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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

NASA Tech Briefs, January 2012

Contents of this issue are: (1) Energy-Based Tetrahedron Sensor for High-Temperature, High-Pressure Environments (2) Handheld Universal Diagnostic Sensor (3) Large-Area Vacuum Ultraviolet Sensors (4) Fiber Bragg Grating Sensor System for Monitoring Smart Composite Aerospace Structures (5) Health-Enabled Smart Sensor Fusion Technology (6) Extended-Range Passive RFID and Sensor Tags (7) Hybrid Collaborative Learning for Classification and Clustering in Sensor Networks (8) Self-Healing, Inflatable, Rigidizable Shelter (9) Improvements in Cold-Plate Fabrication (10) Technique for Radiometer and Antenna Array Calibration - TRAAC (11) Real-Time Cognitive Computing Architecture for Data Fusion in a Dynamic Environment (12) Programmable Digital Controller (13) Use of CCSDS Packets Over SpaceWire to Control Hardware (14) Key Decision Record Creation and Approval Module (15) Enhanced Graphics for Extended Scale Range (16) Debris Examination Using Ballistic and Radar Integrated Software (17) Data Distribution System (DDS) and Solar Dynamic Observatory Ground Station (SDOGS) (18) Integration Manager (19) Eclipse-Free-Time Assessment Tool for IRIS (20) Automated and Manual Rocket Crater Measurement Software (21) MATLAB Stability and Control Toolbox Trim and Static Stability Module (22) Patched Conic Trajectory Code (23) Ring Image Analyzer (24) SureTrak Probability of Impact Display (25) Implementation of a Non-Metallic Barrier in an Electric Motor (26) Multi-Mission Radioisotope Thermoelectric Generator Heat Exchangers for the Mars Science Laboratory Rover (27) Uniform Dust Distributor for Testing Radiative Emittance of Dust-Coated Surfaces (28) MicroProbe Small Unmanned Aerial System (29) Highly Stable and Active Catalyst for Sabatier Reactions (30) Better Proton-Conducting Polymers for Fuel-Cell Membranes (31) CCD Camera Lens Interface for Real-Time Theodolite Alignment (32) Peregrine 100-km Sounding Rocket Project (33) SOFIA Closed- and Open-Door Aerodynamic Analyses (34) Sonic Thermometer for High-Altitude Balloons (35) Near-Infrared Photon-Counting Camera for High-Sensitivity Observations (36) Integrated Optics Achromatic Nuller for Stellar Interferometry (37) High-Speed Digital Interferometry (38) Ultra-Miniature Lidar Scanner for Launch Range Data Collection (39) Shape and Color Features for Object Recognition Search (40) Explanation Capabilities for Behavior-Based Robot Control (41) A DNA-Inspired Encryption Methodology for Secure, Mobile Ad Hoc Networks (42) Quality Control Method for a Micro-Nano-Channel Microfabricated Device (43) Corner-Cube Retroreflector Instrument for Advanced Lunar Laser Ranging (44) Electrospray Collection of Lunar Dust (45) Fabrication of a Kilopixel Array of Superconducting Microcalorimeters with Microstripline Wiring Spacecraft Attitude Tracking and Maneuver Using Combined Magnetic Actuators (46) Coherent Detector for Near-Angle Scattering and Polarization Characterization of Telescope Mirror Coatings

Source record↗
DOE OSTI2018

Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics

Here, the dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Droplet and Particle Methods to Investigate Turbulent Particle Laden Jets

The SARS-CoV-2 pandemic has heightened the interest in particle-laden turbulent jets generated by breathing, talking, coughing and sneezing, and how these can contribute to disease transmission. We present quantitative measurement methods for such flows, while exploring and offering improvements for common shortcomings. We generate jets consisting of either liquid droplets or solid particles in an isothermal, quiescent and electrically isopotential experimental chamber that was constructed to control the effects of ambient forcing on jet behavior. For liquid droplets, we find promise in surface deposition analysis based on fluorescent tracer use. For particles, we explore the performance of commercially available adhesive sampling strips and develop conductive grounded carbon tape based sampling strips. We explore ways in which the smallest of thermal gradients or electrostatic charge issues can affect particle dispersion, and suggest practical methods to address these issues. The developed methods are applied to study the simultaneous deposition of (Formula presented.) 25, 50 and 200 μm solid particles from a particle laden turbulent jet with a mean velocity of 33.2 m/s. The deposition location as a function of particle size was compared to results from a simple numerical RANS model, and illustrates ways in which imprecise initial or boundary conditions can lead to a notable deviation from experimental results. The differences in deposition pattern seen in experimental and numerical results despite a carefully controlled environment and characterized particle ejection indicate the need for a more stringent numerical model validation, especially when studying fate and transport of mid-range (neither purely aerosol or ballistic) sized particles.

42 ENGINEERING↗
NASA NTRS1989

NASA/MSFC nozzle test bed

As part of an effort to improve the state-of-the-art in nozzle technology, a solid propulsion test bed facility is being designed and will be located at Marshall Space Flight Center. The test bed will consist of a plasma arc facility and several small scale rocket motor test facilities ranging in size from the ballistic environmental generator motor with a 1/2 in. diameter throat to the MNASA motor with a 9 and 1/2 in. diameter throat capability. The test bed system will be used primarily to study materials behavior from the standpoint of char, erosion, and thermal stress phenomena.

Crose, James G.↗
NASA NTRS2000

Discharge Coefficients for Axisymmetric Supersonic Nozzles

Computational Fluid Dynamics (CFD) analysis was used to compute effective nozzle discharge coefficients for subscale sharp-edged converging/diverging nozzles, with a variety of convergence half-angles, motor operating conditions, and two propellants with different ballistics. Convergence half-angles ranged from 0 to 80 deg. Analysis was conducted at total temperatures from 2946K (5303R) to 3346K (6023R) and over total pressures ranged from 2.72 MPa (395 psia) to 20.68 MPa (3000 psia). Area ratios (A(sub e)/A*) ranged from 7.43 to 9.39. Ratio of specific heats (gamma) ranged from 1.13 to 1.18. Throat and exit Reynolds numbers were calculated to be 8.26 x 10(exp 5) and 5.51 x 10(exp 5), respectively. Present results of nozzle discharge coefficients are reported and correlated as a function of nozzle convergence half-angle (theta(sub c)) and area ratios (A(sub e)/A*) for a constant divergence half-angle (theta(sub d)) of 15 deg. Computed discharge coefficients ranged from 0.88 to 0.97. They are compared with theory and experimental data available in literature. Available turbulence models with respect to grid refinements and heat transfer are discussed.

Ahmad, Rashid A.↗
NASA NTRS2014

Effects of High-Density Impacts on Shielding Capability

Spacecraft are shielded from micrometeoroids and orbital debris (MMOD) impacts to meet requirements for crew safety and/or mission success. In the past, orbital debris particles have been considered to be composed entirely of aluminum (medium-density material) for the purposes of MMOD shielding design and verification. Meteoroids have been considered to be low-density porous materials, with an average density of 1 g/cu cm. Recently, NASA released a new orbital debris environment model, referred to as ORDEM 3.0, that indicates orbital debris contains a substantial fraction of high-density material for which steel is used in MMOD risk assessments [Ref.1]. Similarly, an update to the meteoroid environment model is also under consideration to include a high-density component of that environment. This paper provides results of hypervelocity impact tests and hydrocode simulations on typical spacecraft MMOD shields using steel projectiles. It was found that previous ballistic limit equations (BLEs) that define the protection capability of the MMOD shields did not predict the results from the steel impact tests and hydrocode simulations (typically, the predictions from these equations were too optimistic). The ballistic limit equations required updates to more accurately represent shield protection capability from the range of densities in the orbital debris environment. Ballistic limit equations were derived from the results of the work and are provided in the paper.

Christiansen, Eric L.↗
DOE OSTI2012

Steering and collimating ballistic electrons with amphoteric refraction

We show that amphoteric refraction of ballistic electrons, i.e., positive or negative refraction depending on the incidence angle, occurs at an interface between an isotropic and an anisotropic medium and can be employed to steer and collimate electron beams. The steering angle is determined by the materials' parameters, but the degree of collimation can be tuned in a significant range by changing the energy of ballistic electrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Effect of substrate temperature on sputter-deposited boron carbide films

Sputter deposition of B4C films with tailored physical properties remains a challenge. Here, we systematically study how substrate temperature influences the properties of B4C films deposited by direct current magnetron sputtering onto planar substrates held at temperatures in the range of 100-510°C. Results show that all films are amorphous stoichiometric B4C, with low O content of ~1 at. %. Films deposited onto substrates at 100°C exhibit high compressive residual stress and decreased mechanical properties. Therefore, for elevated substrate temperatures in the range of 180-510°C, film mass density, surface roughness, Young’s modulus, and hardness are weakly dependent on substrate temperature. However, in this temperature range, an increase in substrate temperature leads to larger residual compressive stress accompanied by a corresponding reduction in the concentration of nanoscale inhomogeneities. At least for the landing atom ballistics conditions studied here, a substrate temperature range of ~185-250°C is optimum for growing films with near-zero intrinsic residual stress. The overall weak substrate temperature dependence of film properties revealed in this work is favorable for the development of a robust deposition process, particularly for the case of deposition onto non-planar substrates where temperature control is often challenging.

36 MATERIALS SCIENCE↗
NASA NTRS2007

Materials Database Development for Ballistic Impact Modeling

A set of experimental data is being generated under the Fundamental Aeronautics Program Supersonics project to help create and validate accurate computational impact models of jet engine impact events. The data generated will include material property data generated at a range of different strain rates, from 1x10(exp -4)/sec to 5x10(exp 4)/sec, over a range of temperatures. In addition, carefully instrumented ballistic impact tests will be conducted on flat plates and curved structures to provide material and structural response information to help validate the computational models. The material property data and the ballistic impact data will be generated using materials from the same lot, as far as possible. It was found in preliminary testing that the surface finish of test specimens has an effect on measured high strain rate tension response of AL2024. Both the maximum stress and maximum elongation are greater on specimens with a smoother finish. This report gives an overview of the testing that is being conducted and presents results of preliminary testing of the surface finish study.

Pereira, J. Michael↗
DOE OSTI2015

Defocusing of an ion beam propagating in background plasma due to two-stream instability

The current and charge neutralization of charged particle beams by background plasma enable ballistic beam propagation and have a wide range of applications in inertial fusion and high energy density physics. However, the beam-plasma interaction can result in the development of collective instabilities that may have deleterious effects on ballistic propagation of an ion beam. In the case of fast, light-ion beams, non-linear fields created by instabilities can lead to significant defocusing of the beam. We study an ion beam pulse propagating in a background plasma, which is subjected to two-stream instability between the beam ions and plasma electrons, using PIC code LSP. The defocusing effects of the instability on the beam can be much more pronounced in small radius beams. We show through simulations that a beamlet produced from an ion beam passed through an aperture can be used as a diagnostic tool to identify the presence of the two-stream instability and quantify its defocusing effects. The effect can be observed on the Neutralized Drift Compression Experiment-II facility by measuring the spot size of the extracted beamlet propagating through several meters of plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2019

Ballistic Entries for Saturn, Uranus, and Neptune with HEEET TPS

One important observation from the Ice Giants Study was that the predicted and margined thicknesses of HEEET were greater than could be woven with the currently established loom capabilities. Since the cost of a loom upgrade could be substantial and time consuming, the present work explored the entry trajectory space to determine what combinations of entry parameters would result in HEEET thicknesses that fit within the existing loom infrastructure. Toward this end, the entry trajectory space, parameterized by ballistic coefficient and entry flight path angle, was systematically explored for 45° sphere-cone geometries of 3 different radii – 0.2 m, 0.3 m, and 0.4 m – which covered the range from Galileo-derived probes considered in the Ice Giants Study, and a follow-on study on the possibility of using a single probe architecture (in terms of size and mass) for various destinations, including Venus, Saturn, Uranus, and Neptune. The entry velocities, latitudes, and azimuths at Uranus and Neptune used in the present work were taken from the Ice Giants Study. For each 3DOF trajectory generated by a NASA Ames in-house code, TRAJ, the material response and thickness were computed using another NASA Ames code, FIAT, along with a margins policy proposed by the HEEET project. In the present work, ballistic coefficients ranging from 200 kg/sq m to 350 kg/sq m were considered along with entry flight path angles ranging from -16° to -36° (primarily to allow deceleration loads to vary between 50 g and 200 g).

Atmospheric Entry↗
NASA NTRS2019

Exploration of Atmospheric Entries at Uranus & Neptune with HEEET as Heatshield TPS

One important observation from the recent Ice Giants Study sponsored by NASA was that the predicted and margined thicknesses of HEEET (new NASA TPS technology) were much greater than could be woven with the currently established loom capabilities. Since the cost of a loom upgrade would be substantial, the present work explores the entry trajectory space to determine what combinations of entry parameters would result in HEEET thicknesses that fit within the existing loom infrastructure. Toward this end, the entry trajectory space, parameterized by ballistic coefficient and entry flight path angle, was systematically explored for 45° sphere-cone geometries of 3 different radii 0.2 m, 0.3 m, and 0.4 m which covered the range from Galileo-derived probes considered in the Ice Giants Study, and a follow-on study on the possibility of using a single probe architecture (in terms of size and mass) for various destinations, including Venus, Saturn, Uranus, and Neptune. The entry velocities, latitudes, and azimuths at Uranus and Neptune used in the present work were taken from the Ice Giants Study. For each 3D OF trajectory generated by a NASA Ames in-house code, TRAJ, the material response and thickness were computed using another NASA Ames code, FIAT, along with a margins policy proposed by the HEEET project. In the present work, ballistic coefficients ranging from 200 kg/sqm to 350 kg/sqm were considered along with entry flight path angles ranging from -16° to -36° (primarily to allow deceleration loads to vary between 50 g and 200 g).

Prabhu, Dinesh K.↗
NASA NTRS2019

Exploration of Atmospheric Entries at Uranus & Neptune with HEEET as Heatshield TPS

One important observation from the Ice Giants Study was that the predicted and margined thicknesses of HEEET were greater than could be woven with the currently established loom capabilities. Since the cost of a loom upgrade would be substantial, the present work explored the entry trajectory space to determine what combinations of entry parameters would result in HEEET thicknesses that fit within the existing loom infrastructure. Toward this end, the entry trajectory space, parameterized by ballistic coefficient and entry flight path angle, was systematically explored for 45° sphere-cone geometries of 3 different radii – 0.2 m, 0.3 m, and 0.4 m – which covered the range from Galileo-derived probes considered in the Ice Giants Study, and a follow-on study [4] on the possibility of using a single probe architecture (in terms of size and mass) for various destinations, including Venus, Saturn, Uranus, and Neptune. The entry velocities, latitudes, and azimuths at Uranus and Neptune used in the present work were taken from the Ice Giants Study [1]. For each 3DOF trajectory generated by a NASA Ames in-house code, TRAJ [5], the material response and thickness were computed using another NASA Ames code, FIAT [6], along with a margins policy proposed by the HEEET project [7]. In the present work, ballistic coefficients ranging from 200 kg/m2 to 350 kg/m2 were considered along with entry flight path angles ranging from -16° to -36° (primarily to allow deceleration loads to vary between 50 g and 200 g).

HEEET↗
DOE OSTI2019

Thermoelectric Mechanism of Field Emission from Carbon Nanostructures

A model describing peculiarities of field emission from carbon nanomaterials is considered. The model is based on inclusion by drag of electrons by ballistic phonons in the temperature gradient range in the emission center. The model does not require any additional assumptions concerning a special energy structure of the emission center. Quantitative estimates of the thermopower coefficient obtained based on the emission model are in good agreement with experimental results.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS2016

Bumper 3 Update for IADC Protection Manual

The Bumper code has been the standard in use by NASA and contractors to perform meteoroid/debris risk assessments since 1990. It has undergone extensive revisions and updates [NASA JSC HITF website; Christiansen et al., 1992, 1997]. NASA Johnson Space Center (JSC) has applied BUMPER to risk assessments for Space Station, Shuttle, Mir, Extravehicular Mobility Units (EMU) space suits, and other spacecraft (e.g., LDEF, Iridium, TDRS, and Hubble Space Telescope). Bumper continues to be updated with changes in the ballistic limit equations describing failure threshold of various spacecraft components, as well as changes in the meteoroid and debris environment models. Significant efforts are expended to validate Bumper and benchmark it to other meteoroid/debris risk assessment codes. Bumper 3 is a refactored version of Bumper II. The structure of the code was extensively modified to improve maintenance, performance and flexibility. The architecture was changed to separate the frequently updated ballistic limit equations from the relatively stable common core functions of the program. These updates allow NASA to produce specific editions of the Bumper 3 that are tailored for specific customer requirements. The core consists of common code necessary to process the Micrometeoroid and Orbital Debris (MMOD) environment models, assess shadowing and calculate MMOD risk. The library of target response subroutines includes a board range of different types of MMOD shield ballistic limit equations as well as equations describing damage to various spacecraft subsystems or hardware (thermal protection materials, windows, radiators, solar arrays, cables, etc.). The core and library of ballistic response subroutines are maintained under configuration control. A change in the core will affect all editions of the code, whereas a change in one or more of the response subroutines will affect all editions of the code that contain the particular response subroutines which are modified. Note that the Bumper II program is no longer maintained or distributed by NASA.

Christiansen, Eric L.↗
DOE OSTI2021

Excellent ballistic impact resistance of Al 0.3 CoCrFeNi multi-principal element alloy with unique bimodal microstructure

Multi-principal element alloys represent a new paradigm in structural alloy design with superior mechanical properties and promising ballistic performance. Here, the mechanical response of Al 0.3 CoCrFeNi alloy, with unique bimodal microstructure, was evaluated at quasistatic, dynamic, and ballistic strain rates. The microstructure after quasistatic deformation was dominated by highly deformed grains. High density of deformation bands was observed at dynamic strain rates but there was no indication of adiabatic shear bands, cracks, or twinning. The ballistic response was evaluated by impacting a 12 mm thick plate with 6.35 mm WC projectiles at velocities ranging from 1066 to 1465 m/s. The deformed microstructure after ballistic impact was dominated by adiabatic shear bands, shear band induced cracks, microbands, and dynamic recrystallization. The superior ballistic response of this alloy compared with similar Al x CoCrFeNi alloys was attributed to its bimodal microstructure, nano-scale L1 2 precipitation, and grain boundary B2 precipitates. Deformation mechanisms at quasistatic and dynamic strain rates were primarily characterized by extensive dislocation slip and low density of stacking faults. Deformation mechanisms at ballistic strain rates were characterized by grain rotation, disordering of the L1 2 phase, and high density of stacking faults.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Thermal Protection System to Enable Ice Giant Aerocapture Mission for Delivering Both an Orbiter and an In Situ Probe

The Ice Giants have been identified as high priority science destinations in the last Decadal Survey [1] and could benefit from aerocapture as the primary method for orbit insertion [2]. A mass-efficient aerocapture system will enable the delivery of an orbiter along with an atmospheric probe (for in situ measurements to anchor global data collected by the orbiter) and possibly a lander at Triton [3]. Aerocapture could be executed either using low L/D rigid aeroshell with lift modulation (LMA) [4] or using deployable aeroshell using drag modulation (DMA) [3]. Nearly two decades ago, a NASA-funded team performed Neptune-Triton aerocapture studies with a mid-L/D lifting configuration [5] for achieving orbit using LMA. This study showed aerocapture challenges. Due to very high peak entry conditions combined with very high heat-load, a suite of TPS materials was required and this suite was deemed problematic from a qualification perspective, due test facility limitations. In the past 20 years, progress made in GN&C for lift-guided entry missions such as MSL, Orion EFT1, Mars 2020 and the upcoming Artemis missions, and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity and most technologies are in hand to propose missions with aerocapture [6] [7]. Aerocapture using DMA, currently in development, is an option for Ice Giant Missions. While DMA is simpler in some sense, due to ballistic entry and no need for lift-guided maneuvering, it has challenges and it’s maturity is lower. LMA and DMA both require one or more ablative Thermal Protection System (TPS) materials for the rigid aeroshell element. The ablative TPS needs to be robust and mass efficient due to the high heat loads and size of the rigid aeroshell. Currently, there are capable ablative thermal protection materials, e.g., Heatshield for Extreme Entry Environments Technology (HEEET), 3-D woven Mid-Density Carbon- Phenolic (3MDCP), and PICA (Phenolic-Impregnated Carbon Ablator) that are mature, i.e., at TRL 6 or higher. NASA also invested in Conformal PICA that was matured to TRL 5. Our goal is to evaluate the applicability of high TRL TPS and consider other design options. We first establish bounding aerocapture trajectories for a wide range of arrival conditions and the associated aerothermal environment. Based on the environments, we then determine the predicted TPS mass for the aeroshell [4]. In this presentation, we will outline the process by which we establish bounding aerocapture trajectories for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, which are shown to be a range of velocities that can reduce the trip time from ~14 years to 8 years. The above velocity range translates to ~12 km/s to ~24 km/s arrival velocities at the planetary entry interface [2]. The velocity reduction required to achieve orbit ranges between ~2.5 km/s to 9.5 km/s for both Neptune and Triton. Propulsive insertion alone, due to the amount of fuel required to achieve the required velocity reduction, limits the science returned [2]. We establish the bounding aerocapture trajectories for a low L/D (~ 0.4) configuration for three different ballistic coefficients. The ballistic coefficient range is determined from three different aeroshell diameters of 3m, 4m and 5m and with an entry system mass of 2200 kg. With the above range of design parameters, we then determine conservative/bounding estimates of aerothermal environments by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to first assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are computed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on total trip time reduction and other design parameters for a range of TPS. This is a large range for TPS mass fraction. We show PICA and HEEET can indeed enable aerocapture missions, but the missions incur a mass penalty. TPS mass savings, can be further reduced with the use of conformal PICA. Advancing the development of Conformal PICA to make it robust across the entire aerothermal environment (peak heat-flux, pressure and shear) range will result in TPS mass fractions of < 10% for Ice Giant aerocapture missions such as the Neptune-Triton mission. Aerocapture allows for not only shortening the trip time but enables larger mass to be placed in orbit. Furthermore, probes deployed from orbit will benefit in reduced entry environments allowing for a lower risk TPS implementation as compared to mission designs where the probe is released prior to orbit insertion. One of the challenges for the Ice Giant community is to ensure mission designs that maximize science and allow flexibility in the placement of the entry probe. The traditional approach to release the probe ahead of the orbiter may not optimize returned science. In this presentation, we will make the case for mature TPS such as HEEET and PICA. While these materials can enable aerocapture missions, completing the development of conformal PICA and extending Conformal PICA to be more robust, will have significant impact to TPS mass efficiency and significantly enhance science return for future Gas- and Ice-Giant missions.

E Venkatapathy↗
NASA NTRS1980

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

Longuski, J. M.↗