Optimum earth re-entry corridors
Steepest ascent optimization procedure for reentry trajectory of manned aerospace vehicles
REENTRY TRAJECTORY↗
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A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations
Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.
Radiation↗
Range of Density Variability from Surface To 120 km Altitude
A re-entry space vehicle development program, such as Project Apollo, requires a knowledge of the variability of atmospheric density from the surface of the earth to re-entry altitude (120 km). This report summarizes the data on density given in the most recent literature on the subject. The range of atmospheric density with respect to the ARDC 1959 Model Atmosphere is determined and shown graphically. From the surface to 30 km altitude abundant information on density is available. From 30 to 90 km altitude the summarized reports of observations made at a limited number of stations have been used. Between 90 and 120 km altitude the density is somewhat speculative, there being but few measurements available. Therefore, the qualitative values for the variability of density above 30 km must be considered tentative. Variations of atmospheric density by latitude and seasons made it necessary to develop a family of curves rather than a single profile. Three curves are presented to show the range of density deviation versus altitudes with respect to the ARDC 1959 Model Atmosphere. Each curve is used for a specific latitude range and season.
Orvel E Smith↗
Re-entry of nuclear rockets into earth's atmosphere
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Weiner, R. I.↗
Subsonic Longitudinal Aerodynamic Characteristics of Disks with Elliptic Cross Sections and Thickness-Diameter Ratios from 0.225 to 0.425
General interest in manned space flight has provided a stimulus for the investigation of shapes which appear to be attractive for application to re-entry vehicles. Such vehicles can be classed as either nonlifting or lifting. Nonlifting types, such as used in Project Mercury, have certain advantages which include structural simplicity, no requirement for an elaborate flight-control system, ease of mating with the booster, and short exposure times to high heating rates during entry. Advantages of lifting types, by comparison, include lower peak heating rates and decelerations, the possibility for a conventional horizontal landing, and the ability to maneuver, thus providing control over longitudinal and lateral range and a wider entry corridor on return from planetary or lunar missions. A lifting shape which appears attractive in terms of the considerations is a thick disk. At high attitudes, the weight to drag ratio is low and the radius of curvature of the surface exposed to the airstream is large, a combination of parameters which results in reduced convective heating rates. The low-speed lift-drag ratios associated with this type of shape appear sufficiently high to permit a conventional horizontal landing. The investigation reported herein was undertaken to assess the effects of thickness on the aerodynamic characteristics of disk shapes suitable for lifting re-entry into the earth's atmosphere and potentially capable of conventional horizontal landing. The models had elliptic cross sections which varied in thickness from 0.225 to 0.425 diameter. The tests were conducted in the Ames 12-Foot Pressure Wind Tunnel over a Mach number range from 0.25 to 0.90 at a Reynolds number of 3.3x10 (exp 6) and at Reynolds numbers to 16x10 (exp 6) at a Mach number of 0.25. Tests on similar shapes have been conducted at subsonic, transonic, and supersonic speeds and the results have been presented.
Demele, Fred A.↗
The OSIRIS-REx Sample Return Capsule re-entry: A coordinated seismo-acoustic observational campaign for the study of meteor phenomena
Objects entering Earth’s atmosphere at hypersonic velocities may generate powerful acoustic waves. Depending on atmospheric conditions and acoustic propagation paths, they may be captured using ground or balloon-borne microbarometers and microphones. Impacts into the Earth’s atmosphere by asteroids in a meter-size range are sporadic and unannounced, and thus, well-documented scientific observations of asteroids are rare and generally happen by chance. Arriving from interplanetary space at hypervelocity, spacecraft are considered analogues for low velocity meteoroids and asteroids impacting the Earth’s atmosphere, and as such provide unprecedented and unique opportunity to carry out planned observational campaigns and perform detailed studies of meteor phenomena. However, since the end of the Apollo era, only four instances of a hypersonic re-entry of an artificial body from interplanetary space with an incident speed of 11-12 km/s have been observed and studied. These were the Sample Return Capsules (SRCs) that brought physical samples of extraterrestrial material back to Earth (Genesis, Stardust, Hayabusa 1, Hayabusa 2). These re-entries were also detected by infrasound and/or seismic sensors. The next opportunity to observe an artificial meteor will be on 24 September 2023 with the re-entry of NASA’s OSIRIS-REx SRC that will bring samples of the carbonaceous near-Earth asteroid Bennu. The re-entry consists of several flight phases, including hypersonic and supersonic, providing a unique opportunity to observe these by infrasound and seismic sensors. We will discuss observational campaign efforts aimed to capture geophysical signals generated by the OSIRIS-REx SRC re-entry. This campaign utilizes an unparalleled number of instruments, both ground and airborne, strategically positioned in the immediate and extended region around the projected re-entry trajectory to maximize the scientific output.
47 - OTHER INSTRUMENTATION↗
NON-EQUILIBRIUM AND EQUILIBRIUM RADIATION AT SUPERSATELLITE RE-ENTRY VELOCITIES
Presentation of engineering estimates of radiation heating of vehicles reentering the earths atmosphere from lunar or interplanetary missions
SPACECRAFT REENTRY↗
Array-Based Seismic Measurements of OSIRIS-REx’s Re-Entry
The return home of the OSIRIS-REx spacecraft in September 2023 marked only the fifth time that an artificial object entered the Earth’s atmosphere at interplanetary velocities. Although rare, such events serve as valuable analogs for natural meteoroid re-entries; enabling study of hypersonic dynamics, shock wave generation, and acoustic-to-seismic coupling. Here, in this study, we report on the signatures recorded by a dense (100 m scale) 11-station array located almost directly underneath the capsule’s point of peak atmospheric heating in northern Nevada. Seismic data are presented, which allow inferences to be made about the shape of the shock wave’s footprint on the surface, the capsule’s trajectory, and its flight parameters.
58 GEOSCIENCES↗
Design comparison of lunar return configurations
Parabolic manned re-entry design comparisons are made between two classes of slender and blunt configurations capable of conventional horizontal and vertical earth landings. Aerodynamic modulation using flaps and control augmentation requirements are discussed in terms of their effect upon re-entry trajectories and landing footprints. Within the environment defined by the re-entry trajectories, the convective and radiative modes of heat transfer are compared, their differences discussed, and the problems associated with the configurations for planetary return missions indicated. Thermal protection systems are discussed and the factors influencing the selection of a given system for the re-entry environment are indicated. Comparison between reflective and absorptive systems are made and the merits of each for a given flight time indicated. A thermo-structural analysis is presented which shows the trade-oft between structural operating temperature and heat protection system thickness requirements. Total heat shield and structural weights are compared for the landing footprints presented and their variation with range shown. Finally, the areas of uncertainty in the aero-thermo structural design analysis are indicated for each class of configuration studied, and the weight differences between conventional horizontal landing and vertical descent configurations are given.
Parabolic flight↗
Simulation of atmospheric drag
To accurately simulate the trajectory of an artificial satellite or space probe, the deceleration from atmospheric drag must be considered. In addition to the Earth, there is evidence that Mars, Venus and Jupiter have sufficiently dense atmospheres to affect the motion of a space vehicle. This paper discusses some problems involved in simulating planetary atmospheres themselves, and the results of making certain simplifying assumptions. The object of this report is to come up with a recommendation for a method of simulating atmospheric drag representing a complexity commensurate with the state of the art. It should be noted that the mission of ·the vehicle has to be considered. There are three missions in which atmospheric drag could play an important part. The first mission is a low eccentricity orbit about the Earth or another planet. The second mission is a planetary re-entry and .the third is a flyby orbit of the space vehicle. The three cases will be referred to as the "orbiting'", "reentry" and "fly -by" cases.
COMPUTER SIMULATION↗
ANALYSIS OF QUARTZ AND TEFLON SHIELDS FOR A PARTICULAR RE-ENTRY MISSION
The transient performance of ablation type heat protection shields is treated herein for the surface of a vehicle returning from outer space to the earth. The vehicle weighs 8640 kg, has a ballistic factor of 500 lb/ft2, re-enters with a speed of 11 km/sec at 120 km altitude, has a lift over drag ratio of -0.5, and is subjected to a maximum deceleration of 7.7 times the gravity constant. By use of well-known equations for the heat transfer and the mass transfer at a heated surface, a numerical calculation method is derived which, for the investigated ablation processes, yields exact transient solutions of the fundamental system of partial differential equations. The method is applied to various quartz shields and to one Teflon shield, which all evaporate so readily under the conditions of the problem at hand that practically no flow of molten shield material exists. The solutions also show comparatively small temperature changes parallel to the surface. The results show that the nose of the vehicle is cooled predominantly by the evaporation of the quartz or the Teflon; the rest of the vehicle's surface is cooled by radiation of the quartz or evaporation of the Teflon. The large mass transfer effects on the nose of the vehicle are detrimental since the resulting low surface temperatures prevent the radiative heat transfer out of the shield, which does not involve any mass loss, from being the desirable governing cooling factor.
ABLATING MATERIAL↗
Return launch and re-entry vehicles.
Manned lunar return launch and reentry vehicles, emphasizing spacecraft and system weight in relation to mission mode and propulsion
WEIGHT FACTOR↗
Study of the Oscillatory Motion of Manned Vehicles Entering the Earth's Atmosphere
An analysis is made of the oscillatory motion of vehicles which traverse arbitrarily prescribed trajectories through the atmosphere. Expressions for the oscillatory motion are derived as continuous functions of the properties of the trajectory. Results are applied to a study of the oscillatory behavior of re-entry vehicles which have decelerations that remain within limits of human tolerance. It is found that a deficiency of aerodynamic damping for such vehicles may have more serious consequences than it does for comparable ballistic missiles.
Sommer, Simon C.↗
Preface to the Focus Section on Geophysical Observations of the OSIRIS-REx Sample Return Capsule Re-Entry
Here, this focus issue of Seismological Research Letters compiles observational results and theoretical interpretations related to the OSIRIS-REx SRC re-entry and multidisciplinary analyses highlighting broader scientific applications of such events (Carr et al., 2025; Clemente et al., 2025; Fernando et al., 2025; KC et al., 2025; Silber and Bowman, 2025). The articles contribute toward a geophysical understanding of how hypersonic objects interact with Earth’s atmosphere and how generated acoustic waves propagate through the atmosphere and couple into the ground as measurable seismic signals.
58 GEOSCIENCES↗
Multi-arrival infrasound from meteoroids: Fragmentation signatures versus propagation effects in a fine-scale layered atmosphere
Infrasonic signatures of meteoroid fragmentation are frequently ambiguous: do multiple arrivals signify a complex breakup or merely the distorting effects of a layered atmosphere? Resolving this ambiguity is critical for accurate energy estimates and source reconstruction. In this study, we address this challenge by analyzing a unique regional dataset of well-constrained meteoroid events observed by the Southern Ontario Meteor Network and the co-located Elginfield Infrasound Array. We employ pseudo-differential parabolic equation (PPE) simulations to quantify how fine-scale gravity-wave structures in the stratosphere and lower thermosphere modify acoustic waveforms at ranges <300 km. Our modeling reveals that while fine-scale layering can stretch signals and generate diffuse oscillatory tails, it does not produce discrete, high-amplitude pulse splitting at ranges below ∼140 km. By applying these results to the rare multi-arrival event 20060305, we demonstrate that its distinct double arrival at 100 km range is inconsistent with atmospheric multipathing and provides definitive evidence of separate fragmentation episodes. These findings establish new diagnostic criteria for separating source physics from propagation artifacts, improving the reliability of infrasound as a monitoring tool for natural bolides, space debris re-entries, and catastrophic launch failures.
79 ASTRONOMY AND ASTROPHYSICS↗
Detection of a Space Capsule Entering Earth’s Atmosphere with Distributed Acoustic Sensing (DAS)
On 24 September 2023, the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer sample return capsule (SRC) entered Earth’s atmosphere after successfully collecting samples from an asteroid. The known trajectory and timing of this return provided a rare opportunity to strategically instrument sites to record geophysical signals produced by the capsule because it travelled at hypersonic speeds through the atmosphere. For this work, we deployed two distributed acoustic sensing (DAS) interrogators to sample over 12 km of surface-draped fiber-optic cables, as well as six collocated seismometer-infrasound sensor pairs, spread across two sites near Eureka, Nevada. This campaign-style rapid deployment is the first reported recording of an SRC re-entry with any distributed fiber-optic sensing technology. The DAS interrogators recorded an impulsive arrival with an extended coda which had features that were similar to recordings from both the seismometers and infrasound sensors. While the signal-to-noise ratio of the DAS data was lower than the seismic-infrasound data, the extremely dense spacing of fiber-optic sensors allowed for more phases to be clearly distinguished and the visualization of the continuous transformation of the wavefront as it impacted the ground. Unexpectedly, the DAS recordings contain less low-frequency content than is present in both the seismic and infrasound data. The deployment conditions strongly affected the recorded DAS data; in particular, we observed that fiber selection and placement exert strong controls on data quality.
58 GEOSCIENCES↗
A comparative analysis of the performance of long-range hypervelocity vehicles
Long-range hypervelocity vehicles are studied in terms of their motion in powered flight, and their motion and aerodynamic heating in unpowered flight. Powered flight is analyzed for an idealized propulsion system which rather closely approaches present-day rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors is studying ballistic missiles (NACA RM A53D28), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. The ballistic vehicle is found to be the least efficient of the several types studied in the sense that it generally requires the highest velocity at the end of powered flight in order to attain a given range. This disadvantage may be offset, however, by reducing convective heat transfer to the re-entry body through the artifice of increasing pressure drag in relation to friction drag - that is, by using a blunt body. Thus the kinetic energy required by the vehicle at the end of powered flight may be reduced by minimizing the mass of coolant material involved.
Eggers, Alfred J , Jr↗
Three-Dimensional Orbits of Earth Satellites, Including Effects of Earth Oblateness and Atmospheric Rotation
The principal purpose of the present paper is to present sets of equations which may be used for calculating complete trajectories of earth satellites from outer space to the ground under the influence of air drag and gravity, including oblateness effects, and to apply these to several examples of entry trajectories starting from a circular orbit. Equations of motion, based on an "instantaneous ellipse" technique, with polar angle as independent variable, were found suitable for automatic computation of orbits in which the trajectory consists of a number of revolutions. This method is suitable as long as the trajectory does not become nearly vertical. In the terminal phase of the trajectories, which are nearly vertical, equations of motion in spherical polar coordinates with time as the independent variable were found to be more suitable. In the first illustrative example the effects of the oblateness component of the earth's gravitational field and of atmospheric rotation were studied for equatorial orbits. The satellites were launched into circular orbits at a height of 120 miles, an altitude sufficiently high that a number of revolutions could be studied. The importance of the oblateness component of the earth's gravitational field is shown by the fact that a satellite launched at circular orbital speed, neglecting oblateness, has a perigee some 67,000 feet lower when oblateness forces are included in the equations of motion than when they are not included. Also, the loss in altitude per revolution is double that of a satellite following an orbit not subject to oblateness. The effect of atmospheric rotation on the loss of altitude per revolution was small. As might be surmised, the regression of the line of nodes as predicted by celestial mechanics is unchanged when drag is included. It is clear that the inclination of the orbital plane to the equator will be relatively unaffected by drag for no atmospheric rotation since the drag lies in the orbital plane in this case. With the inclusion of atmospheric rotation it was found that the inclination of the plane changed about one-millionth of a radian per revolution. Thus the prediction of the position of the orbital plane of an earth satellite is not complicated by the introduction of drag. The line of apsides, which without drag but with oblateness moves slowly in space, tends to move with the satellite when drag is included in the calculations. As a results, the usual linearized solutions based on oblateness alone must be basically altered when drag is included to take into account the rapid movement of the line of apsides. In the second illustrative example the final revolution was calculated to impact for a number of trajectories in an orbital plane inclined at 650 to the equator. Of particular interest is the large effect the oblateness gravitational field and atmospheric rotation can have on the impact point. For a value of CDA/m of unity, and for an initial downward angle at 80 miles altitude of 0.01 radian, such as might be utilized for manned re-entry, oblateness had an influence of about 300 miles in the impact point, and atmospheric rotation had about a 150-mile influence.
Nielsen, Jack N.↗