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At least 433 records · Page 24

Sodium Atoms in the Lunar Exotail: Observed Velocity and Spatial Distributions

The lunar sodium tail extends long distances due to radiation pressure on sodium atoms in the lunar exosphere. Our earlier observations determined the average radial velocity of sodium atoms moving down the lunar tail beyond Earth along the Sun-Moon-Earth line (i.e., the anti-lunar point) to be 12.4 km/s. Here we use the Wisconsin H-alpha Mapper to obtain the first kinematically resolved maps of the intensity and velocity distribution of this emission over a 15 x times 15 deg region on the sky near the anti-lunar point. We present both spatially and spectrally resolved observations obtained over four nights around new moon in October 2007. The spatial distribution of the sodium atoms is elongated along the ecliptic with the location of the peak intensity drifting 3 degrees east along the ecliptic per night. Preliminary modeling results suggest that the spatial and velocity distributions in the sodium exotail are sensitive to the near surface lunar sodium velocity distribution and that observations of this sort along with detailed modeling offer new opportunities to describe the time history of lunar surface sputtering over several days.

Line, Michael R.↗

New Insights into the First Two PSP Solar Encounters Enabled by Modeling Analysis with ADAPT-WSA

Parker Solar Probe's (PSP's) unique orbital path allows us to observe the solar wind closer to the Sun than ever before. Essential to advancing our knowledge of solar wind and energetic particle formation is identifying the sources of PSP observations. We report on results for the first two PSP solar encounters derived using the Wang–Sheeley–Arge (WSA) model driven by Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model maps. We derive the coronal magnetic field and the 1 R⊙ source regions of the PSP-observed solar wind. We validate our results with the solar wind speed and magnetic polarity observed at PSP. When modeling results are very reliable, we derive time series of model-derived spacecraft separation from the heliospheric current sheet, magnetic expansion factor, coronal hole boundary distance, and photospheric field strength along the field lines estimated to be connected to the spacecraft. We present new results for Encounter 1, which show time evolution of the far-side mid-latitude coronal hole that PSP corotates with. We discuss how this evolution coincides with solar wind speed, density, and temperature observed at the spacecraft. During Encounter 2, a new active region emerges on the solar far side, making it difficult to model. We show that ADAPT-WSA output agrees well with PSP observations once this active region rotates onto the near side, allowing us to reliably estimate the solar wind sources retrospectively for most of the encounter. We close with ways in which coronal modeling enables scientific interpretation of these encounters that would otherwise not have been possible.

Solar wind↗

An Optimization Approach to Support Science Decision Making for Lunar Surface Exploration

Introduction: Scientific exploration is one of the three pillars of NASA’s Moon2Mars architecture, with crew surface extra vehicular activities (EVA) serving a critical enabling function. Development of surface EVA operational planning and execution, specifically integrating science and flight control teams (FCT), is currently being explored through analog scenarios. This integration, exercised, for example, through the Joint EVA and Hu-man Surface Mobility Test Team (JETT), allows for science input on EVA activities in near real-time through a Science Evaluation Room (SER), or Arte-mis science backroom, which integrates with the broader FCT through the Science Officer. The SER works within the FCT to support dynamic EVA planning in response to changes in operational constraints as well as science opportunities and re-prioritization, increasing the mission science return and accelerating the accomplishment of the Moon2Mars science objectives. The SER works within the FCT to provide recommendations to traverse execution in near real-time. One challenge is the requirement to deliver SER inputs to the FCT on operationally relevant timelines. Failure to do so may result in suboptimal execution of science exploration EVAs or even loss of key science objectives. To close this gap, we present a network optimization tool to allow the SER to provide rapid input to the FCT in response to changes in operational constraints or science opportunities. Inputs are predicated on approved science objectives, and clear rationale must be provided to the FCT for any requested change. Accordingly, this tool incorporates the Science Traceability Matrix (STM), SER prioritization scheme, and station characterization and action planning with operational constraints such as duration, traverse speed, and distance to maximize science objectives based on SER priorities, consistent with FCT operational requirements. Method: As a proof of concept, we used an existing linear programing software package used to simulate optimal routes through cellular metabolism. We built a Demonstrative Model with three STM objectives and four stations on a region of the Moon. The objectives were given an arbitrary prioritization and mapped to the stations through four possible crew actions. (Figs. 1 and 2). This station to STM mapping is consistent with the method used by the JETT5 Science Team to develop analog surface EVA science planning. We used a grid system with the landing site at the origin and the four stations placed across the positive x,y quadrant. Actions were assigned to each station and the accomplishment of those actions resulted in a numerical “reward” based on the ability of that action to achieve science objectives. The aggregate reward from each individual STM objective contributes to a global score (Science Yield), weighted by its priority. Operational constraints included a requirement to start and end at the landing site, 5 minutes each for initial station characterization and “clean up,” and variable total EVA time, traverse rate (fixed to 0.5 meters per second in our example), and time to perform each action (10, 5, 7, and 15 min for actions 1, 2, 3, and 4, respectively). Additional constraints and variables will be added in the future (e.g., sample mass, number of stations, traverse route constraints, illumination). Optimization. We converted the connections (arcs) between these stations (nodes) into a mixed integer linear programming optimization problem (arcs = constraints, nodes = variables) with the objective to maximize Science Yield. For any action, the Science Yield is equal to the relevance of that action to an STM objective [3, 2, and 1 point(s) for High, Med., and Low relevance, respectively], multiplied by the STM Objective Priority [3, 2, and 1 point(s) for High, Med., and Low priority, respectively]. This resulted in a model that computes the optimal station and action combination to maximize the Science Yield. These weightings can be adjusted by the SER as desired. Results: We explored three test cases for the Demonstrative Model. First, we set the maximum EVA duration to 120 minutes and computed the optimal route (Fig. 3A). The model suggested per-forming Actions 1 and 2 at Station P01, followed by Actions 1 and 2 at Station P02, and finally Actions 1 and 3 at Station P04 before returning to the Landing Site. Second, we adjusted the STM Objective Priori-ty order and computed the new optimal route (Fig. 3B). Under this situation, the model suggested per-forming all Actions at Station P02 followed by all Actions at Station P03. The previous test cases were relevant to SER planning activities. Next, we explored providing mid-EVA replanning input to the FCT. Scenario: While executing the Route in Fig. 3A the crew finishes at Station P01 and FCT decides that the EVA needs to finish in 45 minutes back at the Landing Site. FCT asks SER to recommend changes to the plan to accommodate this operation-al change. Using the model and incorporating these new constraints (start at Station P01, max. time of 45 min), the model suggested performing Actions 2 and 4 at Station P03 (Fig. 4), requiring 41 minutes to complete and return to the Landing Site. Interestingly, Station 3 was not part of the original route. Using the model, we determined the EVA would need 66 minutes, instead of 45, in order for the original Station P04 to yield a larger Science Yield than Station P03. The parametrization and simulation was per-formed in less than a minute, demonstrating the operational relevance of the approach. Future Efforts: The results from the Demonstrative Model suggest this tool can accelerate SER decision making on operationally relevant timelines. Use in analog activities, such as JETT5 or follow-ons, which have over a dozen stations for a crew to explore and over a dozen actions per station, will provide needed validation of the utility of this tool for planning EVAs, replanning mid-EVA, or planning follow-on EVAs based on previous results. Further integration with FCT execution monitoring tools may provide additional efficiency gains, al-lowing rapid and iterative exploration of operation-al and science decision space by the FCT and SER.

Science Operations↗

B2 1141 + 37 - A giant radio galaxy with remarkable radio and optical properties

Observations of the giant radio galaxy B2 1141+37, which has a widely separated two-component radio structure and is optically identified with a tight chain of galaxies, are reported. The source was observed at 4900 MHz with the VLA at an effective integration time of 17 min. The map obtained shows two radio lobes with maxima coinciding with those in a previous 1415 MHz map and intensities about 1.5 times smaller than those obtained by extrapolating the spectrum defined by the flux density at 408 and 1415 MHz. Measurements of the redshifts of the two brightest galaxies identified with the radio source with an image intensified dissector scanner result in values of 0.1145 and 0.1155, which imply, with a Hubble constant of 50 km/sec per Mpc, a distance of 687 Mpc to the radio source and a separation of 1.0 Mpc between the lobes making it one of the largest radio sources known.

Ulrich, M. H.↗

The infall velocity toward Virgo, the Hubble constant, and a search for motion toward the microwave background

The perturbation of the local velocity field due to the overdensity of the Virgo complex (VC) is investigated theoretically, using an idealized spherically symmetric Virgocentric flow model and testing for a correlation between cos theta (where theta is the angle from the VC direction to eight groups and clusters with velocity 800-2500 km/s) and the relevant velocity residuals. The data and results are presented in extensive tables, graphs, and a map in extragalactic coordinates. The infall of the Local Group (LG) toward the VC is estimated as 200 + or - 50 km/s, corresponding to a mean mass/light ratio M/L(B) = about 70 for a sphere centered at the VC core and extending to the LG. The rate of free expansion within the VC is estimated as 52 + or 2 km/s Mpc for a VC distance of 21.6 Mpc. It is pointed out that the LG infall toward the VC cannot account for observations of an apparent 630-km/s motion of the LG toward the microwave background.

Tammann, G. A.↗

Global Distribution of Mercury's Neutrals from MESSENGER Measurements Combined with a Tomographic Method

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft entered orbit about Mercury on March 18, 2011. Since then, the Ultraviolet and Visible Spectrometer (UVVS) onboard this spacecraft has been observing Mercury's collisionless exosphere. We present measurements by MESSENGER UVVS of the sodium, calcium, and magnesium distributions that were obtained during multiple passes through the tail over a period of one month. Global maps of the exosphere were constructed daily from such measurements using a recently developed tomographic technique. During this period, Mercury moved towards the Sun from being about 0.44 astronomical units (AU) to approximately 0.32 AU from the Sun. Hence, our reconstructions provide information about the three-dimensional structure of the exosphere, the source processes for these species, and their dependence with orbital distance during the entire in-leg of Mercury's orbit.

Sarantos, Menelaos↗

Expanding the Measurement Capabilities of the mARC II Arc-Jet to Map the Operating Envelope for High-Enthalpy Air Flows

The mARC II is a 30 kW arc-jet facility at NASA Ames Research Center developed to produce high-enthalpy flows for low-cost technology development purposes. In this work, we introduce new measurement capabilities following the latest facility upgrades and begin characterizing the operating envelope for the two-disk arc-heater configuration with air as the working gas. The lower bound of the envelope corresponds to the lowest set current and the farthest sensor distance from the nozzle (𝐼set = 40 A, 𝑧 = 69 mm), while the upper bound corresponds to the highest current and closest sensor distance (𝐼set = 200 A, 𝑧 = 2 mm). Stagnation point heat flux was measured using a water-cooled Gardon gauge (⌀4.76 mm, 3/16" hemispherical), with values ranging from 15 ≤ q̇₀ ≤ 900 W/cm2. Stagnation pressure was measured using a water-cooled Pitot probe (⌀4.76 mm, 3/16" hemispherical), with values ranging from 18 ≤ p₀ ≤ 1100 Pa. The upgraded vacuum system is demonstrated to significantly extend the lower end of the operating envelope of the mARC II. Additionally, measurements of bulk enthalpy (3 ≤ h ≤ 13 MJ/kg) and stagnation enthalpy (4 ≤ h₀ ≤ 34 MJ/kg) demonstrate the mARC II facility's high-enthalpy capabilities. Completion of the operating envelope characterization is ongoing in tandem with the development of complementary diagnostic capabilities and numerical simulations.

TPS↗

Expanding the Measurement Capabilities of the mARC II Arc-Jet to Map the Operating Envelope for High-Enthalpy Air Flows

The mARC II is a 30 kW arc-jet facility at NASA Ames Research Center developed to produce high-enthalpy flows for low-cost technology development purposes. In this work, we introduce new measurement capabilities following the latest facility upgrades and begin characterizing the operating envelope for the two-disk arc-heater configuration with air as the working gas. The lower bound of the envelope corresponds to the lowest set current and the farthest sensor distance from the nozzle (𝐼set = 40 A, 𝑧 = 69 mm), while the upper bound corresponds to the highest current and closest sensor distance (𝐼set = 200 A, 𝑧 = 2 mm). Stagnation point heat flux was measured using a water-cooled Gardon gauge (⌀4.76 mm, 3/16" hemispherical), with values ranging from 15 ≤ q̇₀ ≤ 900 W/cm 2 . Stagnation pressure was measured using a water-cooled Pitot probe (⌀4.76 mm, 3/16" hemispherical), with values ranging from 18 ≤ p₀ ≤ 1100 Pa. The upgraded vacuum system is demonstrated to significantly extend the lower end of the operating envelope of the mARC II. Additionally, measurements of bulk enthalpy (3 ≤ h ≤ 13 MJ/kg) and stagnation enthalpy (4 ≤ h₀ ≤ 34 MJ/kg) demonstrate the mARC II facility's high-enthalpy capabilities. Completion of the operating envelope characterization is ongoing in tandem with the development of complementary diagnostic capabilities and numerical simulations.

instrumentation↗

Stratigraphic Subdivision of the Transvaal Dolomite from ERTS imagery

ERTS imagery has revealed the presence of broad stratigraphic subdivisions in the previously undifferentiated Transvaal Dolomite of the western Tranvaal, Republic of South Africa. While detailed field mapping in areas of good outcrop, as well as borehole logging has recently led to the recognition of a stratigraphy in the Transvaal Dolomite of the central Transvaal, poor outcrop in the western Transvaal has to date prevented this. The ERTS-imagery, however, clearly reveals the presence of six, and in the far west seven, distinct stratigraphic zones extending along strike for a distance of at least 200 km. The investigation clearly demonstrates the potential applications of ERTS-imagery in geological studies, even in a country where the geology is supposedly well known.

Grootenboer, J.↗

The dependence of the shape and stability of captive rotating drops on multiple parameters

Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Ungar, L. H.↗

Thermal-infrared and visual imaging of comet Giacobini-Zinner

Thermal-infrared and visual images obtained simultaneously of comet Giacobini-Zinner on UT 1985 August 4.4 are presented. The 10.8-micron map, which spans several arc minutes with 8-arcsec resolution, is the first ground-based infrared image of a comet. Considerable spatial structure is evident in the map, including a curved dust tail consisting primarily of dust grains larger than 100 microns. The width of this large-grain tail implies that these grains depart the nucleus with velocities less than 3 m/s. The distribution of grain albedo is determined for the central 1 arcmin. It is speculated that an observed increase in the albedo by a factor of 2 with distance from the nucleus and prolonged radius vector results from the confinement to the orbital plane of large fluffy grains previously considered for GZ by others; the lower albedo of this dust could result from multiple internal scattering increasing the probability of absorption of incident light. It is estimated that dust was departing the nucleus at the rate of about 8 x 10 to the 5th g/s, comparable to that derived for many other comets.

Telesco, C. M.↗

The Three-dimensional Structure of the Eta Carinae Homunculus

We investigate, using the modeling code SHAPE, the three-dimensional structure of the bipolar Homunculus nebula surrounding Eta Carinae as mapped by new ESO VLT/X-Shooter observations of the H2 (lambda) = 2.12125 micrometers emission line. Our results reveal for the first time important deviations from the axisymmetric bipolar morphology: 1) circumpolar trenches in each lobe positioned point-symmetrically from the center and 2) offplanar protrusions in the equatorial region from each lobe at longitudinal (approximately 55 degrees) and latitudinal (10 degrees to 20 degrees) distances from the projected apastron direction of the binary orbit. The angular distance between the protrusions (approximately 110 degrees) is similar to the angular extent of each polar trench (approximately 130 degrees) and nearly equal to the opening angle of the wind-wind collision cavity (approximately 110 degrees). As in previous studies, we confirm a hole near the centre of each polar lobe and no detectable near-IR H2 emission from the thin optical skirt seen prominently in visible imagery. We conclude that the interaction between the outflows and/or radiation from the central binary stars and their orientation in space has had, and possibly still has, a strong influence on the Homunculus. This implies that prevailing theoretical models of the Homunculus are incomplete as most assume a single star origin that produces an axisymmetric nebula.We discuss how the newly found features might be related to the Homunculus ejection, the central binary and the interacting stellar winds.

bipolar Homunculus nebula↗

A graph theoretic approach to scene matching

The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors.

Ranganath, Heggere S.↗

Multi-scale variation in spatial heterogeneity for microbial community structure in an eastern Virginia agricultural field

To better understand the distribution of soil microbial communities at multiple spatial scales, a survey was conducted to examine the spatial organization of community structure in a wheat field in eastern Virginia (USA). Nearly 200 soil samples were collected at a variety of separation distances ranging from 2.5 cm to 11 m. Whole-community DNA was extracted from each sample, and community structure was compared using amplified fragment length polymorphism (AFLP) DNA fingerprinting. Relative similarity was calculated between each pair of samples and compared using geostatistical variogram analysis to study autocorrelation as a function of separation distance. Spatial autocorrelation was found at scales ranging from 30 cm to more than 6 m, depending on the sampling extent considered. In some locations, up to four different correlation length scales were detected. The presence of nested scales of variability suggests that the environmental factors regulating the development of the communities in this soil may operate at different scales. Kriging was used to generate maps of the spatial organization of communities across the plot, and the results demonstrated that bacterial distributions can be highly structured, even within a habitat that appears relatively homogeneous at the plot and field scale. Different subsets of the microbial community were distributed differently across the plot, and this is thought to be due to the variable response of individual populations to spatial heterogeneity associated with soil properties. c2003 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.

NASA Discipline Life Support Systems↗

Underwater Multi-Node Radio Communication Solutions for Planetary Exploration

The exploration of the presumably life harboring subsurface ocean of Europa will provide scientists with extensive new knowledge in the search for extraterrestrial life. A highly miniaturized payload is required to penetrate a narrow passage through the thick ice crust covering Europa's surface. Underwater wireless communications may be the most viable means of communication for such exploratory missions, accounting for size and weight restrictions. This presents a challenge to achieve satisfactory data rates and a range that permits autonomous underwater vehicles (AUVs) to communicate within their region of operation, as well as with a surface lander or orbiter. This work presents thorough prototype experimentation on an underwater communication system established between several nodes using RF signals. During an eight-week internship experience at NASA's Ames Research Center in September-October 2014, our team developed a Europa exploration mission concept, built representative hardware, and carried out tests to assess the feasibility of key aspects of the concept. Experiments demonstrating the viability of RF communication underwater comprised inspecting the effect of depth and horizontal distance on signal strength as well as the optimum positioning of antennas. To test the system's performance, two submersibles were designed and built. A commercially available remotely operated vehicle (ROV) was also modified and used as a main communication node. The two submersibles were wirelessly connected and accommodated sensors capable of characterizing water properties and equipped with 2.4 GHz, 1 mW transceivers to communicate the measured data. The communication procedure is that the main communication node requests the collected data from the two submersibles when in range and receives it instantly through RF. This work models what may take place during an actual mission to Europa. The developed mission concept involved a hybrid communication system consisting of acoustic and RF signals to enhance the capability of the nodes to communicate over greater distances. The AUVs will need to avoid obstacles and maneuver around to collect data based on predefined algorithms. Thus, they will be provided with two positioning systems; the inertial navigation system, backed with an acoustic positioning system to mitigate drift. The AUVs divide the ocean into planes and explore along circular paths increasing in diameter with depth. Moreover, they make use of miniaturized sensors to map the surrounding environment. In this paper, the ROV and the submersibles are described, along with sections explaining the mechanism of communication and the testing procedures conducted to yield results.

Europa↗

Coronal roots of solar wind streams: 3-D MHD modeling

Weak (discontinuous) solutions of the 3-D MHD equations look like a promising tool to model the transonic solar wind with structural elements: current sheets, coronal plumes etc. Using the observational information about various coronal emissions one can include these structural elements into the 3-D MHD solar wind model by embedding the discontinuities of given type. Such 3-D MHD structured solar wind is calculated self-consistently: variants are examined via numerical experiments. In particular, the behavior of coronal plumes in the transonic solar wind flow, is modeled. The input information for numerical modeling (for example, the magnetic field map at the very base of the solar corona) can be adjusted so that fast stream arises over the center of the coronal hole, over the coronal hole boundaries and, even, over the region with closed magnetic topology. 3-D MHD equations have the analytical solution which can serve as a model of supersonic trans-alfvenic solar wind in the (5-20) solar radii heliocentric distance interval. The transverse, nonradial total (gas + magnetic field) pressure balance in the flow is the corner-stone of this solution. The solution describes the filamentation (ray-like structure of the solar corona) and streaming (formation of high-speed streams with velocities up to 800 km/sec) as a consequence of the magnetic field spatial inhomogeneous structure and trans-alfvenic character of the flow. The magnetic field works in the model as a 'controller' for the solar wind streaming and filamentation.

Pisanko, Yu. V.↗

A comparison between Lageos laser ranging and VLBI determined baselines

Two independent measurement techniques, Lageos satellite laser ranging (SLR), and very long baseline interferometry (VLBI) are compared in the measurement of distances (or baselines) between several locations in the continental U.S. The results of this analysis is summarized where both the SLR and VLBI baseline lengths and their differences (SLR minus VLBI) are presented. A comparison of the 22 baselines shows a mean difference of 1.0 + or - 1.1 cm with a scatter about zero of 5.2 cm. No apparent systematic scale difference between the networks is evident. A map of the baselines is included and indicates their differences, SLR minus VLBI, in centimeters.

Kolenkiewicz, R.↗

Map Projection Induced Variations in Locations of Polygon Geofence Edges

This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.

Neeley, Paula↗