitude, along with errors in satellite position, propagate into the overall pointing vector.

Carney, Michael P.↗