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At least 1,693 records · Page 94

Age and Pathway Diagnostics for a Stratospheric General Circulation Model

Using a variety of age diagnostic experiments we examine the stratospheric age spectrum of the Goddard Finite Volume Generd Circulation Model. Pulse tracer release age-of-air computations are compared to forward and backward trajectory computations. These comparisons show good agreement, and the age-of-air also compares well with observed long lived tracers. Pathway diagnostics show how air arrives in the lowermost stratosphere and the age structure of that region. Using tracers with different lifetimes we can estimate the age spectrum - this technique should be useful in diagnosing transport from various trace gas observations.

Schoeberl, Mark R.↗

Structural Design and Analysis of the Upper Pressure Shell Section of a Composite Crew Module

This paper presents the results of the structural design and analysis of the upper pressure shell section of a carbon composite demonstration structure for the Composite Crew Module (CCM) Project. The project is managed by the NASA Engineering and Safety Center with participants from eight NASA Centers, the Air Force Research Laboratory, and multiple aerospace contractors including ATK/Swales, Northrop Grumman, Lockheed Martin, Collier Research Corporation, Genesis Engineering, and Janicki Industries. The paper discusses details of the upper pressure shell section design of the CCM and presents the structural analysis results using the HyperSizer structural sizing software and the MSC Nastran finite element analysis software. The HyperSizer results showed that the controlling load case driving most of the sizing in the upper pressure shell section was the internal pressure load case. The regions around the cutouts were controlled by internal pressure and the main parachute load cases. The global finite element analysis results showed that the majority of the elements of the CCM had a positive margin of safety with the exception of a few hot spots around the cutouts. These hot spots are currently being investigated with a more detailed analysis. Local finite element models of the Low Impact Docking System (LIDS) interface ring and the forward bay gussets with greater mesh fidelity were created for local sizing and analysis. The sizing of the LIDS interface ring was driven by the drogue parachute loads, Trans-Lunar Insertion (TLI) loads, and internal pressure. The drogue parachute loads controlled the sizing of the gusset cap on the drogue gusset and TLI loads controlled the sizing of the other five gusset caps. The main parachute loads controlled the sizing of the lower ends of the gusset caps on the main parachute fittings. The results showed that the gusset web/pressure shell and gusset web/gusset cap interfaces bonded using Pi-preform joints had local hot spots in the Pi-preform termination regions. These regions require a detailed three-dimensional analysis, which is currently being performed, to accurately address the load distribution near the Pi-preform termination in the upper and lower gusset caps.

Sleight, David W.↗

Freezable Radiator Model Correlation Improvements and Fluids Study

Freezable radiators offer an attractive solution to the issue of thermal control system scalability. As thermal environments change, a freezable radiator will effectively scale the total heat rejection it is capable of as a function of the thermal environment and flow rate through the radiator. Scalable thermal control systems are a critical technology for spacecraft that will endure missions with widely varying thermal requirements. These changing requirements are a result of the space craft s surroundings and because of different thermal rejection requirements during different mission phases. However, freezing and thawing (recovering) a radiator is a process that has historically proven very difficult to predict through modeling, resulting in highly inaccurate predictions of recovery time. To attempt to improve this, tests were conducted in 2009 to determine whether the behavior of a simple stagnating radiator could be predicted or emulated in a Thermal Desktop(trademark) numerical model. A 50-50 mixture of DowFrost HD and water was used as the working fluid. Efforts to scale this model to a full scale design, as well as efforts to characterize various thermal control fluids at low temperatures are also discussed. Previous testing and modeling efforts showed that freezable radiators could be operated as intended, and be fairly, if not perfectly predicted by numerical models. This paper documents the improvements made to the numerical model, and outcomes of fluid studies that were determined necessary to go forward with further radiator testing.

Lillibridge, Sean↗

NEO Test Stand Analysis

A project within SwampWorks is building a test stand to hold regolith to study how dust is ejected when exposed to the hot exhaust plume of a rocket engine. The test stand needs to be analyzed, finalized, and fabrication drawings generated to move forward. Modifications of the test stand assembly were made with Creo 2 modeling software. Structural analysis calculations were developed by hand to confirm if the structure will hold the expected loads while optimizing support positions. These calculations when iterated through MatLab demonstrated the optimized position of the vertical support to be 98'' from the far end of the stand. All remaining deflections were shown to be under the 0.6'' requirement and internal stresses to meet NASA Ground Support Equipment (GSE) Safety Standards. Though at the time of writing, fabrication drawings have yet to be generated, but are expected shortly after.

Internship↗

Validation of a Thermo-Ablative Model of Elastomeric Internal Insulation Materials

In thermo-ablative material modeling, as in many fields of analysis, the quality of the existing models significantly exceeds that of the experimental data required for their validation. In an effort to narrow this gap, a laboratory-scale internal insulation test bed was developed that exposes insulation samples to realistic solid rocket motor (SRM) internal environments while being instrumented to record real-time rates of both model inputs (i.e., chamber pressure, total surface heat flux, and radiative heat flux) as well as model outputs (i.e., material decomposition depths (MDDs) and in-depth material temperatures). In this work, the measured SRM internal environment parameters were used in conjunction with equilibrium thermochemistry codes as inputs to one-dimensional thermo-ablative models of the PBINBR and CFEPDM insulation samples used in the lab-scale test firings. The computed MDD histories were then compared with those deduced from real-time X-ray radiography of the insulation samples, and the calculated in-depth temperatures were compared with those measured by embedded thermocouples. The results of this exercise emphasize the challenges of modeling and testing elastomeric materials in SRM environments while illuminating the path forward to improved fidelity.

Martin, Heath T.↗

Correlation of Full-Scale Isolated Proprotor Performance and Loads

A full-scale isolated proprotor test is currently being conducted in the USAF National Full-Scale Aerodynamics Complex (NFAC) 40- by 80-Foot Wind Tunnel at NASA Ames. The test article is a 3-bladed research rotor derived from the right-hand rotor of the AW609; this rotor was manufactured by Bell Helicopter under contract to NASA. In this paper, this research rotor is referred to as "699". The test, nearly completed, is an integral part of the initial checkout test of the newly developed Tiltrotor Test Rig (TTR), whose purpose is to test advanced, full-scale proprotors in the NFAC. Figure 1 shows the TTR/699 installed in the 40- by 80-Foot test section. The TTR rotor axis is horizontal and the rig rotates in yaw on the wind tunnel turntable for conversion (transition) and helicopter mode testing. To date, a substantial amount of wind tunnel test data has already been acquired. The completed operational conditions include hover, airplane mode (cruise, wind tunnel airspeed V=61 to 267 knots), and the helicopter and conversion conditions (with a comprehensive sweep of the TTR yaw angle ranging, to date, from 90-deg yaw helicopter mode to 30-deg yaw conversion mode, at varying airspeeds). This 699 proprotor performance and loads correlation study uses these newly acquired wind tunnel test data. This paper represents the third analytical study, coming after two earlier analytical studies on the TTR/699; that is, a 2018 paper on pre-test predictions of 699 performance and loads, Ref. 1, and an upcoming January 2019 paper on aeroelastic stability analysis of the TTR/699 installed in the 40- by 80-Foot Wind Tunnel, Ref. 2. Reference 8 will present an overview of the entire TTR/699 test program. For completeness, Ref. 3 addresses the development and initial testing of the TTR. Background information on the TTR effort at NASA Ames can be found at the Aeromechanics website: https://rotorcraft.arc.nasa.gov/Research/Facilities/ttr.html. To the authors' knowledge, the full-scale results presented in this paper are the first of their kind. A literature survey brought up several existing correlation studies, but these were either based on small-scale test data (for example, the studies performed by the University of Maryland) or full-scale aircraft flight test data (for example, flight tests conducted by Bell Helicopter). Separately, the 2009 NASA study involving the JVX rotor is relevant (see Ref.4). The JVX is closely similar to the 699 in size and aerodynamics, and is accordingly a good reference for performance calculations. In Ref. 1 (as mentioned above), pre-test reality checks of the current analytical model were made by comparing JVX and 699 predictions in hover and forward flight (airplane mode).

Isolated Proprotor Performance↗

Toward Coupled Data Assimilation in NASA’s GEOS: Developments in the Ocean Context

The Global Modeling & Assimilation Office (GMAO) at NASA GSFC produces analyses and predictions of the Earth system using various configurations of the Goddard Earth Observing System (GEOS) model and assimilation system. The current sub-seasonal-to-seasonal prediction system (GEOS-S2S) is based on a coupled atmosphere-ocean-land-ice configuration of GEOS which includes the Modular Ocean Model version 5 (MOM5) run at approximately 50-km resolution and a de-coupled OI-based ocean analysis that uses an initialization of MOM5 forced by the MERRA-2 reanalysis. GMAO will soon implement an updated GEOS-S2S system that will run at 25-km resolution and adopt aspects of the hybrid four-dimensional ensemble-variational (H4DEnVar) system already running in the production-version atmospheric analysis system, including a Local Ensemble Transform Kalman Filter (LETKF) to provide initial conditions for the oceanic state. This presentation will focus on developments to sustain the GMAO's systems on longer time horizons, where more radical transformations will be required to adapt to advanced computing environments, higher resolution and more diverse model components, and new observations for the Earth system. Results will describe progress toward a version of the GEOS coupled system that will be based around the Joint Effort for Data assimilation Integration (JEDI) framework being developed within Joint Center for Satellite Data Assimilation (JCSDA) and include an updated ocean model, MOM6. Discussion will focus specifically on the use of a Unified Forward Operator (UFO) for simulating observations and the Object Oriented Prediction System (OOPS) for providing the state estimate. These features are being developed as a multi-agency effort under the auspices of the JCSDA and are being adopted in the GMAO for all its applications of coupled data assimilation including S2S, numerical weather prediction, and reanalysis.

Mahajan, Rahul↗

Development of a High-Fidelity CLARREO Pathfinder Simulator

CLARREO Pathfinder is a hyperspectral instrument designed to resolve reflectance of solar radiation from Earth in the wavelength range of 350 nm to 2300 nm with an uncertainty of 0.3% (k=2) or less. Its success will demonstrate CLARREO’s ability to provide on-orbit SI-Traceable calibration of measured spectral reflectance with an advanced accuracy. The CLARREO pathfinder simulator has been developed to generate high-fidelity inter-calibration event data products that can be used for pre-launch inter-calibration algorithm study. A high-fidelity simulation for CLARREO inter-calibration events includes computationally intensive radiative transfer calculations for observations within each individual collocation footprint. A principal component based radiative transfer model is incorporated in the simulator to enable an ultra-fast forward simulation, ensuring a low latency data processing for month- to year-long intercalibration events. This paper introduces the design and development of the CLARREO pathfinder simulator and some of its applications for inter-calibration matching error evaluation.

Wan Wu↗

Electromagnetic wave scattering at near-grazing incidence from a gently undulating, rough surface

Models to estimate the reflection coefficient of a statistically rough surface, for example the works of Beckmann, Smith, and Vesecky are discussed. Bistatic radar experiments carried out during the Apollo 16 mission provide a data set with which to compare theoretical models and experimental data. These bistatic S-band radar experiments provide experimental estimates of the Moon's bistatic, forward scatter, reflection coefficient for grazing angles of 2.5 to 78 deg. Theoretical expressions for the reflection coefficient are developed for comparison with these experimental data. At grazing angles below 10 deg the models of Smith and Vesecky compare favorably with the data. Beckmann's model falls significantly more rapidly with decreasing grazing angle than does the data.

Vesecky, J. F.↗

Subsonic Round and Rectangular Twin Jet Flow Effects

Subsonic and supersonic aircraft concepts proposed by NASAs Fundamental Aeronautics Program have integrated propulsion systems with asymmetric nozzles. The asymmetry in the exhaust of these propulsion systems creates asymmetric flow and acoustic fields. The flow asymmetries investigated in the current study are from two parallel round, 2:1, and 8:1 aspect ratio rectangular jets at the same nozzle conditions. The flow field was measured with streamwise and cross-stream particle image velocimetry (PIV). A large dataset of single and twin jet flow field measurements was acquired at subsonic jet conditions. The effects of twin jet spacing and forward flight were investigated. For round, 2:1, and 8:1 rectangular twin jets at their closest spacings, turbulence levels between the two jets decreased due to enhanced jet mixing at near static conditions. When the flight Mach number was increased to 0.25, the flow around the twin jet model created a velocity deficit between the two nozzles. This velocity deficit diminished the effect of forward flight causing an increase in turbulent kinetic energy relative to a single jet. Both of these twin jet flow field effects decreased with increasing twin jet spacing relative to a single jet. These variations in turbulent kinetic energy correlate with changes in far-field sound pressure level.

Jet↗

60 years of science in ICF: from conception to scientific breakeven on the National Ignition Facility

The recent achievements of a burning plasma, fusion ignition, and scientific energy gain with deuterium-tritium (DT) fuel at Lawrence Livermore National Laboratory’s National Ignition Facility (NIF) represents a major milestone in the development of inertial confinement fusion (ICF) and all of fusion research. In these experiments, fuel pressures well in excess of hundreds of GBars were achieved in the compressed fuel, and robust alpha heating of the fuel, far in excess of the energy provided by the implosion, were demonstrated for the first time. These achievements occurred 60 years after the inception of ICF and the first laser demonstration, and were made possible by more than five decades of research at laser facilities around the world. Advances in laser technology both in wavelength and precision, motivated by improved understanding of laser-plasma interaction physics and the demands of targets; improvements in target fabrication inspired by the need to control and minimize hydrodynamic instabilities in the implosion; and multi-dimensional simulations and diagnostics have been critical to this achievement. This paper will summarize the scientific and technical advances, the surprises, and the challenges that had to be overcome to achieve these goals.

fusion↗

High concentrations of ice: Investigations using polarimetric radar observations combined with in situ measurements and cloud modeling (Final Report)

This DOE-funded joint project had the over-arching goal of understanding the reasons for observed size distributions of ice particles in cold clouds. Its approach involves the use of cloud models and field observations by radar and aircraft of real storms. The project addresses three major research objectives: (1) Utilize a novel polarimetric radar technique to retrieve size distributions and amounts of ice from radar data collected during the previous DOE ARM field campaigns; (2) Evaluate the results of ice microphysical retrievals using available in situ aircraft measurements and other remote sensors (e.g., vertically pointing cloud radars and wind profilers); (3) Improve the treatment of microphysical processes leading to cloud glaciation and ice multiplication in numerical cloud models. The study was performed by three research organizations: University of Oklahoma, The Hebrew University of Jerusalem, Israel, and Lund University, Sweden. The Israel and Swedish partners were funded by the sub-awards from the University of Oklahoma. Cloud modeling studies have been performed by the research teams at The Hebrew University of Jerusalem (HUJ) and Lund University to identify the origins of high concentrations of cloud ice in areas of high ice water content (HIWC). The Hebrew University Cloud Model (HUCM) with full spectral bin microphysics and the Lund University aerosol-cloud (AC) model with a hybrid bin / bulk microphysics scheme complementing HUCM were utilized for simulations. Both research teams had particular focus on secondary ice production (SIP) as one of the possible sources of enhanced ice concentration. The HUJ group suggested a novel concept of ice multiplication during droplet freezing. It is assumed that splintering and droplet fragmentation during droplet freezing takes place because of dendritic growth within a supercooled drop. The resulting simulations of SIP generated small ice in concentrations exceeding hundreds per liter similar to what was observed in the HIWC regions of the tropical storms. The Lund team explored the SIP mechanisms such as breakup of ice particles due to ice-ice collisions and ice sublimation that are expected to dominate the continental storms. They also quantified the impact of homogeneous nucleation of cloud droplets on the total number concentration of ice at very low temperatures near the tops of the clouds. Additionally, the Lund AC model is able to simulate the effect of aerosols of various types (including biological) on the cloud life cycle and the corresponding ice production. The HUCM / AC model was used to simulate one of the “golden” cases of the DOE MC3E campaign on 20 May 2011. The model output was converted into the fields of polarimetric radar variables using the polarimetric radar forward operator developed at the University of Oklahoma and compared with radar observations and in situ microphysical measurements onboard research aircraft. It was demonstrated that specific differential phase KDP is the best radar parameter to identify the HIWC areas and quantify the corresponding ice parameters. For the first time, the shape of the vertical profile of KDP was realistically reproduced by the cloud model with the KDP maximum in the dendritic growth layer (DGL) centered at the -15°C isotherm. The University of Oklahoma team has developed a methodology for polarimetric radar retrievals of such microphysical parameters of ice as ice water content (IWC), mean volume diameter (Dm), and total number concentration (Nt) of ice particles. These retrievals have been validated using in situ aircraft measurements during 6 field campaigns and proved to be quite robust and reliable. This allowed to build the first climatology of the vertical profiles of polarimetric radar variables and retrieved microphysical parameters for the three types of weather systems: continental MCSs, maritime MCSs, and tropical cyclones / hurricanes (Hu and Ryzhkov 2022). The data were collected by a multitude of the WSR-88D radars in 13 continental and 10 maritime MCSs and 11 landfalling hurricanes. The HIWC areas were identified within the examined storms and the corresponding “HIWC statistics” was compared with the “background” one without HIWC. An overarching conclusion of the study is that maritime tropical storms (MCSs and hurricanes) are characterized by smaller size ice in higher concentration compared to the continental MCSs. High ice water content in the HIWC areas is primarily caused by a strong jump in a number concentration of ice particles rather than the increase of their size compared to the “background” environment. This may point to the homogeneous nucleation of excessive amounts of supercooled droplets and / or secondary ice production as the possible origins of HIWC. Such a climatology provides a good observational reference for the modelers to evaluate the performance of their models. As an example, the in-depth analysis of the 20 May 2011 MC3E case shows that the advanced cloud models developed in the course of this study still tend to underestimate the number concentration of ice in the HIWC areas although they succeed in reproducing realistically looking vertical profiles of IWC and Nt. The results of the project research are summarized in 13 journal papers.

54 ENVIRONMENTAL SCIENCES↗

Ultraviolet Spectropolarimetry: on the Origin of Rapidly Rotating B Stars

UV spectroscopy and spectropolarimetry hold the key to understanding certain aspects of massive stars that are largely inaccessible (or exceptionally difficult) with optical or longer wavelength observations. As we demonstrate, this is especially true for the rapidly-rotating Be and Bn stars, owing to their high temperatures, geometric asymmetries, binary properties, evolutionary history, as well as mass ejection and disks (in the case of Be stars). UV spectropolarimetric observations are extremely sensitive to the photospheric consequences of rapid rotation (i.e. oblateness, temperature, and surface gravity gradients), far beyond the reach of optical wavelengths. Our polarized radiative-transfer modelling predicts that with low-resolution UV spectropolarimetry covering 120–300 nm, and with a reasonable SNR, the inclination angle of a rapid rotator can be determined to within 5 degrees, and the rotation rate to within 1%. The origin of rapid rotation in Be/n stars can be explained by either single-star or binary evolution, but their relative importance is largely unknown. Some Be stars have hot sub-luminous (sdO) companions, which at an earlier phase transferred their envelope (and with it mass and angular momentum) to the present-day rapid rotator. Although sdO stars are small and relatively faint, their flux peaks in the UV making this the optimal observational wavelength regime. Through spectral modelling of a wide range of simulated Be/n+sdO configurations, we demonstrate that high-resolution high-signal-to-noise ratio UV spectroscopy can detect an sdO star even when ∼1,000 times fainter in the UV than its Be/n star companion. This degree of sensitivity is needed to more fully explore the parameter space of Be/n+sdO binaries, which so far has been limited to about a dozen systems with relatively luminous sdO stars. We suggest that a UV spectropolarimetric survey of Be/n stars is the next step forward in understanding this population. Such a dataset would, when combined with population synthesis models, allow for the determination of the relative importance of the possible evolutionary pathways traversed by these stars, which is also crucial for understanding their future evolution and fate.

Ultraviolet astronomy↗

Eastern U.S. Continental Shelf Carbon Budget: Integrating Models,Data Assimilation, and Analysis

The U.S. East Coast Continental Shelf (USECoS) project was initiated in 2004 with the overall goal of developing carbon budgets for Mid-Atlantic and South Atlantic regions of the eastern U.S. coast. We addressed this goal through a series of specific research questions that were designed to understand carbon inputs and fates in the two regions, dominant food web pathways for carbon cycling, and similarities/differences in carbon cycling in the two continental shelf systems. The USECoS project represents a major effort to simultaneously synthesize and integrate diverse data sets, field measurements, models, and modeling approaches. We expect that the type of approach taken here will result in more insight than would be possible if each component of the program moved forward independently. The primary significance of this project is in providing a strong quantitative basis for the development of future observational and modeling studies of carbon budgets of continental shelf systems. A strong aspect of the USECoS project is the integration of modeling and extensive physical, chemical, and biological data sets, which provides an opportunity for modeling and data analyses to inform one another from the outset. This research is particularly germane to NASA's carbon cycle research focus and coastal research initiative and the U.S. Climate Change Research Program, all of which support the goals of the North American Carbon Program. We highlight primary approaches that have been used, and some of the challenges and results that have come from interactions among our team of investigators. The global scale and interdisciplinary nature of the science questions that we now face in Earth Science are such that integrated teams of investigators are needed to address them.

Hofmann, Eileen↗

High angle-of-attack characteristics of a forward-swept wing fighter configuration

The NASA-Langley Research Center is currently investigating the high angle-of-attack characteristics of a forward-swept wing fighter technology demonstrator in a cooperative program with the Defense Advanced Research Projects Agency. The program includes static and dynamic wind-tunnel force tests, free-flight model tests, spin-tunnel tests, and piloted simulation. Particular emphasis is placed on identifying the contributions of the forward-swept wing to the configuration aerodynamics at high angles of attack. Results are presented to illustrate the wing contributions in terms of aerodynamic stability, flow visualization, and observation of free-flight characteristics.

Grafton, S. B.↗

Measured and predicted impingement noise for a model-scale under the wing externally blown flap configuration with a QCSEE type nozzle

Jet/flap interaction noise was measured and predicted for a small-scale model two-flap, under-the-wing, externally blown flap configuration equipped with and without noise suppression devices. The devices consisted of short spanwise fairings centered in relationship to the jet axis and positioned in the slots between the wing and flaps. The nozzle approximated that of the Quiet Clean Short-haul Experimental Engine (QCSEE). Takeoff noise reductions of 6 dB in the flyover and 5 dB in the sideline plane were obtained over a wide range of radiation angles. Approach noise reductions of about 5 dB were obtained only in the forward quadrant of the flyover plane; no reductions were obtained in the sideline plane. Models of several noise sources were combined analytically to form an overall noise prediction, the results from which compared favorably with the measured data. The aerodynamic performance characteristics for these configurations were substantially the same in the takeoff attitude. However, in the approach attitude, the suppressed configuration produced a 6 percent reduction in the flow turning efficiency.

Mckinzie, D. J., Jr.↗

New approach to the design of Schottky barrier diodes for THz mixers

Near-ideal GaAs Schottky barrier diodes especially designed for mixing applications in the THz frequency range are presented. A diode fabrication process for submicron diodes with near-ideal electrical and noise characteristics is described. This process is based on the electrolytic pulse etching of GaAs in combination with an in-situ platinum plating for the formation of the Schottky contacts. Schottky barrier diodes with a diameter of 1 micron fabricated by the process have already shown excellent results in a 650 GHz waveguide mixer at room temperature. A conversion loss of 7.5 dB and a mixer noise temperature of less than 2000 K have been obtained at an intermediate frequency of 4 GHz. The optimization of the diode structure and the technology was possible due to the development of a generalized Schottky barrier diode model which is valid also at high current densities. The common diode design and optimization is discussed on the basis of the classical theory. However, the conventional fomulas are valid only in a limited forward bias range corresponding to currents much smaller than the operating currents under submillimeter mixing conditions. The generalized new model takes into account not only the phenomena occurring at the junction such as current dependent recombination and drift/diffusion velocities, but also mobility and electron temperature variations in the undepleted epi-layer. Calculated diode I/V and noise characteristics are in excellent agreement with the measured values. Thus, the model offers the possibility of optimizing the diode structure and predicting the diode performance under mixing conditions at THz frequencies.

Jelenski, A.↗

Solar wind stream evolution at large heliocentric distances - Experimental demonstration and the test of a model

A stream propagation model which neglects all dissipation effects except those occurring at shock interfaces, was used to compare Pioneer-10 solar wind speed observations, during the time when Pioneer 10, the earth, and the sun were coaligned, with near-earth Imp-7 observations of the solar wind structure, and with the theoretical predictions of the solar wind structure at Pioneer 10 derived from the Imp-7 measurements, using the model. The comparison provides a graphic illustration of the phenomenon of stream steepening in the solar wind with the attendant formation of forward-reverse shock pairs and the gradual decay of stream amplitudes with increasing heliocentric distance. The comparison also provides a qualitative test of the stream propagation model.

Gosling, J. T.↗