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NASA NTRSDate not supplied

The Spacecraft Potential of Wind Over Time

In a space plasma, exposed to ionizing radiation, a conducting object like a spacecraft will generate a net charge as the relevant currents from the plasma and photoelectrons attempt to reach equilibrium over time. This net charging is measured (or inferred from particle measurements) as an electrostatic potential, called the spacecraft potential. The Wind spacecraft will be 30 years old on November 1, 2023 and as such, has one of the longest baselines of continuous spacecraft potential measurements of any space mission. We determine the spacecraft potential from observations of photoelectrons in the thermal particle data. We examine the variations over time finding oscillations that correlate with solar rotation. This preliminary study examines for other effects but is ultimately for the purpose of generating a properly calibrated velocity moment dataset for the entire Wind mission.

Lynn B. Wilson III↗

NASA NTRS1980

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Kamat, M. P.↗

NASA NTRS1980

On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions

The paper shows how trains of nonlinear, dispersive waves can be produced by allowing a region of mixed fluid, with a potential energy greater than its surroundings, to collapse towards its equilibrium state. The number of waves and their amplitude depend on the properties of the mixed region and of the ambient stratification. Three different geometrical configurations have been chosen and while each gives qualitatively the same results the form taken by the generated waves and the final equilibrium shape of the mixed region depend critically on these geometrical factors. The internal waves produced by this mechanism are related to waves produced in natural systems and it is shown that the observations support at least one possible explanation for those found in the oceans and planetary atmospheres.

Maxworthy, T.↗

NASA NTRS1985

Computational chemistry and aeroassisted orbital transfer vehicles

An analysis of the radiative heating phenomena encountered during a typical aeroassisted orbital transfer vehicle (AOTV) trajectory was made to determine the potential impact of computational chemistry on AOTV design technology. Both equilibrium and nonequilibrium radiation mechanisms were considered. This analysis showed that computational chemistry can be used to predict (1) radiative intensity factors and spectroscopic data; (2) the excitation rates of both atoms and molecules; (3) high-temperature reaction rate constants for metathesis and charge exchange reactions; (4) particle ionization and neutralization rates and cross sections; and (5) spectral line widths.

Cooper, D. M.↗

NASA NTRS1992

Measurements of the fundamental thermodynamic parameters of Li/BCX and Li/SOCl2 cells

Two experimental techniques - equilibrium or reversible cell discharge and measurement of open circuit potential as a function of temperature - are used to determine the thermodynamic data needed to estimate the heat generation characteristics of Li/BCX and Li/SOCl2 cells. The results obtained showed that the reversible cell potential, the temperature dependence of the reversible cell potential, and the thermoneutral potential of the BCX cell were 3.74 V, -0.857 +/- 0.198 mV/K, and 3.994 +/- 0.0603 V, respectively. The respective values obtained for the Li/SOCl2 cell were 3.67 V, -0.776 +/- 0.255 mV/K, and 3.893 +/- 0.0776 V. The difference between the thermoneutral potential of Li/BCX and Li/SCl2 cells is attributable to the difference in their electroactive components.

Kalu, E. E.↗

NASA NTRS1994

(H2)2 mole-fraction altitude profile in the atmosphere of Jupiter: A computational study

The mole fraction x(sub 2) of (H2)2 in equilibrium mixture with H2 under the atmospheric conditions of Jupiter is evaluated from the dimerization equilibrium constant calculated by quantum-chemical treatments and also from the Lennard-Jones potential. The treatments are of an ab initio type with the second and fourth order Moller-Plesset perturbation techniques and a basis set superposition error evaluation. The computed dimerization equilibrium constant is combined with observed height profiles of temperature and pressure. In six treatments considered it is found that the mole fraction decreases with increasing height. Various approximations suggest the dimeric mole fraction at the Jupiter 1 atm pressure level between 0.04 and 1.06%.

Slanina, Zdenek↗

NASA NTRS2013

AGATE: Adversarial Game Analysis for Tactical Evaluation

AGATE generates a set of ranked strategies that enables an autonomous vehicle to track/trail another vehicle that is trying to break the contact using evasive tactics. The software is efficient (can be run on a laptop), scales well with environmental complexity, and is suitable for use onboard an autonomous vehicle. The software will run in near-real-time (2 Hz) on most commercial laptops. Existing software is usually run offline in a planning mode, and is not used to control an unmanned vehicle actively. JPL has developed a system for AGATE that uses adversarial game theory (AGT) methods (in particular, leader-follower and pursuit-evasion) to enable an autonomous vehicle (AV) to maintain tracking/ trailing operations on a target that is employing evasive tactics. The AV trailing, tracking, and reacquisition operations are characterized by imperfect information, and are an example of a non-zero sum game (a positive payoff for the AV is not necessarily an equal loss for the target being tracked and, potentially, additional adversarial boats). Previously, JPL successfully applied the Nash equilibrium method for onboard control of an autonomous ground vehicle (AGV) travelling over hazardous terrain.

Huntsberger, Terrance L.↗

NASA NTRS2000

The Density-Potential (N(sub e)-V(sub s/c)) Relation in the High-Latitude Prenoon Ionosphere

Sounding of the Cleft Ion Fountain Energization Region (SCIFER) Thermal Electron Capped Hemisphere Spectrometer (TECHS) data are used to study the plasma density, spacecraft potential relation (N(sub e)-V(sub s/c)) in the prenoon topside auroral and cleft ionosphere during a period of low solar activity. The SCIFER TECHS data show a power-law electron temperature dependence on ambient density across the transition from positive to negative spacecraft potential values in the high-latitude ionosphere. The illuminated ionospheric N(sub e)-V(sub s/c) relation is numerically modeled by imposing equilibrium of current flowing to/from the conductive surfaces of the payload. This modeling demonstrates a strong dependence of spacecraft potential on electron temperature across a wide range of densities. This electron temperature dependence is especially significant in the negative spacecraft potential regime. SCIFER TECHS observations of the N(sub e)-V(sub s/c) relation are used to extend the previous magnetospheric observation-model results to the higher density ionospheric regime.

Adrian, M. L.↗

NASA NTRS1990

Ballooning mode instability at the plasmapause

The ballooning mode instability, which can excite hydromagnetic waves at the plasmapause, is studied in the presence of azimuthal plasma flows induced during geomagnetically disturbed periods. A general sufficient criterion for the ballooning mode stability is derived, for a change in the potential energy greater than or equal to 0, which involves the integration over an entire field line. A local stability analysis at the equatorial plasmapause region shows that the ballooning modes could be spontaneously generated via instability under at least two conditions: one is similar to the usual interchange condition, and the second to the quasi-interchange modes. Both of these local instability conditions can be derived from the general stability criterion. Finally an exact solution for the equilibrium state with flow is derived analytically, and the change in the potential energy is computed numerically. It is found that, in the cases studied, the flow does not spontaneously excite the ballooning modes; it only further stabilizes (or destabilizes) the ballooning spectrum if originally the system is stable (or unstable). The analysis would be useful for the interpretation of some of the low-frequency modes observed at the ground and near the equatorial plasmapause.

Lakhina, G. S.↗

NASA NTRS1979

Analytical study of the time dependent spacecraft-plasma interaction

A study of the time dependent interaction of an initially uniform equilibrium plasma with a plane conducting surface was made in order to achieve a more complete understanding of the dynamics of the charging process and of the approach to the floating potential on the surface. Numerical solutions of the cold ion equations of motion in conjunction with equilibrium electrons and Poisson's equation show the formation of an ion-rich sheath near the surface and the coupling of the non-neutral region to the undisturbed plasma through a quasineutral rarefaction. Analytical treatment of the quasineutral region showed excellent agreement (within 1 percent) with the numerical results.

Cipolla, J. W., Jr.↗

NASA NTRS2018

Behavior of Langmuir Probes in Non-Equilibrium Plasmas

Langmuir probes are diagnostic tools used to determine electron temperature, number density, and plasma potential. Irving Langmuir first used an electrostatic probe in the 1920s to find these characteristics in ionized gases. Single, double, and triple Langmuir probes are commonly used in plasma diagnostics because of their relative simplicity. In the single probe, a swept voltage is applied between the probe tip and circuit common to acquire a waveform showing the collected current as a function of applied voltage. A double Langmuir probe consists of two tips, both inserted into the plasma, with a voltage applied between them. As this voltage is swept, a current-voltage characteristic is measured. In a triple probe three probe tips are electrically coupled to each other with constant non-swept voltages applied between each of the tips. The voltages are selected to represent three points on the single Langmuir probe I-V curve. Elimination of the voltage sweep makes it possible to measure time-varying plasma properties in transient plasmas. Triple Langmuir probe measurements have been widely employed for various types of plasmas, including pulsed and time-varying plasmas such as those seen in pulsed plasma thrusters (PPTs), dense plasma focus devices, plasma flows, and fusion experiments. The typical Langmuir probe analysis for determining electron temperature and number density of the plasma (for a single, double, or triple Langmuir probe) includes an assumption that the plasma is in thermal equilibrium. While the this assumption may be justified for some applications, it is unlikely that it is fully justifiable for pulsed and time-varying plasmas or for the entire time a plasma device is in use. In the present work, we model the responses of Langmuir probes as they are inserted into a range of simple equilibrium and non-equilibrium plasmas. We return to basic governing equations of probe current collection and compute the current to the probes for a distribution function consisting of two Maxwellian distributions with different temperatures (the two-temperature Maxwellian). A variation of this method is also employed, where one of the Maxwellians is offset from zero (in velocity space) to add a suprathermal beam of electrons to the tail of the main Maxwellian distribution (the bump-on-the-tail distribution function). For a range of parameters in these non-Maxwellian distributions, we compute the current collection to the probes. Comparing the distribution function that was assumed a priori with the plasma density and temperature one would infer when applying standard probe theory to analyze the collected currents serves to illustrate the effect a non- Maxwellian plasma would have on results interpreted using the equilibrium probe current collection theory, allowing us to state the magnitudes of these deviations as a function of the assumed distribution function properties.

Polzin, Kurt A.↗

NASA NTRSDate not supplied

Geochemical Insights Into Volcanic and Lithospheric Evolution of Mars

Introduction: The Martian lithosphere plays a pivotal role in volcanic processes, altering surface features, climate shifts, and the planet's early habitability. Crucially, the rigid lithosphere significantly influences Mars' long-term thermal conditions. Studying various geological eons’ volcanic compositions unveils how the lithosphere has evolved, even though understanding the early Noachian volcanic chemistry remains challenging due to weathering and resurfacing. In this study, newly discovered Noachian volcanic terranes[1-2] along with Hesperian and Amazonian volcanic terranes[3] are considered(Figure 1), to infer the evolution of the Martian lithosphere. Figure 1:Mars topographic map derived from MOLA-HRSC data [4] highlights the study regions including the Noachian volcanic terranes, Arabia Terra (AT), Thaumasia Minor (TM), and the Southwest Margin of Icaria Planum (SWIP)[5].Additionally, the Hesperian volcanic terranes such as Syrtis Major (SM), Hesperia Planum (HP), and, the Amazonian volcanic terranes encompass Elysium Mons (EM), Alba Patera (AP), and Olympus Mons (OM) are marked. Methods and Datasets: We use the most recent elemental mass fraction maps derived from gamma spectroscopy data from the Mars Odyssey 2001mission [6]to ascertain the bulk composition of the Martian landscape. Utilizing the updated geochemical provinces dataset of Mars[7], we consider bulk chemistry variations within our study regions. The maps, at a resolution of 50×50, encompass elements like Al, Ca, Fe, Si, K, Th, H2O, Cl, and S, detected through Gamma-Ray Spectroscopy (GRS) with decimeter scale depth sensitivity[6].Additional major and minor elements like Mg, Na, Ti, P, and Mn, using mass balance methods [8]serve as inputs for melting and crystallization simulations. We employ the pMELTS model with FMQ-3to FMQ oxygen fugacity to estimate the Pressure(P)and melting degree(F)in various eons of volcanic terranes. We have also used conventional thermobarometric calculations to determine their formation P-T conditions, using silica activity and olivine-melt Mg-exchange thermometry[9-10]. Results: Chemical Composition of Studied Volcanic Terranes: To assess formation conditions, we have investigated if GRS-measured compositions signify primary igneous processes by evaluating weathering through the Chemical Index of Alteration (CIA), K/Th ratios, and ternary plots for aqueous alteration. Consistent K/Th ratios and low CIA (<50) across volcanic regions suggest minimal large-scale weathering, affirming well-preserved igneous material extending at decimeter depths. In addition, the calculated bulk compositions align with Martian mantle equilibrium, confirming studied volcanic terranes-Arabia Terra, Thaumasia Minor, and SWIP -as primary or less altered compositions, reinforcing their representativeness at a regional GRS scale on Mars. We have also estimated the bulk compositions of Hesperian and Amazonian volcanic terranes shown in Figure 1. All volcanic terranes represent the primary or minimally altered composition. Temporal Evolution of Martian Volcanic Terranes: Our results show P-T conditions ranging from 1.3-1.6 GPa and 1350-1390°C for Noachian terranes, while Hesperian volcanic terranes vary from 1.6-1.7 GPa and 1370-1395°C, and Amazonian volcanic terranes range between 1.9-2.8 GPa and 1380-1415°C. Our analyses correspond to lithospheric thicknesses/ depth of melting for Noachian which ranges from110-135 km, 120-235 km for Hesperian terranes, and 160-235 km for Amazonian terranes. Partial melting percentages (F) range from 8-12% for Noachian, 10-11% for Hesperian, and 10-12% for Amazonian. We have also calculated mantle potential temperatures (Tp) to show variations across epochs(Figure 2). Heat flux estimation shows variations from 51-65 mW/m2 for Noachian, 38-45 mW/m2for Hesperian, and 27-39 mW/m2for Amazonian terranes, implying temporal changes in lithospheric thickness and heat flow. Comparison of Noachian volcanic terranes with Hesperian and Amazonian reveals variations in lithospheric thickness and heat flux, indicating potential implications for Martian surface conditions, including volcanic activity, climate evolution, and early habitability. Figure 2: P-T diagram displays formation conditions of studied Martian volcanic regions using GRS data, alongside Noachian-age surface basalt samples from Gusev, Gale, and Jezero. Dashed lines represent Martian mantle potential temperatures, calculated by adding the latent heat of fusion to the equilibrium temperature at which melt and solid mantle coexist and subtracting the Martian adiabatic gradient corresponding to the depth of melt. The solid line shows the Martian mantle solidus [11].Discussion& Implication: The study explores Martian volcanic activity across eons. Uniform lithospheric thickness from the Noachian to Hesperian eons suggests persistent weak plumes until Hesperian, influencing heat flow variations. Noachian's high heat flux, likely due to concentrated radioactive elements, shows spatial heterogeneity, indicating early Mars' differentiated mantle. Volcanic outgassing plays avital role in the formation of the Martian climate, likely sustained water on the surface, influencing warm-wet or cold-dry conditions. Hesperian's favorable lithospheric heat flow (45 mW/m2) supports extended water existence, resembling Earth's conditions. Whereas, Amazonian's diminished heat flux (25 mW/m2) corresponds to water loss and arid climate. Hesperian's similar lithospheric thickness to mid-Noachian implies prolonged water retention, influencing climate and potential for astrobiological research, expanding perspectives for future Martian missions. Future work: As volcanism was active throughout its history. The emergence of Mars' extensive volcanic regions, known as large igneous provinces, which are linked to intermittent volcanic activity driven by mantle plumes, poses challenges to understanding the scale and persistence of these phenomena in Martian convection models. Therefore, understanding the regional-scale changes in eruptive processes within Martian volcanic provinces over time remains unclear and crucial for deciphering the evolution of the Martian interior without Earth-like plate tectonics. We will continue this work with petrological and thermoelastic analyses to study the compositional and spatiotemporal evolution of the Elysium Volcanic Province.

A Rani↗

NASA NTRS1982

Raindrop oscillations

A model of the change in shape of a raindrop is presented. Raindrops measured by two orthogonal cameras were classified by shape and orientation to determine the nature of the oscillation. A physical model based on potential energy was then developed to study the amplitude variation of oscillating drops. The model results show that oscillations occur about the equilibrium axis ratio, but the time average axis ratio if significantly more spherical for large amplitudes because of asymmetry in the surface potential energy. A generalization of the model to oscillations produced by turbulence yields average axis ratios that are consistent with the camera measurements. The model results for average axis ratios were applied to rainfall studies with a dual polarized radar.

Beard, K. V.↗

NASA NTRS1981

Properties of the X 1 Sigma state of BF

A perturbation theoretical approach for treating electron correlation has been used to calculate the potential energy curve and dipole moment function of BF near its equilibrium bond length. A dipole moment of 0.89 D (B- F+) is predicted at R sub e. When the bond is stretched by approximately 0.2 A the dipole reverses sign.

Kurtz, H. A.↗

NASA NTRS1989

Electrocatalysts for oxygen electrodes in fuel cells and water electrolyzers for space applications

In most instances separate electrocatalysts are needed to promote the reduction of O2 in the fuel cell mode and to generate O2 in the energy storage-water electrolysis mode in aqueous electrochemical systems operating at low and moderate temperatures (T greater than or equal to 200 C). Interesting exceptions are the lead and bismuth ruthenate pyrochlores in alkaline electrolytes. These catalysts on high area carbon supports have high catalytic activity for both O2 reduction and generation (1,2). Rotating ring-disk electrode measurements provide evidence that the O2 reduction proceeds by a parallel four-electron pathway. The ruthenates can also be used as self-supported catalysts to avoid the problems associated with carbon oxidation, but the electrode performance so far achieved in the research at Case Western Reserve University (CWRU) is considerably less. At the potentials involved in the anodic mode the ruthenate pyrochlores have substantial equilibrium solubility in concentrated alkaline electrolyte. This results in the loss of catalyst into the bulk solution and a decline in catalytic activity. Furthermore, the hydrogen generation counter electrode may become contaminated with reduction products from the pyrochlores (lead, ruthenium). A possible approach to this problem is to immobilize the pyrochlore catalyst within an ionic-conducting solid polymer, which would replace the fluid electrolyte within the porous gas diffusion O2 electrode. For bulk alkaline electrolyte, an anion-exchange polymer is needed with a transference number close to unity for the Oh(-) ion. Preliminary short-term measurements with lead ruthenates using a commercially available partially-fluorinated anion-exchange membrane as an overlayer on the porous gas-fed electrode indicate lower anodic polarization and virtually unchanged cathodic polarization.

Prakash, Jai↗

NASA NTRS1989

Electrocatalysis for oxygen electrodes in fuel cells and water electrolyzers for space applications

Prakash, Jai↗

NASA NTRS2019

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA's exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA's Entry Systems Modeling (ESM) Project, which serves as the Agency's only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specific models for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures.

Barnhardt, Michael D.↗

NASA NTRS2021

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA’s exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA’s Entry Systems Modeling (ESM) Project, which serves as the Agency’s only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specificmodels for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures. Results for both configurations have demonstrated the ability to land within the 50-meter precision requirement demanded by Mars human exploration missions, while also reducing propellant requirements by enabling more efficient control through entry and descent. Ongoing research in GN&C is developing mechanical specifications for the systems and establishing engineering feasibility.

aerothermodynamics↗