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NASA NTRS1980

Light curves for bump Cepheids computed with a dynamically zoned pulsation code

The dynamically zoned pulsation code developed by Castor, Davis, and Davison was used to recalculate the Goddard model and to calculate three other Cepheid models with the same period (9.8 days). This family of models shows how the bumps and other features of the light and velocity curves change as the mass is varied at constant period. The use of a code that is capable of producing reliable light curves demonstrates that the light and velocity curves for 9.8 day Cepheid models with standard homogeneous compositions do not show bumps like those that are observed unless the mass is significantly lower than the 'evolutionary mass.' The light and velocity curves for the Goddard model presented here are similar to those computed independently by Fischel, Sparks, and Karp. They should be useful as standards for future investigators.

Adams, T. F.↗
NASA NTRS1989

Hierarchical Ada robot programming system (HARPS)- A complete and working telerobot control system based on the NASREM model

HARPS is a telerobot control system that can perform some simple but useful tasks. This capability is demonstrated by performing the ORU exchange demonstration. HARPS is based on NASREM (NASA Standard Reference Model). All software is developed in Ada, and the project incorporates a number of different CASE (computer-aided software engineering) tools. NASREM was found to be a valid and useful model for building a telerobot control system. Its hierarchical and distributed structure creates a natural and logical flow for implementing large complex robust control systems. The ability of Ada to create and enforce abstraction enhanced the implementation of such control systems.

Leake, Stephen↗
NASA NTRS2001

Modeling and Prediction of Wildfire Hazard in Southern California, Integration of Models with Imaging Spectrometry

Large urban wildfires throughout southern California have caused billions of dollars of damage and significant loss of life over the last few decades. Rapid urban growth along the wildland interface, high fuel loads and a potential increase in the frequency of large fires due to climatic change suggest that the problem will worsen in the future. Improved fire spread prediction and reduced uncertainty in assessing fire hazard would be significant, both economically and socially. Current problems in the modeling of fire spread include the role of plant community differences, spatial heterogeneity in fuels and spatio-temporal changes in fuels. In this research, we evaluated the potential of Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Airborne Synthetic Aperture Radar (AIRSAR) data for providing improved maps of wildfire fuel properties. Analysis concentrated in two areas of Southern California, the Santa Monica Mountains and Santa Barbara Front Range. Wildfire fuel information can be divided into four basic categories: fuel type, fuel load (live green and woody biomass), fuel moisture and fuel condition (live vs senesced fuels). To map fuel type, AVIRIS data were used to map vegetation species using Multiple Endmember Spectral Mixture Analysis (MESMA) and Binary Decision Trees. Green live biomass and canopy moisture were mapped using AVIRIS through analysis of the 980 nm liquid water absorption feature and compared to alternate measures of moisture and field measurements. Woody biomass was mapped using L and P band cross polarimetric data acquired in 1998 and 1999. Fuel condition was mapped using spectral mixture analysis to map green vegetation (green leaves), nonphotosynthetic vegetation (NPV; stems, wood and litter), shade and soil. Summaries describing the potential of hyperspectral and SAR data for fuel mapping are provided by Roberts et al. and Dennison et al. To utilize remotely sensed data to assess fire hazard, fuel-type maps were translated into standard fuel models accessible to the FARSITE fire spread simulator. The FARSITE model and BEHAVE are considered industry standards for fire behavior analysis. Anderson level fuels map, generated using a binary decision tree classifier are available for multiple dates in the Santa Monica Mountains and at least one date for Santa Barbara. Fuel maps that will fill in the areas between Santa Barbara and the Santa Monica Mountains study sites are in progress, as part of a NASA Regional Earth Science Application Center, the Southern California Wildfire Hazard Center. Species-level maps, were supplied to fire managing agencies (Los Angeles County Fire, California Department of Forestry). Research results were published extensively in the refereed and non-refereed literature. Educational outreach included funding of several graduate students, undergraduate intern training and an article featured in the California Alliance for Minorities Program (CAMP) Quarterly Journal.

Roberts, Dar A.↗
NASA NTRS1991

Primordial nucleosynthesis redux

The abundances of D, He-3, He-4, and Li-7, are presently recalculated within the framework of primordial nucleosynthesis in the standard hot big band model, in order to estimate the primordial abundances of the light elements. A comparison between theory and experiment demonstrates the consistency of standard model predictions; the baryon density parameter is constrained on the basis of a nucleon-to-photon ratio of 2.8-4.0. These bounds imply that the bulk of the baryons in the universe are dark, requiring that the universe be dominated by nonbaryonic matter.

Walker, Terry P.↗
NASA NTRS1998

Direct Acceleration of Pickup Ions at The Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

We have modeled the injection and acceleration of pickup ions at the solar wind termination shock and investigated the parameters needed to produce the observed Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo technique was employed, which in effect solves the Boltzmann equation and is not restricted to near-isotropic particle distribution functions. This technique models the injection of thermal and pickup ions, the acceleration of these ions, and the determination of the shock structure under the influence of the accelerated ions. The essential effects of injection are treated in a mostly self-consistent manner, including effects from shock obliquity, cross- field diffusion, and pitch-angle scattering. Using recent determinations of pickup ion densities, we are able to match the absolute flux of hydrogen in the ACRs by assuming that pickup ion scattering mean free paths, at the termination shock, are much less than an AU and that modestly strong cross-field diffusion occurs. Simultaneously, we match the flux ratios He(+)/H(+) or O(+)/H(+) to within a factor approx. 5. If the conditions of strong scattering apply, no pre-termination-shock injection phase is required and the injection and acceleration of pickup ions at the termination shock is totally analogous to the injection and acceleration of ions at highly oblique interplanetary shocks recently observed by the Ulysses spacecraft. The fact that ACR fluxes can be modeled with standard shock assumptions suggests that the much-discussed "injection problem" for highly oblique shocks stems from incomplete (either mathematical or computer) modeling of these shocks rather than from any actual difficulty shocks may have in injecting and accelerating thermal or quasi-thermal particles.

Ellison, Donald C.↗
NASA NTRS2017

Single Degree-of-Freedom Modeling of SLS Liquid Hydrogen Pre-Valve Flow Guide to Enable Rapid Transient Analysis

A unique single degree-of-freedom approximation technique has been developed to enable rapid application of a temporally-defined multi-spectral semi-narrow-band loading for generation of realistic stress/cycle values compared to a resonant analysis. The technique uses the harmonic analysis at resonance of a high-fidelity finite element model to produce a transfer function, which is then used to calibrate the response of the SDOF model. A standard numerical ordinary differential equation solver is then used to obtain the temporal response, and its histogram is used in a fatigue/fracture model. This technique is related to other SDOF methods used widely in industry, such as Miles' Equation and the Shock Response Spectra, but it is unique in that it produces a realistic time history of the response. The most obvious error in the process, which is the effect of closely-spaced modes, was also assessed using the parallel application of several SDOF models, and the error is shown to be small. The application of this unique and tractable reduced-order methodology has enabled the SLS program to avoid substantial cost and schedule penalties if a redesign or change of material were required. It has also enabled quick analysis of a number of other structures undergoing the same or similar excitation fields, and quick assessment when the excitation and structural configuration has been altered due to design changes in the system.

Brown, Andrew M.↗
NASA NTRS2018

Estimating Mangrove Aboveground Biomass from Airborne LiDAR Data: a Case Study from the Zambezi River Delta

Mangroves are ecologically and economically important forested wetlands with the highest carbon (C) density of all terrestrial ecosystems. Because of their exceptionally large C stocks and importance as a coastal buffer, their protection and restoration has been proposed as an effective mitigation strategy for climate change. The inclusion of mangroves in mitigation strategies requires the quantification of C stocks (both above and belowground) and changes to accurately calculate emissions and sequestration. A growing number of countries are becoming interested in using mitigation initiatives, such as REDD+ (reducing emissions from deforestation and forest degradation), in these unique coastal forests. However, it is not yet clear how methods to measure C traditionally used for other ecosystems can be modified to estimate biomass in mangroves with the precision and accuracy needed for these initiatives. Airborne Lidar (ALS) data has often been proposed as the most accurate way for larger scale assessments but the application of ALS for coastal wetlands is scarce, primarily due to a lack of contemporaneous ALS and field measurements. Here, we evaluated the variability in field and Lidar-based estimates of aboveground biomass (AGB) through the combination of different local and regional allometric models and standardized height metrics that are comparable across spatial resolutions and sensor types, the end result being a simplified approach for accurately estimating mangrove AGB at large scales and determining the uncertainty by combining multiple allometric models.We then quantified wall-to-wall AGB stocks of a tall mangrove forest in the Zambezi Delta, Mozambique. Our results indicate that the Lidar H100 height metric correlates well with AGB estimates, with R(exp 2) between 0.80 and 0.88 and RMSE of 33% or less. When comparing Lidar H100 AGB derived from three allometric models, mean AGB values range from 192 Mg ha(exp −1) up to 252 Mg ha(exp −1).We suggest the best model to predict AGB was based on the East Africa specific allometry and a power-based regression that used Lidar H100 as the height input with an R(exp 2) of 0.85 and an RMSE of 122 Mg ha(exp −1) or 33%. The total AGB of the Lidar inventoried mangrove area (6654 ha) was 1 350 902 Mg with a mean AGB of 203 Mg ha(exp −1) +/-166 Mg ha(exp −1). Because the allometry suggested here was developed using standardized height metrics, it is recommended that the models can generate AGB estimates using other remote sensing instruments that are more readily accessible over other mangrove ecosystems on a large scale, and as part of future carbon monitoring efforts in mangroves.

Fatoyinbo, Temilola↗
NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗
NASA NTRS1994

The evolution of X-ray clusters in a cold plus hot dark matter universe

We present the first self-consistently computed results on the evolution of X-ray properties of galaxy clusters in a cold + hot dark matter (CHDM) model. We have performed a hydrodynamic plus N-body simulation for the COBE-compatible CHDM model with standard mass components: Omega(sub hot) = 0.3, Omega (sub cold) = 0.6 and Omega(sub baryon) = 0.1 (h = 0.5). In contrast with the CDM model, which fails to reproduce the observed temperature distribution function dN/dT (Bryan et al. 1994b), the CHDM model fits the observational dN/dT quite well. Our results on X-ray luminosity are less firm but even more intriguing. We find that the resulting X-ray luminosity functions at redshifts z = 0.0, 0.2, 0.4, 0.7 are well fit by observations, where they overlap. The fact that both temperatures and luminosities provide a reasonable fit to the available observational data indicates that, unless we are missing some essential physics, there is neither room nor need for a large fraction of gas in rich clusters: 10% (or less) in baryons is sufficient to explain their X-ray properties. We also see a tight correlation between X-ray luminosity and gas temperature.

Bryan, Greg L.↗
NASA NTRS1989

Neutron star evolution with internal heating

The thermal evolution predicted by current models of the superfluid-crust interaction is noted to differ substantially from the thermal evolution predicted by models without internal heating as well as previous models of heating. Heating rates approaching the maximum predicted by current models enhance the photon luminosity of the star in the neutrino cooling era, and dramatically alter the thermal evolution in the photon cooling era. Standard cooling models are consistent with current pulsar temperature estimates and upper limits, except those for the Vela pulsar, which are lower than predicted.

Shibazaki, Noriaki↗
NASA NTRS2006

A New Empirical Thermospheric Density Model JB2006 using New Solar Indices

A new empirical atmospheric density model is developed using the CIRA72 (Jacchia 71) model as the basis for the diffusion equations. New solar indices based on orbit based sensor data are used for the solar irradiances in the extreme and far ultraviolet wavelengths. New exospheric temperature and semiannual density equations are employed to represent the major thermospheric density variations. Temperature correction equations are also developed for diurnal and latitudinal effects, and finally density correction factors are used for model corrections required at high altitude (1500-4000 km). The new model, Jacchia-Bowman 2006, is validated through comparisons of accurate daily density drag data previously computed for numerous satellite. For 400 km altitude the standard deviation of 16% for the standard Jacchia model is reduced to 10% for the new JB2006 model for periods of low geomagnetic storm activity.

Bowman, Bruce R.↗
NASA NTRS1988

X-ray induced stellar mass loss near active galactic nuclei

The effects of UV and X-ray radiation on stars in active galactic nuclei (AGN) are critically evaluated. Mass loss rates in X-ray-induced winds are evaluated for realistic red giant models, and the effects of the ablation of stellar envelopes by radiation pressure are considered. The importance of X-ray-induced mass loss in the standard quasar model is evaluated and whether it can provide a source of accretion fuel or emission-line clouds is discussed. It is concluded that thermal winds driven by X-ray heating are a minor total supply of mass to AGN, but that thermal plus line-driven winds and stellar ablation may increase the mass loss and improve the chances for supplying a fraction of the necessary mass supply to the central object. It is speculated that when steady winds are inefficient, complex time-dependent processes due to X-ray energy injection deep into a stellar atmosphere could still release significant mass from stars.

Voit, G. Mark↗
NASA NTRS2004

O VI Emission from the Interstellar Medium

This project's primary goal was to examine the Local Bubble, a large hot bubble surrounding the solar neighborhood. In order to do this, we observed the 1032 and 1038 A resonance line emission from O VI in the bubble and used the,results to comment on models for the Local Bubble and its embedded clouds. In order to maximize the signal to noise of our spectrum, we combined the awarded guest investigator observation with unpublished FUSE In Orbit Checkout observations. The resulting spectrum was sufficiently good as to enable us to place tight 2 sigma upper limits on the intensities of the 1032 and the 1038 A resonance lines. We also measured or placed upper limits on the other cosmic lines in the bandpass, including C III and C II. These are the first known ultraviolet emission line measurements and/or upper limits for the gas in the Local Bubble (as opposed to gas anywhere along long lines of sight). With the O VI upper limits, we were able to quantitatively evaluate competing theories for the origins of the Local Bubble. The upper limits are well below those expected in the Breitschwerdt model (which proposes that during its its early development, the Local Bubble rapidly expanded beyond its nascent cloud and, as a result, is now vastly underionized). The upper limits on the O VI resonance line doublet intensity and the measurement of the C III intensity, garnered from this project, combined with measurements of the O VI column density, garnered from another project, are so far below the predictions, that they make a good case for eliminating the Breitschwerdt model from the field of possibilities. Thus, instead of being vastly underionized, the Local Bubble is near ionizational equilibrium. In addition, the upper limits challenge the other well-known model for the Local Bubble. In that model, the Local Bubble was blown by a series of supernova explosions and winds and contains a myriad of evaporating clouds. The intensity of the O VI resonance line doublet predicted from models exceeds the observationally determined 2 sigma upper limits. The discrepancy prompts the exciting suggestion that there may be some astrophysics yet to be considered in standard hydrodynamic models. These measurements performed a second useful function. By subtract- ing them from the O VI intensity observed on long sight-lines through the Galactic halo and Local Bubble, we were able to estimate the intensity originating the Galactic halo.

Shelton, Robin L.↗
NASA NTRS2006

Comparison of Orbital Parameters for GEO Debris Predicted by LEGEND and Observed by MODEST: Can Sources of Orbital Debris be Identified?

Since 2002 the National Aeronautics and Space Administration (NASA) has carried out an optical survey of the debris environment in the geosynchronous Earth-orbit (GEO) region with the Michigan Orbital Debris Survey Telescope (MODEST) in Chile. The survey coverage has been similar for 4 of the 5 years allowing us to follow the orbital evolution of Correlated Targets (CTs), both controlled and un-controlled objects, and Un-Correlated Targets (UCTs). Under gravitational perturbations the distributions of uncontrolled objects, both CTs and UCTs, in GEO orbits will evolve in predictable patterns, particularly evident in the inclination and right ascension of the ascending node (RAAN) distributions. There are several clusters (others have used a "cloud" nomenclature) in observed distributions that show evolution from year to year in their inclination and ascending node elements. However, when MODEST is in survey mode (field-of-view approx.1.3deg) it provides only short 5-8 minute orbital arcs which can only be fit under the assumption of a circular orbit approximation (ACO) to determine the orbital parameters. These ACO elements are useful only in a statistical sense as dedicated observing runs would be required to obtain sufficient orbital coverage to determine a set of accurate orbital elements and then to follow their evolution. Identification of the source(s) for these "clusters of UCTs" would be advantageous to the overall definition of the GEO orbital debris environment. This paper will set out to determine if the ACO elements can be used to in a statistical sense to identify the source of the "clustering of UCTs" roughly centered on an inclination of 12deg and a RAAN of 345deg. The breakup of the Titan 3C-4 transtage on February 21, 1992 has been modeled using NASA s LEGEND (LEO-to-GEO Environment Debris) code to generate a GEO debris cloud. Breakup fragments are created based on the NASA Standard Breakup Model (including fragment size, area-to-mass (A/M), and delta-V distributions). Once fragments are created, they are propagated forward in time with a subroutine GEOPROP. Perturbations included in GEOPROP are those due to solar/lunar gravity, radiation pressure, and major geopotential terms. The question to be addressed: are the UCTs detected by MODEST in this inclination/RAAN region related to the Titan 3C-4 breakup? Discussion will include the observational biases in attempting to detect a specific, uncontrolled target during given observing session. These restrictions include: (1) the length of the observing session which is 8 hours or less at any given date or declination; (2) the assumption of ACO elements for detected object when the breakup model predicts debris with non-zero eccentricities; (3) the size and illumination or brightness of the debris predicted by the model and the telescope/sky limiting magnitude.

Barker, Edwin S.↗
NASA NTRS2020

Grain Formation around the AGB Star L2 Puppis Based On ALMA Observations

While models of grain formation in the outflows of carbon-rich stars have been relatively successful, models of outflows from oxygen-rich, asymptotic giant branch stars have been less fortunate. Under current modeling, it is difficult to produce sufficient amounts of silicate grains with high enough opacity to form a dust-driven wind from these stars. To investigate the cause of this difference, this work is a comparison between typical outflow model results and a model using input from Atacama Large Millimeter/submillimeter Array observations of L2Puppis. The temperatures from these observations are much lower than would typically be used in the standard outflow model. In addition, the observed gas densities are much higher than predicted from typical outflow models. Both of these differences make the formation of silicate grains much more favorable than predicted in current outflow models. We then explore the effects of other possible nonideal conditions including the efficiency of cluster growth prior to nucleation, the efficiency of grain growth following nucleation and the variation of grain coupling to stellar radiation during grain growth. Finally, we calculate the potential enhancement in grain production based on possible increased refractory abundances resulting from the vaporization of millimeter-scale and larger particles left over from the presence of a former planetary system.

Joseph A Nuth↗
NASA NTRS1997

Atmospheric Angular Momentum Fluctuations During 1979-1988 Simulated by Global Circulation Models

Changes in major global dynamical phenomena in the Earth's atmosphere are manifested in the time series of atmospheric angular momentum (AAM), as determined directly from meteorological observations and indirectly from geodetic observations of small fluctuations in the rotation of the solid Earth which are proportional to length of day. AAM fluctuations are intimately linked with energetic processes throughout the whole atmosphere and also with the stresses at the Earth's surface produced largely by turbulent momentum transport in the oceanic and continental boundary layers and by the action of normal pressure forces on orographic features. A stringent test of any numerical global circulation model (GCM) is therefore provided by a quantitative assessment of its ability to represent AAM fluctuations on all relevant timescales, ranging from months to several years. From monthly data provided by the Atmospheric Model Intercomparison Project (AMIP) of the World Climate Research Programme, we have investigated seasonal and interannual fluctuations and the decadal mean in the axial component of AAM in 23 AMIP GCMs over the period 1979-1988. The decadal means are generally well simulated, with the model median value (1.58 x 10(exp 26) kg sq m/s) being only 3.5% larger than the observed mean and with 10 of the models being within 5% of the observed. The seasonal cycle is well reproduced, with the median amplitude of the models seasonal standard deviations being only 2.4% larger than observed. Half the seasonal amplitudes lie within 15% of the observed, and the median correlation found between the observed and model seasonal cycles is 0.95. The dominant seasonal error is an underestimation of AAM during northern hemisphere winter associated with errors in the position of subtropical jets. Less robust are the modeled interannual variations, although the median correlation of 0.61 between model simulations and observed AAM is statistically significant. The two El Nino-Southem Oscillation events that occurred during the AMIP decade 1979-1988 have the expected positive AAM anomalies, although the AAM signature of the 1982-1983 event tends to be underestimated and that of the 1986-1987 event overestimated.

Hide, R.↗
NASA NTRS1997

Atmospheric Angular Momentum Fluctuations During 1979-1988 Simulated by Global Circulation Models

Changes in major global dynamical phenomena in the Earth's atmosphere are manifested in the time series of atmospheric angular momentum (AAM), as determined directly from meteorological observations and indirectly from geodetic observations of small fluctuations in the rotation of the solid Earth which are proportional to length of day. AAM fluctuations are intimately linked with energetic processes throughout the whole atmosphere and also with the stresses at the Earth's surface produced largely by turbulent momentum transport in the oceanic and continental boundary layers and by the action of normal pressure forces on orographic features. A stringent test of any numerical global circulation model (GCM) is therefore provided by a quantitative assessment of its ability to represent AAM fluctuations on all relevant timescales, ranging from months to several years. From monthly data provided by the Atmospheric Model Intercomparison Project (AMIP) of the World Climate Research Programme, we have investigated seasonal and interannual fluctuations and the decadal mean in the axial component of AAM in 23 AMIP GCMs over the period 1979-1 988. The decadal means are generally well simulated, with the model median value (1.58 x 10(exp 26) kg sq m/s) being only 3.5% larger than the observed mean and with 10 of the models being within 5% of the observed. The seasonal cycle is well reproduced, with the median amplitude of the models' seasonal standard deviations being only 2.4% larger than observed. Half the seasonal amplitudes lie within 15% of the observed, and the median correlation found between the observed and model seasonal cycles is 0.95. The dominant seasonal error is an under- estimation of AAM during northern hemisphere winter associated with errors in the position of subtropical jets. Less robust are the modeled interannual variations, although the median correlation of 0.61 between model simulations and observed AAM is statistically significant. The two El Nino-Southern Oscillation events that occurred during the AMIP decade 1979-1988 have the expected positive AAM anomalies, although the AAM signature of the 1982-1983 event tends to be underestimated and that of the 1986-1987 event overestimated.

Hide, R.↗
NASA NTRS2011

Martian Atmospheric Modeling of Scale Factors for MarsGRAM 2005 and the MAVEN Project

For spacecraft missions to Mars, especially the navigation of Martian orbiters and landers, an extensive knowledge of the Martian atmosphere is extremely important. The generally-accepted NASA standard for modeling (MarsGRAM), which was developed at Marshall Space Flight Center. MarsGRAM is useful for task such as aerobraking, performance analysis and operations planning for aerobraking, entry descent and landing, and aerocapture. Unfortunately, the densities for the Martian atmosphere in MarsGRAM are based on table look-up and not on an analytical algorithm. Also, these values can vary drastically from the densities actually experienced by the spacecraft. This does not have much of an impact on simple integrations but drastically affects its usefulness in other applications, especially those in navigation. For example, the navigation team for the Mars Atmosphere Volatile Environment (MAVEN) Project uses MarsGRAM to target the desired atmospheric density for the orbiter's pariapse passage, its closet approach to the planet. After the satellite's passage through pariapsis the computed density is compared to the MarsGRAM model and a scale factor is assigned to the model to account for the difference. Therefore, large variations in the atmosphere from the model can cause unexpected deviations from the spacecraft's planned trajectory. In order to account for this, an analytic stochastic model of the scale factor's behavior is desired. The development of this model will allow for the MAVEN navigation team to determine the probability of various Martian atmospheric variations and their effects on the spacecraft.

Martian atmosphere↗