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Highlights of TOMS Version 9 Total Ozone Algorithm

The fundamental basis of TOMS total ozone algorithm was developed some 45 years ago by Dave and Mateer. It was designed to estimate total ozone from satellite measurements of the backscattered UV radiances at few discrete wavelengths in the Huggins ozone absorption band (310-340 nm). Over the years, as the need for higher accuracy in measuring total ozone from space has increased, several improvements to the basic algorithms have been made. They include: better correction for the effects of aerosols and clouds, an improved method to account for the variation in shape of ozone profiles with season, latitude, and total ozone, and a multi-wavelength correction for remaining profile shape errors. These improvements have made it possible to retrieve total ozone with just 3 spectral channels of moderate spectral resolution (approx. 1 nm) with accuracy comparable to state-of-the-art spectral fitting algorithms like DOAS that require high spectral resolution measurements at large number of wavelengths. One of the deficiencies of the TOMS algorithm has been that it doesn't provide an error estimate. This is a particular problem in high latitudes when the profile shape errors become significant and vary with latitude, season, total ozone, and instrument viewing geometry. The primary objective of the TOMS V9 algorithm is to account for these effects in estimating the error bars. This is done by a straightforward implementation of the Rodgers optimum estimation method using a priori ozone profiles and their error covariances matrices constructed using Aura MLS and ozonesonde data. The algorithm produces a vertical ozone profile that contains 1-2.5 pieces of information (degrees of freedom of signal) depending upon solar zenith angle (SZA). The profile is integrated to obtain the total column. We provide information that shows the altitude range in which the profile is best determined by the measurements. One can use this information in data assimilation and analysis. A side benefit of this algorithm is that it is considerably simpler than the present algorithm that uses a database of 1512 profiles to retrieve total ozone. These profiles are tedious to construct and modify. Though conceptually similar to the SBUV V8 algorithm that was developed about a decade ago, the SBUV and TOMS V9 algorithms differ in detail. The TOMS algorithm uses 3 wavelengths to retrieve the profile while the SBUV algorithm uses 6-9 wavelengths, so TOMS provides less profile information. However both algorithms have comparable total ozone information and TOMS V9 can be easily adapted to use additional wavelengths from instruments like GOME, OMI and OMPS to provide better profile information at smaller SZAs. The other significant difference between the two algorithms is that while the SBUV algorithm has been optimized for deriving monthly zonal means by making an appropriate choice of the a priori error covariance matrix, the TOMS algorithm has been optimized for tracking short-term variability using month and latitude dependent covariance matrices.

Bhartia, Pawan↗

High Momentum Transfer Nucleon Elastic Electromagnetic Form Factor Measurements Using Super BigBite Spectrometer at Jefferson Lab

The nucleons - protons and neutrons - are the basic building blocks of atomic nuclei. We now know that the nucleon consists of fundamental particles called quarks and gluons. The quarks interact with each other by exchanging gluons via the strong interaction. Understanding the quark-gluon structure of the nucleon, especially the confinement of quarks within the nucleon in its ground state, remains one of the main unsolved puzzles of particle physics. The nucleon electromagnetic form factors are directly related to the internal structure of the nucleon. A new generation of high precision experiments, GEp-V, GEn-II, GEn-RP, and GMn, measuring the ground state nucleon space-like electro-magnetic form factor at high momentum transfer is underway at Jefferson Lab experimental Hall-A as part of the Super Bigbite Spectrometer (SBS) program. This series of experiments will provide a new level of understanding of the nucleon structure. These experiments are highly demanding due to the extremely fast drop off of the elastic cross section with the increasing four-momentum transfer squared(Q2). This thesis provides an overview of the SBS physics program and reports on the extensive R&D program carried out to achieve the high rate running conditions essential for carrying out the SBS experiments. SBS will provide an intermediate solid angle of approximately 35 msr, which is significantly larger than the solid angle of other dipole based spectrometers at Jefferson lab. Of course, there are much larger acceptance spectrometers at Jefferson Lab, CLAS12 for example. What is special about SBS is that it provides a sizable acceptance while operating at the highest possible luminosity at Jefferson Lab. With this combination of medium acceptance and the highest available luminosity, SBS provides an unparalleled opportunity to explore the nucleon in its ground state with unprecedented resolution. The relatively large acceptance of SBS is achieved by using a large gap dipole magnet and placing it close to the target. An unavoidable consequence of this is that the SBS GEM trackers and other detectors have a clear line-of-sight view of the target and a portion of the beam-line. As a result, the background hit rate in the SBS front GEM trackers is expected to be up to 500 kHz/cm2, over the entire active area of 6000 cm2. To the best of our knowledge, this extremely high rate over such a large area is unprecedented in any particle tracking system used anywhere in the world before. Correctly reconstructing the particle tracks of interest in this very high background environment is achieved by using especially adapted high rate techniques at every step of the tracking process: optimizing the GEM module and tracker design at the hardware level, using high bandwidth electronics and real time Field Programmable Gate Array (FPGA) based background suppression techniques at the Data Acquisition (DAQ) level, and developing highly specialized tracking algorithms to pick out the signal hits from among the vast amount of background hits. In order to ensure a smooth start and running of the SBS experiments, it is extremely crucial that these techniques are developed, implemented, and tested under realistic conditions well before the actual start of the SBS experimental program. A detailed Geant4 simulation of the experiment was combined with a digitization package to generate the detector level pseudodata similar to what is expected in the actual experiments. The digitization procedures were calibrated against actual GEM data from cosmic-ray runs, X-ray tests, beam test runs in experimental Hall-A, and the PRad experiment in Hall B. Then, optimized tracking algorithms were developed and implemented in an analysis program used to analyze these pseudo-data and to extract expected high-level parameters. These extracted quantities were then compared with the input parameters from the simulation to verify and determine the performance characteristics for the SBS tracker. From this work, a final tracking efficiency of 69% at 25% occupancy was achieved, with the required reconstruction accuracy, for the GMn experiment, the first experiment in the SBS program, with background level at 100 kHz/cm2. These demonstrated parameters are adequate for the successful running of not only the GMn experiment but as well as for GEn-RP and GEn-II experiments, the second and third experiments in the program. This work builds the solid ground to further improve the tracking performance for these experiments and achieve similar conditions for the running of the GEp-V experiment, the most demanding experiment in the SBS program, with an expected background level at 500 kHz/cm2.

Di, Danning↗

Lunar Plant Experiment: Testing Plant Germination in Lunar Gravity and Ionizing Radiation

We present an open design for a first plant growth module on the Moon (LPX). The primary science goal of lunar habitat is to investigate germination and initial plant growth when subject to the combined effects of lunar gravity and lunar surface radiation. The LPX module has been designed to be a flexible base unit that can be adapted to fly to the lunar surface on a variety of landers and rovers. LPX has size and shape of a 1 Unit CubeSat (10 centimeters on a side) and a total mass of 0.3 kilograms. The base will contain a seed module holding around 50 Arabidopsis seeds and provide approximately 0.5 liters of normal air at standard pressure. By the action of a small pump, water will be released after landing to initiate germination. Images will document the germination, initial growth, phototropism, and circumnutation of the small plants while sunlight remains available. A CO2 sensor tracks the release of CO2 during germination and the subsequent uptake of CO2 by photosynthesis. Simulations indicate that the CO2 peak level will be an increase by 2250 parts per million after 2 earth-days and then decline to about 1000 parts per million after 7 earth-days. The camera and CO2 sensor interfaces are USB. The water pump initiation requires a 5-volt signal. After initiation of germination by the addition of water, the habitat must be maintained above 22 degrees Centigrade to allow for plant growth and below 27 degrees Centigrade to prevent damage to the plants. This relatively tight temperature tolerance will require thermal control systems using reflecting surfaces and insulation that must be specifically designed for each lander or rover. The plant growth unit will function to tilt angles of 20 degrees along any axis. Total image data volume required to gauge the plant growth rate and leaf area is 1 megabyte (minimum data required) to 40 megabytes (preferred data). The lid of the habitat will allow adequate sunlight for plant growth. To provide for optimum growth, light levels in the plant growth stage need to be between 75 and 150 micromoles per meter squared per second interval.

first plant growth↗

Sky-Scanning Sun-Tracking Airborne Radiometer (3STAR): Instrument Design, Flight Testing, and Tracking Performance

The Sky-Scanning, Sun-Tracking Airborne Radiometer (3STAR) adapts commercial radiometer technology developed for the ocean color research community to airborne measurement of spectrally resolved solar irradiance and sky radiance. These atmospheric observations are used to derive aerosol optical depth (AOD), supporting localized AOD inputs for atmospheric correction of satellite and airborne data over terrestrial and aquatic (including optically dark) targets. The ability to regionally “tune” atmospheric correction schemes with relevant spatial AOD supports constraining atmospheric correction of remote sensing reflectance. Very wide dynamic range has been achieved for multi-channel band-pass-filter-radiometers originally designed for deployment into the water column. By actively tracking and directly pointing to the Sun, the light attenuation by aerosol particles in the atmospheric column can be quantified. These measurements improve knowledge of atmospheric constituents and the atmospheric corrections required to improve remote sensing capabilities for interpreting reflectance measurements from the Earth surface. 3STAR incorporates a custom Sun-tracking/sky-scanning pointing head, a Sun-tracking camera, and a commercially available, cylindrical, 19-channel radiometer tube assembly. An accurate and responsive mount and tracking system has been developed and certified to NASA and Naval Air Systems Command (NAVAIR) airworthiness standards for deployment into the aircraft slipstream. Ground and flight testing indicate typical tracking errors of less than 0.1 degrees, well within the field of view of the radiometer as required to minimize measurement uncertainty from alignment error. Preliminary AOD measurements compare to within 0.013 with 15 measurements from an Aerosol Robotic Network (AERONET) Cimel instrument at 500 nm wavelength and low solar angle.

Atmosphere↗

X-59 Sonic Boom Test Results from the NASA Glenn 8- by 6-Foot Supersonic Wind Tunnel

A wind tunnel test was conducted to investigate near-field sonic boom pressure signatures from a model of the X-59 Low-Boom Flight Demonstrator aircraft. A 1.62%-scale model of the aircraft in the C612A configuration was fabricated for the wind tunnel test, which took place in the NASA Glenn 8- by 6-Foot Supersonic Wind Tunnel in September and October 2021. The model had provisions for two different mounting options: a swept blade strut that attached at the top of model ahead of the inlet, and rear-entry sting that was made as one piece with a dummy nacelle, and which had a 2”-long cylindrical segment aft of the nozzle exit before tapering up in size. The blade strut allowed for a clean aft end of the model for evaluation of the shocks from that region, while the sting avoided the significant distortions of the flow and shocks from the blade strut along the top of the model. Both the sting and the strut had adapters that attached to a force balance. The model had alternate parts for ±0.5° deflections of the flaps, ailerons, and stabilator, and ±1° deflections of the T-tail horizontal surface. Off-body static pressure measurements of the flow field below the model were made by use of a pressure rail which had 420 orifices along its tip. The model was positioned at various heights from the rail by vertical movement of the wind tunnel strut, and at various longitudinal stations relative to the rail by means of a linear actuator mounted between the tunnel strut and the balance. The longitudinal positioning allowed multiple pressure signatures to be obtained along different portions of the rail. These signatures were aligned by accounting for the model longitudinal movement and then averaged to take out the effects of tunnel flow distortions and the interference of the rail flow field and shocks on the model pressure signatures. The test was run at approximate Mach numbers of 1.36, 1.4, and 1.47, and the model was set at various angles of attack and roll relative to the rail. Plots of the model signatures for all the variations of Mach number, model angles, control deflections, and height relative to the rail are provided throughout the report. Repeatability was generally very good and gave confidence in the quality of the measurements. The signatures measured at various heights from the rail provided insight into the aging of the model shocks as they propagated from 1.2 to 3 body lengths from the model. Off-track signatures up to 45° from centerline obtained by rolling the model gave indications of the shock flow fields across the width of the sonic boom carpet. The deflections of the various control surfaces allowed assessment of the boom sensitivity to the control surface movements.

Sonic boom↗

Using dual-energy x-ray imaging to enhance automated lung tumor tracking during real-time adaptive radiotherapy

Purpose: Real-time, markerless localization of lung tumors with kV imaging is often inhibited by ribs obscuring the tumor and poor soft-tissue contrast. This study investigates the use of dual-energy imaging, which can generate radiographs with reduced bone visibility, to enhance automated lung tumor tracking for real-time adaptive radiotherapy. Methods: kV images of an anthropomorphic breathing chest phantom were experimentally acquired and radiographs of actual lung cancer patients were Monte-Carlo-simulated at three imaging settings: low-energy (70 kVp, 1.5 mAs), high-energy (140 kVp, 2.5 mAs, 1 mm additional tin filtration), and clinical (120 kVp, 0.25 mAs). Regular dual-energy images were calculated by weighted logarithmic subtraction of high- and low-energy images and filter-free dual-energy images were generated from clinical and low-energy radiographs. The weighting factor to calculate the dual-energy images was determined by means of a novel objective score. The usefulness of dual-energy imaging for real-time tracking with an automated template matching algorithm was investigated. Results: Regular dual-energy imaging was able to increase tracking accuracy in left–right images of the anthropomorphic phantom as well as in 7 out of 24 investigated patient cases. Tracking accuracy remained comparable in three cases and decreased in five cases. Filter-free dual-energy imaging was only able to increase accuracy in 2 out of 24 cases. In four cases no change in accuracy was observed and tracking accuracy worsened in nine cases. In 9 out of 24 cases, it was not possible to define a tracking template due to poor soft-tissue contrast regardless of input images. The mean localization errors using clinical, regular dual-energy, and filter-free dual-energy radiographs were 3.85, 3.32, and 5.24 mm, respectively. Tracking success was dependent on tumor position, tumor size, imaging beam angle, and patient size. Conclusions: This study has highlighted the influence of patient anatomy on the success rate of real-time markerless tumor tracking using dual-energy imaging. Additionally, the importance of the spectral separation of the imaging beams used to generate the dual-energy images has been shown.

60 APPLIED LIFE SCIENCES↗

Single-Bubble Flow Boiling Phenomena - Interface Tracking Simulation

Boiling, as one of the most efficient heat transfer mechanisms, is widely used in various engineering systems. Better understanding and modeling of this process remains a major challenge in multiphase flow research. The distribution of vapor in boiling system affects the heat transfer rate and may cause unfavorable conditions, such as heater burn-out. A number of flow regimes have been observed experimentally. In general, there are three regimes under boiling conditions: nucleate boiling, transition boiling, and film boiling. The nucleate boiling regime is categorized into partial boiling regime and fully developed nucleate boiling, according to behavior of bubble dynamics and heat transfer characteristics. In the first region, as the wall temperature increases, the fraction of the wall surface subject to nucleate boiling increases until bubble formation occupies the entire heated surface. Heat transfer in this region is a complex mixture of single-phase forced convection and nucleate boiling. As bubble density increases, bubbles turn to coalesce and form insulating vapor patches, which impedes liquid flow back to the surface. The heat transfer rate under this condition reduces dramatically. This point is called Critical Heat Flux (CHF), which leads to boiling crisis. The behavior of boiling crisis is dependent on local fluid conditions due to bubble growth and departure. Experiments are the ultimate tool for boiling model development and verification, but they still lack some capabilities needed for better understanding of the local mechanism of this phenomena. It's difficult to capture many important details at the pressure/temperature conditions of interest using experimental techniques, such as full three dimensional measurements of velocity and temperature distribution and estimates of heat flux partitioning during the boiling process. The interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. The advances of high performance computing (HPC) in recent years made it possible to apply DNS to a wide variety of adiabatic flows. Some work has been done to implement evaporation / condensation models as well. Lee and Nydahl performed a numerical simulation of bubble growth and departure assuming that the bubble has the shape of a truncated sphere and a micro-layer exists during bubble growth. A 2-D cylindrical bubbles simulation has been done by Son with a simplified model to predict the heat flux in a thin liquid micro-layer. A direct simulation of 2D film boiling is conducted by Juric and Tryggvason. The film boiling, below critical pressure with a modified Level Set Method, is studied by Son and Dhir. Ose and Kunugi have developed a boiling and condensation model on subcooled boiling phenomena. Fuchs performed numerical simulations of bubble growth and departure considering wall conduction effects. Fully transient heat and fluid flow is modeled with a free surface of a rising bubble and a periodic calculation of the whole cycling of a growing, detaching, and rising bubble. Mukherjee and Kandikar have done a numerical simulation of an evaporating meniscus on a moving heated surface with level set method. The heat transfer associated with the advancing and receding contact angle has been studied. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate single-bubble growth scenarios. For a single bubble simulation in infinite liquid, the analytical solution exists and can be compared with the numerical results for verification purposes. The presented capabilities will be utilized in the large scale DNS of boiling flows in the future. The finite-element based code, PHASTA is used for the simulation. It is a parallel, hierarchic, higher-order accurate, adaptive, stabilized, transient analysis flow solver, which has been shown to be an effective tool for a wide range of single and two-phase flow problems. It has been shown to be highly scalable on top supercomputers ({approx}85% scaling on up to 3 million mesh partitions using a 92 billion element mesh . PHASTA has been shown to reliably predict the details of adiabatic bubbly flows as well as single-phase flows with heat transfer. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate a single-bubble growth scenario. For a single bubble growth in superheated water, the analytical solution exists and can be compared with the numerical results for verification purposes. The second-order accurate spatial and time discretization is used for the flow solver in the presented work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Monitoring Land Surface Albedo and Vegetation Dynamics Using High Spatial and Temporal Resolution Synthetic Time Series from Landsat and the MODIS BRDF/NBAR/Albedo Product

Seasonal vegetation phenology can significantly alter surface albedo which in turn affects the global energy balance and the albedo warmingcooling feedbacks that impact climate change. To monitor and quantify the surface dynamics of heterogeneous landscapes, high temporal and spatial resolution synthetic time series of albedo and the enhanced vegetation index (EVI) were generated from the 500-meter Moderate Resolution Imaging Spectroradiometer (MODIS) operational Collection V006 daily BRDF (Bidirectional Reflectance Distribution Function) / NBAR (Nadir BRDF-Adjusted Reflectance) / albedo products and 30-meter Landsat 5 albedo and near-nadir reflectance data through the use of the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM). The traditional Landsat Albedo (Shuai et al., 2011) makes use of the MODIS BRDFAlbedo products (MCD43) by assigning appropriate BRDFs from coincident MODIS products to each Landsat image to generate a 30-meter Landsat albedo product for that acquisition date. The available cloud free Landsat 5 albedos (due to clouds, generated every 16 days at best) were used in conjunction with the daily MODIS albedos to determine the appropriate 30-meter albedos for the intervening daily time steps in this study. These enhanced daily 30-meter spatial resolution synthetic time series were then used to track albedo and vegetation phenology dynamics over three Ameriflux tower sites (Harvard Forest in 2007, Santa Rita in 2011 and Walker Branch in 2005). These Ameriflux sites were chosen as they are all quite nearby new towers coming on line for the National Ecological Observatory Network (NEON), and thus represent locations which will be served by spatially paired albedo measures in the near future. The availability of data from the NEON towers will greatly expand the sources of tower albedometer data available for evaluation of satellite products. At these three Ameriflux tower sites the synthetic time series of broadband shortwave albedos were evaluated using the tower albedo measurements with a Root Mean Square Error (RMSE) less than 0.013 and a bias within the range of 0.006. These synthetic time series provide much greater spatial detail than the 500 meter gridded MODIS data, especially over more heterogeneous surfaces, which improves the efforts to characterize and monitor the spatial variation across species and communities. The mean of the difference between maximum and minimum synthetic time series of albedo within the MODIS pixels over a subset of satellite data of Harvard Forest (16 kilometers by 14 kilometers) was as high as 0.2 during the snow-covered period and reduced to around 0.1 during the snow-free period. Similarly, we have used STARFM to also couple MODIS Nadir BRDF-Adjusted Reflectances (NBAR) values with Landsat 5 reflectances to generate daily synthetic times series of NBAR and thus Enhanced Vegetation Index (NBAR-EVI) at a 30-meter resolution. While normally STARFM is used with directional reflectances, the use of the view angle corrected daily MODIS NBAR values will provide more consistent time series. These synthetic times series of EVI are shown to capture seasonal vegetation dynamics with finer spatial and temporal details, especially over heterogeneous land surfaces.

Vegetation Index↗

Maneuver Design and Calibration for the Genesis Spacecraft

Genesis is the fifth mission selected as part of NASA's Discovery Program. The objective of Genesis is to collect solar wind samples for a period of approximately two years while in a halo orbit about the Earth-Sun L I point. At the end of this period, the samples are to be returned to a specific recovery point on the Earth for subsequent analysis. This goal has never been attempted before and presents a formidable challenge in terms of mission design and operations, particularly planning and execution of propulsive maneuvers. To achieve a level of cost-effectiveness consistent with a Discovery-class mission, the Genesis spacecraft design was adapted to the maximum extent possible from designs used on earlier missions, such as Mars Global Surveyor (MGS) and Stardust, another sample collection mission. The spacecraft design for Genesis is shown. Spin stabilization was chosen for attitude control, in lieu of three-axis stabilization, with neither reaction wheels nor accelerometers included. This precludes closed-loop control of propulsive maneuvers and implies that any attitude changes, including spin changes and precessions, will behave like translational propulsive maneuvers and affect the spacecraft trajectory. Moreover, to minimize contamination risk to the samples collected, all thrusters were placed on the side opposite the sample collection canister. The orientation and characteristics of thrusters are indicated. For large maneuvers (>2.5 m/s), two 5 lbf thrusters will be used for delta v, with precession to the burn attitude, followed by spin-up from 1.6 to 10 rpm before the burn and spin down to 1.6 rpm afterwards, then precession back to the original spin attitude. For small maneuvers (<2.5 m/s), no spin change is needed and four 0.2 lbf thrusters are used for Av. Single or double 360 deg. precession changes are required whenever the desired delta v falls inside the two-way turn circle (about 0.4 m/s) based on the mass properties, spin rate and lever arm lengths based on thruster locations. In such instances, delta v resulting from spacecraft precession cannot be used effectively as a component of the desired delta v, and must therefore be removed by precessing at least one complete revolution around the turn circle. To eliminate cross-track execution errors, a second revolution in the opposite direction would also be performed. This paper will address the design of propulsive maneuvers in light of the aforementioned challenges and other constraints. Maneuver design will be performed jointly by the Navigation Team at JPL and the Spacecraft Team at LMA, based on the process indicated . Typical maneuver timelines will be presented which address considerations introduced by attitude changes. These include nutation, which is introduced by precessing or spinning down and must be given sufficient time to damp out prior to execution of subsequent events, as well as sun and earth pointing constraints, which must be considered to ensure sufficient spacecraft power and to minimize telecommunications interruptions, respectively. The paper will include a description of how individual propulsive maneuvers are resolved into components to account for delta v from translational burns and spacecraft attitude changes required to carry out such maneuvers. Contributions to maneuver delta v arising from attitude changes, based on mass properties for the period just after launch, are indicated. Similar curves will be presented spanning all mission phases from launch through return. A set of closed-form equations for resolving maneuver components, base on a specific delta v required for correction or deterministic changes to the spacecraft trajectory will be presented, as well. In addition to nominal maneuvers, special calibration maneuvers are planned to improve open-loop modeling of maneuvers and to reduce execution errors. Uncalibrated execution errors are indicated. Such errors could be reduced by 50% or more over the course of the mission. Special calibrations are of particular importance for the return leg of the mission, since the sample canister must be returned to a specific location within the Utah Test and Training Range (UTTR) for mid-air retrieval. An entry angle tolerance of no less than +/- 0.08 deg. is required to achieve this objective. Biasing of the final return maneuvers coupled with a specific maneuver mode to use a series of well-characterized spin changes to effect these maneuvers is part of the current Genesis baseline mission plan. Another important objective of calibrations is to better characterize precession maneuvers. Such maneuvers are part of most propulsive maneuvers, but are also required periodically to maintain sun-pointing for power or daily during solar-wind pointing during collection periods. Although relatively small, such maneuvers will have a significant cumulative impact on orbit determination, particularly in the halo portion of the mission. The current mission design also calls for three stationkeeping maneuvers during each halo orbit of approximately six months duration. These stationkeeping maneuvers may be sufficiently small that single or double 360 deg. precession changes may be required. Because there are no accelerometers on board the spacecraft, calibration can only be performed with the aid of ground-based radiometric tracking. To establish a high degree of accuracy in characterizing the magnitude of burns, the spacecraft spin axis should be along the line of sight to the Earth, providing Doppler measurements with <1 mm/sec accuracy in S-Band. Emission constraints allow such alignment only during certain portions of the mission when the Earth-spacecraft-sun geometry is favorable. The impact of precessions, or burns at times when geometry is not favorable, can be assessed by reconstruction of the spacecraft trajectory using tracking arcs of several days before and after the event.

Williams, Kenneth E.↗