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At least 937 records · Page 52

Design and Implementation of Satellite Formations and Constellations

The direction to develop small low cost spacecraft has led many scientists to recognize the advantage of flying spacecraft in constellations and formations to achieve the correlated instrument measurements formerly possible only by flying many instruments on a single large platform. Yet, constellations and formation flying impose additional complications on orbit selection and orbit maintenance, especially when each spacecraft has its own orbit or science requirements. The purpose of this paper is to develop an operational control method for maintenance of these missions. Examples will be taken from the Earth Observing-1 (EO-1) spacecraft that is part of the New Millennium Program (NMP) and from proposed Earth System Science Program Office (ESSPO) constellations. Results can be used to determine the appropriateness of constellations and formation flying for a particular case as well as the operational impacts. Applications to the ESSPO and NMP are highly considered in analysis and applications. After constellation and formation analysis is completed, implementation of a maneuver maintenance strategy becomes the driver. Advances in technology and automation by GSFC's Guidance, Navigation, and Control Center allow more of the burden of the orbit selection and maneuver maintenance to be automated and ultimately placed onboard the spacecraft, mitigating most of the associated operational concerns. This paper presents the GSFC closed-loop control method to fly in either constellations or formations through the use of an autonomous closed loop three-axis navigation control and innovative orbit maintenance support. Simulation results using AutoCon(Trademark) and FreeFlyer(Trademark) with various fidelity levels of modeling and algorithms are presented.

Folta, David↗

Geostationary Lightning Mapper for GOES-R and Beyond

The Geostationary Lightning Mapper (GLM) is a single channel, near-IR imager/optical transient event detector, used to detect, locate and measure total lightning activity over the full-disk as part of a 3-axis stabilized, geostationary weather satellite system. The next generation NOAA Geostationary Operational Environmental Satellite (GOES-R) series with a planned launch readiness in December 2014 will carry a GLM that will provide continuous day and night observations of lightning from the west coast of Africa (GOES-E) to New Zealand (GOES-W) when the constellation is fUlly operational. The mission objectives for the GLM are to 1) provide continuous, full-disk lightning measurements for storm warning and nowcasting, 2) provide early warning of tornadic activity, and 3) accumulate a long-term database to track decadal changes of lightning. The GLM owes its heritage to the NASA Lightning Imaging Sensor (1997-Present) and the Optical Transient Detector (1995-2000), which were developed for the Earth Observing System and have produced a combined 13 year data record of global lightning activity. Instrument formulation studies were completed in March 2007 and the implementation phase to develop a prototype model and up to four flight models will be underway in the latter part of 2007. In parallel with the instrument development, a GOES-R Risk Reduction Team and Algorithm Working Group Lightning Applications Team have begun to develop the Level 2 algorithms and applications. Proxy total lightning data from the NASA Lightning Imaging Sensor on the Tropical Rainfall Measuring Mission (TRMM) satellite and regional test beds (e.g., Lightning Mapping Arrays in North Alabama and the Washington DC Metropolitan area) are being used to develop the pre-launch algorithms and applications, and also improve our knowledge of thunderstorm initiation and evolution. Real time lightning mapping data are being provided in an experimental mode to selected National Weather Service (NWS) forecast offices in Southern and Eastern Region. This effort is designed to help improve our understanding of the application of these data in operational settings.

Goodman, Steven J.↗

Waterhammer Testing and Modeling of the Ares I Upper Stage Reaction Control System

NASA's Ares I rocket is the agency's first step in completing the goals of the Constellation Program, which plans to deliver a new generation of space explorers into low earth orbit for future missions to the International Space Station, the moon, and other destinations within the solar system. Ares I is a two-stage rocket topped by the Orion crew capsule and its service module. The launch vehicle's First Stage is a single, five-segment reusable solid rocket booster (RSRB), derived from the Space Shuttle Program's four segment RSRB. The vehicle's Upper Stage, being designed at Marshall Space Flight Center (MSFC), is propelled by a single J-2X Main Engine fueled with liquid oxygen and liquid hydrogen. During active Upper Stage flight of the Ares I launch vehicle, the Upper Stage Reaction Control System (US ReCS) will perform attitude control operations for the vehicle. The US ReCS will provide three-axis attitude control capability (roll, pitch, and yaw) for the Upper Stage while the J-2X is not firing and roll control capability while the engine is firing. Because of the requirements imposed upon the system, the design must accommodate rapid pulsing of multiple thrusters simultaneously to maintain attitude control. In support of these design activities and in preparation for Critical Design Review, analytical models of the US ReCS propellant feed system have been developed using the Thermal Hydraulic Library of MSC.EASY5 v.2008, herein referred to as EASY5. EASY5 is a commercially available fluid system modeling package with significant history of modeling space propulsion systems. In Fall 2009, a series of development tests were conducted at MSFC on a cold-flow test article for the US ReCS, herein referred to as System Development Test Article (SDTA). A subset of those tests performed were aimed at examining the effects of waterhammer on a flight-representative system and to ensure that those effects could be quantified with analytical models and incorporated into the design of the flight system. This paper presents an overview of the test article and the test approach, along with a discussion of the analytical modeling methodology. In addition, the results of that subset of development tests, along with analytical model pre-test predictions and post-test model correlations, will also be discussed in detail.

Williams, J. Hunter↗

Delayed entry of solar protons (E/p/ over 0.3 MeV) into the earth's magnetotail

The delayed entry of solar protons into the earth's magnetotail is studied using simultaneous observations from three earth-orbiting spacecraft of a number of interplanetary proton events which exhibited abrupt and relatively large discontinuities in intensity associated with magnetic field discontinuities. It is found that such protons have immediate access to the magnetosheath and that delay times increase discontinuously from essentially zero in the magnetosheath to tens of minutes as an observing point moves inward across the magnetopause. Well-defined delay times from 30 to 160 min occur for points interior to the magnetotail. The inferred entry points lie at downstream distances of 80-500 R(E). No discernible relationship is found between the direction and sense of the interplanetary magnetic field and the entry times in the northern and southern lobes of the magnetotail or the entry tiems at various distances from its central axis. These results favor some form of an open model of the magnetotail.

Van Allen, J. A.↗

Weyl semimetal in the rare-earth hexaboride family supporting a pseudonodal surface and a giant anomalous Hall effect

Rare-earth hexaborides offer a rich tapestry for exploring the interplay of topological orders, magnetism, and electron-correlation effects associated with protected quantum phenomena. Using first-principles modeling, we identify in cerium hexaboride (CeB 6 ) a topological state that harbors a pseudonodal surface (PNS) along with double-Weyl fermions. An analysis of the electronic states in the vicinity of the Fermi level reveals the presence of M z -mirror-symmetry-protected band crossings that involve itinerant (d) and localized (f) states of Ce. These band crossings are found to remain nearly gapless as one goes away from the mirror plane, driving the formation of PNS states. We also demonstrate the presence of coexisting double-Weyl fermions with chiral charges of ±2 on the C 4z rotational axis. By analyzing the Berry curvature field associated with the topological states, we predict that CeB 6 supports a giant anomalous Hall conductivity of -1840Ω -1 cm -1 in the slightly electron-doped regime, which would be larger than the values reported to date in magnetic Weyl semimetals. Our study thus indicates that CeB 6 , which combines ferromagnetic order with topological physics in a heavy-fermion matrix, would provide a promising playground for investigating topological magnetic states with giant anomalous Hall responses.

36 MATERIALS SCIENCE↗

Spacecraft stability and control

The Earth's first artificial satellite, Sputnik 1, slowly tumbled in orbit. The first U.S. satellite, Explorer 1, also tumbled out of control. Today, satellite stability and control has become a higher priority. For a satellite design that is to have a life expectancy of 14 years, appropriate spacecraft flight control systems will be reviewed, stability requirements investigated, and an appropriate flight control system recommended in order to see the design process. Disturbance torques, including aerodynamic, magnetic, gravity gradient, solar, micrometeorite, debris, collision, and internal torques, will be assessed to quantify the disturbance environment so that the required compensating torques can be determined. The control torques, including passive versus active, momentum control, bias momentum, spin stabilization, dual spin, gravity gradient, magnetic, reaction wheels, control moment gyros, inertia augmentation techniques, three-axis control, and reaction control systems (RCSs), will be considered. Conditions for stability will also be considered.

Barret, Chris↗

Spacecraft flight control system design selection process for a geostationary communication satellite

The Earth's first artificial satellite, Sputnik 1, slowly tumbled in orbit. The first U.S. satellite, Explorer 1, also tumbled out of control. Now, as we launch the Mars observer and the Cassini spacecraft, stability and control have become higher priorities. The flight control system design selection process is reviewed using as an example a geostationary communication satellite which is to have a life expectancy of 10 to 14 years. Disturbance torques including aerodynamic, magnetic, gravity gradient, solar, micrometeorite, debris, collision, and internal torques are assessed to quantify the disturbance environment so that the required compensating torque can be determined. Then control torque options, including passive versus active, momentum control, bias momentum, spin stabilization, dual spin, gravity gradient, magnetic, reaction wheels, control moment gyros, nutation dampers, inertia augmentation techniques, three-axis control, reactions control system (RCS), and RCS sizing, are considered. A flight control system design is then selected and preliminary stability criteria are met by the control gains selection.

Barret, C.↗

Reflexive obstacle avoidance for kinematically-redundant manipulators

Dexterous telerobots incorporating 17 or more degrees of freedom operating under coordinated, sensor-driven computer control will play important roles in future space operations. They will also be used on Earth in assignments like fire fighting, construction and battlefield support. A real time, reflexive obstacle avoidance system, seen as a functional requirement for such massively redundant manipulators, was developed using arm-mounted proximity sensors to control manipulator pose. The project involved a review and analysis of alternative proximity sensor technologies for space applications, the development of a general-purpose algorithm for synthesizing sensor inputs, and the implementation of a prototypical system for demonstration and testing. A 7 degree of freedom Robotics Research K-2107HR manipulator was outfitted with ultrasonic proximity sensors as a testbed, and Robotics Research's standard redundant motion control algorithm was modified such that an object detected by sensor arrays located at the elbow effectively applies a force to the manipulator elbow, normal to the axis. The arm is repelled by objects detected by the sensors, causing the robot to steer around objects in the workspace automatically while continuing to move its tool along the commanded path without interruption. The mathematical approach formulated for synthesizing sensor inputs can be employed for redundant robots of any kinematic configuration.

Karlen, James P.↗

Thermal balance testing of MSAT 2 spacecraft

The present work reports on the recently completed infrared thermal balance/thermal vacuum testing of a MSAT satellite, the first satellite to provide mobile communications service for all of continental North America. MSAT is a two spacecraft program, using a three-axis stabilized Hughes HS-601 series Bus as the vehicle for the Canadian designed Payload. The thermal tests which were performed at the Canadian Space Agency's David Florida Laboratory in Ottawa, Canada, lasted approximately 35 days. The infrared (IR) heating rig was designed to provide radiant heat inputs into seven spacecraft zones during Thermal Vacuum (TV) testing. The TV test was divided into multiple phases. It began with a thermal balance cold phase, followed by a thermal cold cycle and a hot balance phase, complemented by a thermal hot cycle to finish with a thermal cycle with continuous monitoring of the Bus and Payload. The spacecraft's external heat fluxes were provided by IR lamp sources. To ensure flux uniformity, highly reflective baffles and IR East and West faces; the Earth facing (Nadir); and the inside of the thrust cylinder. The aft-end panel heat fluxes were provided by a heated LN2 shroud. The radiation flux intensity on the spacecraft zones from the various rig elements was measured using Monitored Background Radiometers (MBR's) and compared with direct calculations and with pretest predictions. The temperature measurement system was based on Uniform Temperature References (UTR's) located inside the chamber such that all feedthroughs were copper-copper. This system was devised to achieve a temperature measurement accuracy of plus/minus 0.5 C for over 850 thermocouples used in the test. A PC-(QNX-based) based real-time data acquisition system was utilized to provide continuous monitoring of all channels based on a 30-second time scan. In addition, the data acquisition system was able to retrieve telemetry stream from the Satellite Test Equipments (STE) station for real-time data manipulation. Preliminary results showed the test to be successful from both the thermal balance side and the electrical testing side.

Samson, Serge↗

Lightning observations from space shuttle

The experimental program of the Earth Sciences and Applications Division at NASA/MSFC includes development of the Lightning Imaging Sensor (LIS) for the NOAA Earth Observing System (EOS) Polar Platform. The research plan is to use existing lightning information to generate simulated data for the LIS experiment. Navigation algorithms were used to transform pixel locations to latitude and longitude values. The simulated data would then be used to test and develop algorithms for the analysis of LIS data. Individual frames of video imagery obtained from Space Shuttle Missions provide the raw data for the simulation. Individual video frames were digitized to get the pixel locations of lightning flashes. The pixel locations will be used to locate the geographical position of the event. Because of a lack of detailed knowledge of camera orientation with respect to the Space Shuttle, video scenes that contain identifiable city lights were chosen for analysis. A method for locating the payload bay camera axis was developed and tested. Two measurements are needed: the pixel location of the apparent horizon and a timed siting of a known location passing the principal line of the image. Individual video frames were navigated and lightning illuminated clouds were located on the map. Satisfactory agreement in location was achieved for cities and LLP lightning locations. Ground truth measurements were compared to satellite observations. A vertical lightning event was identified on the horizon. Very low frequency (VLF) transmission on this particular occassion shows a strong response to negative cloud to cloud flashes.

Boeck, William L.↗

Thermally Altered Subsurface Material of Asteroid 162173 Ryugu

Studies of meteorite analysis and theoretical modeling have indicated the possibility that some carbonaceous near-Earth asteroids are thermally altered due to radiative heating during close approaches to the Sun in addition to parent body processes (Nakamura, 2005; Marchi et al., 2009; Chaumard et al., 2012). In April 2019, the Hayabusa2 mission successfully completed an artificial impact experiment on the carbonaceous near-Earth asteroid 162173 Ryugu (Arakawa et al., 2020), which provided an opportunity to investigate the effects of radiative heating through the exposed subsurface material. Here we report observations of the Ryugu’s subsurface material by the Near-Infrared Spectrometer (NIRS3) on the Hayabusa2 spacecraft. Spectra of the subsurface material exhibit a slightly stronger and peak-shifted hydroxyl absorption feature compared to that observed for the surface, indicating that space weathering and/or radiative heating caused a subtle change in the spectrum of Ryugu surface. However, the shape of the absorption feature still suggests that the subsurface material experienced heating above 300 ˚C similar to the surface. In contrast, our thermal modeling shows that radiative heating does not increase the subsurface temperature at 1 m depth above 200 ˚C even if the semimajor axis is reduced down to 0.344 au. This supports that the Ryugu material would have been preferentially altered due to radiogenic and/or impact heating on the parent body rather than radiative heating.

Asteroids↗

NASA's Soil Moisture Active and Passive (SMAP) Mission

The Soil Moisture Active-Passive (SMAP) Mission is one of the first Earth observation satellites being formulated by NASA in response to the 2007 National Research Council s Decadal Survey. SMAP will make global measurements of soil moisture at the Earth's land surface and its freeze-thaw state. These measurements will allow significantly improved estimates of water, energy and carbon transfers between the land and atmosphere. Soil moisture measurements are also of great importance in assessing flooding and monitoring drought. Knowledge gained from SMAP observations can help mitigate these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing over the boreal latitudes will also reduce a major uncertainty in quantifying the global carbon balance and help to resolve an apparent missing carbon sink over land. The SMAP mission concept will utilize an L-band radar and radiometer sharing a rotating 6-meter mesh reflector antenna flying in a 680 km polar orbit with an 8-day exact ground track repeat aboard a 3-axis stabilized spacecraft to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these surface observations with advanced modeling and data assimilation to provide estimates of deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP recently completed its Phase A Mission Concept Study Phase for NASA and transitioned into Phase B (Formulation and Detailed Design). A number of significant accomplishments occurred during this initial phase of mission development. The SMAP project held several open meetings to solicit community feedback on possible science algorithms, prepared preliminary draft Algorithm Theoretical Basis Documents (ATBDs) for each mission science product, and established a prototype algorithm testbed to enable testing and evaluation of the performance of candidate algorithms. SMAP conducted an Applications Workshop in September 2009 to coordinate with potential application users interested in the mission data. A draft Applications Plan describing the Project s planned outreach to potential applications users has been prepared and will be updated during Phase B. SMAP made a significant evaluation of the potential terrestrial radio frequency interference (RFI) source environment and established radiometer and radar flight hardware and ground processing mitigation approaches. SMAP finalized its science orbit and orbit injection approach to optimize launch mass and prepared launch and commissioning scenarios and timeline. A science data communications approach was developed to maximize available science data volume to improve science margins while maintaining moderately short data product latencies to support many potential applications using existing ground assets and with minimum impact to the flight system. SMAP developed rigid multi-body and flexible body dynamics and control models and system designs for the 6-meter rotating instrument reflector-boom assembly (RBA) and flight system to confirm pointing and control performance, and devised strategies to efficiently implement on-orbit balancing if needed. Industry partners were selected for the spin mechanism assembly (SMA) and RBA. Preliminary designs for the radar and radiometer were initiated, including constructing breadboards of key assemblies.

Kellogg, Kent↗

An Efficient Focal Plane Alignment Methodology with Application to the ASTERIA Nanosatellite Space Telescope

The process of aligning an instrument focal plane toprecursor optics such as a telescope can be a difficult and timeconsuming process. The final alignment must achieve sufficientperformance at multiple locations across the field of view. Inthe case of instruments with infinite conjugates, such as a spacetelescope, there are practical challenges in illuminating the system at multiple off-axis field points simultaneously. Iterationduring the alignment process can cause a lengthy search for localminima within the performance cost function.This paper presents a focal plane alignment methodology thatavoids the above difficulties and obtains the desired level ofoptical performance in an efficient manner. The approach isbased on systematically measuring spot size across a set of fieldpoints and defocus positions, and then using a least squaresfit to determine the optimal location for the focal plane. Thisapproach has the additional benefit of revealing the amount offield curvature present in the instrument. It also provides theanalyst with a direct calculation of the shims needed to place thefocal plane at the computed best-fit location.This approach was successfully applied to the Arcsecond SpaceTelescope Enabling Research In Astrophysics (ASTERIA) payload. ASTERIA is a cubesat mission that was deployed intolow-Earth orbit in November 2017 and operated until December2019. In addition to presenting the theoretical basis for themethodology, this paper will present laboratory measurementsobtained during the payload alignment campaign. This approach is applicable to future space-borne optical instrumentsthat require an efficient methodology for focal plane alignmentwith limited cost or schedule resources.

Smith, Matthew W↗

Voyager: Neptune Encounter Highlights

Voyager encounter data are presented in computer animation (CA) and real (R) animation. The highlights include a view of 2 full rotations of Neptune. It shows spacecraft trajectory 'diving' over Neptune and intercepting Triton's orbit, depicting radiation and occulation zones. Also shown are a renegade orbit of Triton and Voyager's encounter with Neptune's Magnetopause. A model of the spacecraft's complex maneuvers during close encounters of Neptune and Triton is presented. A view from Earth of Neptune's occulation experiment is is shown as well as a recreation of Voyager's final pass. There is detail of Voyager's Image Compensation technique which produces Voyager images. Eighteen images were produced on June 22 - 23, 1989, from 57 million miles away. A 68 day sequence which provides a stroboscopic view - colorization approximates what is seen by the human eye. Real time images recorded live from Voyager on 8/24/89 are presented. Photoclinometry produced the topography of Triton. Three images are used to create a sequence of Neptune's rings. The globe of Neptune and 2 views of the south pole are shown as well as Neptune rotating. The rotation of a scooter is frozen in images showing differential motion. There is a view of rotation of the Great Dark Spot about its own axis. Photoclinometry provides a 3-dimensional perspective using a color mosaic of Triton images. The globe is used to indicate the orientation of Neptune's crescent. The east and west plumes on Triton are shown.

Source record↗

Global Auroral Imaging for the Dynamics Explorer Mission

The two Dynamics Explorer spacecraft, DE-1 and DE-2, were launched on August 3, 1981, into polar coplanar orbits at different altitudes for the purpose of studying interactive processes within the atmosphere-ionosphere-magnetosphere system. The DE-1 spacecraft (high-altitude mission) used an elliptical orbit that was selected to allow: (1) measurements extending from the hot magnetospheric plasma through the plasmasphere to the cool ionosphere; (2) global auroral imaging, wave measurements in the heart of the magnetosphere, and crossing of auroral field lines at several earth radii; and (3) measurements for significant periods of time along a magnetic field flux tube. The orbit of Dynamics Explorer 1 offered an opportunity to obtain global images of Earth's dayglow and auroral luminosities and to acquire consecutive images of the entire auroral oval during the growth, onset, expansion, and recovery phases of substorms. The University of Iowa's Spin-scan Auroral Imaging (SAI) instrument, was on-board DE-1. SAI was activated in orbit and placed in routine operation on September 23, 1981, and has provided outstanding new contributions in the fields of auroral, magnetospheric and geocoronal physics, introduced a powerful tool for the study of global atmospheric ozone, and initiated the first search from space for marine bioluminescence on the surface of the global ocean. The SAI instrumentation consists of three imaging photometers, two for visible wavelengths and the third for vacuum-ultraviolet wavelengths equipped with primary catoptric optics with superpolished mirror surfaces. The primary focusing element is an off-axis section of a parabolic mirror that is used to provide an optical path completely free of support structures for the mirrors.

Frank, L. A.↗

Simple Laser Communications Terminal for Downlink from Earth Orbit at Rates Exceeding 10 Gb/s

A compact, low-cost laser communications transceiver was prototyped for downlinking data at 10 Gb/s from Earth-orbiting spacecraft. The design can be implemented using flight-grade parts. With emphasis on simplicity, compactness, and light weight of the flight transceiver, the reduced-complexity design and development approach involves: 1. A high-bandwidth coarse wavelength division multiplexed (CWDM) (4 2.5 or 10-Gb/s data-rate) downlink transmitter. To simplify the system, emphasis is on the downlink. Optical uplink data rate is modest (due to existing and adequate RF uplink capability). 2. Highly simplified and compact 5-cm diameter clear aperture optics assembly is configured to single transmit and receive aperture laser signals. About 2 W of 4-channel multiplexed (1,540 to 1,555 nm) optically amplified laser power is coupled to the optical assembly through a fiber optic cable. It contains a highly compact, precision-pointing capability two-axis gimbal assembly to coarse point the optics assembly. A fast steering mirror, built into the optical path of the optical assembly, is used to remove residual pointing disturbances from the gimbal. Acquisition, pointing, and tracking are assisted by a beacon laser transmitted from the ground and received by the optical assembly, which will allow transmission of a laser beam. 3. Shifting the link burden to the ground by relying on direct detection optical receivers retrofitted to 1-m-diameter ground telescopes. 4. Favored mass and volume reduction over power-consumption reduction. The two major variables that are available include laser transmit power at either end of the link, and telescope aperture diameter at each end of the link. Increased laser power is traded for smaller-aperture diameters. 5. Use of commercially available spacequalified or qualifiable components with traceability to flight qualification (i.e., a flight-qualified version is commercially available). An example is use of Telecordia-qualified fiber optic communication components including active components (lasers, amplifiers, photodetectors) that, except for vacuum and radiation, meet most of the qualifications required for space. 6. Use of CWDM technique at the flight transmitter for operation at four channels (each at 2.5 Gb/s or a total of 10 Gb/s data rate). Applying this technique allows utilization of larger active area photodetectors at the ground station. This minimizes atmospheric scintillation/turbulence induced losses on the received beam at the ground terminal. 7. Use of forward-error-correction and deep-interleaver codes to minimize atmospheric turbulence effects on the downlink beam. Target mass and power consumption for the flight data transmitter system is less than 10 kg and approximately 60 W for the 400-km orbit (900-km slant range), and 12 kg and 120 W for the 2,000-km orbit (6,000-km slant range). The higher mass and power for the latter are the result of employing a higher-power laser only.

Kovalik, Joseph M.↗

On the nature of the radial and cross track errors for artificial earth satellites

The paper discusses the analysis of the radial and cross track errors of artificial earth satellites in terms of the interference of two one-dimensional celestial mechanical wave trains. The resulting equations for these tracking errors describe the behavior of the uncertainties in the orbital parameters as oscillatory in nature, with a rapidly oscillating term, which is a function of the sum of the observed and computed orbital frequencies, modulated in amplitude by a slowly varying oscillation. This latter term is itself a function of either the difference between these orbital frequencies or between the values of the computed and observed right ascensions, depending upon whether it is the radial or cross track case under consideration. Results indicate that the cross track calculation describes the behavior of uncertainties in the right ascension of the ascending node and the inclination, while the radial calculation gives information on uncertainties in the semi-major axis, the eccentricity, and the argument of perigee.

Bonavito, N. L.↗

On the nature of the radial and cross track errors for artificial earth satellites

The analysis of the radial and cross track errors of artificial earth satellites is discussed in terms of the interference of two one-dimensional celestial mechanical wave trains. Resulting equations for these tracking errors describe the behavior of the uncertainties in the orbital parameters as oscillatory in nature, with a rapidly oscillating term, which is a function of the sum of the observed and computed orbital frequencies, modulated in amplitude by a slowly varying oscillation. This latter term is itself a function of either the difference between these orbital frequencies or between the values of the computed and observed right ascensions, depending upon whether it is the radial or cross track case under consideration. These results indicate that the cross track calculation describes the behavior of uncertainties in the right ascension of the ascending node and the inclination, while the radial calculation gives information on uncertainties in the semi-major axis, the eccentricity, and the argument of perigee. In addition, expressions for the radial and cross track oscillatory frequencies are obtained in terms of the orbital frequencies of the satellites. Data show that the time average of the radial and cross track errors in any case, will both approach zero.

Bonavito, N. L.↗