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DOE OSTI2026

Multi‐Sensor Trajectory Reconstruction of the 24 April 2025 Alaska Fireball and Implications for Planetary Defense

On 24 April 2025 at 18:30:57 UTC, a bright daytime fireball over Southcentral Alaska was detected by 37 seismic stations, 16 single infrasound sensors, and four infrasound arrays, yielding 30 ballistic and multiple fragmentation arrivals. Here, the unprecedented density of seismoacoustic coverage enabled detailed reconstruction of the event using acoustic signals, with fragmentation source locations further guiding the identification of Doppler weather radar signatures of a meteorite fall. Incorporation of a radar-derived terminal point yielded a final trajectory solution, which agreed closely with an independent optical trajectory solution from video analysis. The reconstructed entry parameters from seismoacoustic analysis indicate a velocity of 25.3 km/s, an entry angle of 19°, and an energy release of ∼38 t TNT equivalent. Assuming a chondritic composition, the pre-entry object diameter was ∼0.7 m. Using orbital parameters from the optical solution, we estimate meteoroid composition as most likely an L-type ordinary chondrite. The event occurred in the sub-Arctic, where space-based optical systems face challenges in detection, demonstrating the critical role of dense ground-based seismoacoustic networks in characterizing high-latitude atmospheric entries. This uniquely well-recorded event demonstrates the capability of dense seismoacoustic networks to constrain bolide trajectories, energetics, and fragmentation, with radar and optical data providing critical confirmation and complementary perspectives. These results bridge the methodological gap between planetary-defense monitoring of natural impactors and space-traffic analyses of artificial reentries, illustrating how multi-sensor integration can deliver calibration-grade trajectories even for unpredicted events.

Fireball↗

NASA NTRS1963

Space Flight Handbooks. Volume 3- Planetary Flight Handbook: Supplementary Trajectory Data: Venus to Earth and Mars to Earth - Part 2

Parts 2 and 3 present tabulations of trajectory data for scheduling flights to and from Venus and Mars during the period 1960-2000. Part 2 contains information for outbound flights to these planets; Part 3 contains information for trajectories returning from the planets to Earth. Each Part contains data for single-plane transfers, as well as for broken-plane transfers which employ a midcourse plane-change to eliminate the high speed "ridges." The mathematical analyses employed for all calculations are described in Part 1 of this handbook. To facilitate the construction of round-trip trajectories, the date at the target planet is held fixed while the trip duration is varied in 10-day increments from zero days to the length of that planet's synodic period with Earth. Dates of arrival at the target planet are presented in the extreme right-hand column of Part 2, and dates of departure from the target planet are presented in the extreme left-hand column of Part 3. Thus, by holding Part 2 directly to the left of Part 3, the analyst may easily and rapidly scan all trip possibilities which involve any desired stopover time at the target planet. Within approximately 200 days of each conjunction or opposition, data are presented in 10-day increments at the target planet. Only those trips are listed for which the hyperbolic excess speeds at either or both ends of the trajectory do not exceed 0.6 EMOS (Earth Mean Orbital Speed). For the remaining mission regions, the requirements are so smoothly varying that a 50-day interval in dates at the target planet may be employed; the 10-day interval in trip times is, however, preserved here. In these regions, only those trips are listed for which either or both speeds do not exceed 0.3 EMOS.

INTERPLANETARY FLIGHT↗

NASA NTRS1994

Trajectory-based heating analysis for the European Space Agency/Rosetta Earth Return Vehicle

A coupled, trajectory-based flowfield and material thermal-response analysis is presented for the European Space Agency proposed Rosetta comet nucleus sample return vehicle. The probe returns to earth along a hyperbolic trajectory with an entry velocity of 16.5 km/s and requires an ablative heat shield on the forebody. Combined radiative and convective ablating flowfield analyses were performed for the significant heating portion of the shallow ballistic entry trajectory. Both quasisteady ablation and fully transient analyses were performed for a heat shield composed of carbon-phenolic ablative material. Quasisteady analysis was performed using the two-dimensional axisymmetric codes RASLE and BLIMPK. Transient computational results were obtained from the one-dimensional ablation/conduction code CMA. Results are presented for heating, temperature, and ablation rate distributions over the probe forebody for various trajectory points. Comparison of transient and quasisteady results indicates that, for the heating pulse encountered by this probe, the quasisteady approach is conservative from the standpoint of predicted surface recession.

RADIATIVE ABLATING FLOWFIELD A↗

NASA NTRS2004

A practical six-degree of freedom solar sail dynamics model for optimizing solar sail trajectories with torque constraints

Controlled flight of a solar sail-propelled spacecraft ('sailcraft') is a six-degree-of-freedom dynamics problem. Current state-of-the-art tools that simulate and optimize the trajectories flown by sailcraft do not treat the full kinetic (i.e. force and torque-constrained) motion, instead treating a discrete history of commanded sail attitudes, and either neglecting the sail attitude motion over an integration timestep, or treating the attitude evolution kinematically with a spline or similar treatment. The present paper discusses an aspect of developing a next generation sailcraf trajectory designing optimization tool JPL, for NASA's Solar Sail Spaceflight Simulation Software (SS). The aspect discussed in an experimental approach to modeling full six-degree-of-freedom kinetic motion of a solar sail in a trajectory propagator. Early results from implementing this approach in a new trajectory propagation tool are given.

six-degree-of-freedom↗

NASA NTRS2013

Center-TRACON Automation System (CTAS) En Route Trajectory Predictor Requirements and Capabilities

This requirements framework document is designed to support the capture of requirements and capabilities for state-of-the-art trajectory predictors (TPs). This framework has been developed to assist TP experts in capturing a clear, consistent, and cross-comparable set of requirements and capabilities. The goal is to capture capabilities (types of trajectories that can be built), functional requirements (including inputs and outputs), non-functional requirements (including prediction accuracy and computational performance), approaches for constraint relaxation, and input uncertainties. The sections of this framework are based on the Common Trajectory Predictor structure developed by the FAA/Eurocontrol Cooperative R&D Action Plan 16 Committee on Common Trajectory Prediction. It is assumed that the reader is familiar with the Common TP Structure.1 This initial draft is intended as a first cut capture of the En Route TS Capabilities and Requirements. As such, it contains many annotations indicating possible logic errors in the CTAS code or in the description provided. It is intended to work out the details of the annotations with NASA and to update this document at a later time.

framework↗

NASA NTRS2013

The Impact of Trajectory Prediction Uncertainty on Air Traffic Controller Performance and Acceptability

A Human-In-The-Loop air traffic control simulation investigated the impact of uncertainties in trajectory predictions on NextGen Trajectory-Based Operations concepts, seeking to understand when the automation would become unacceptable to controllers or when performance targets could no longer be met. Retired air traffic controllers staffed two en route transition sectors, delivering arrival traffic to the northwest corner-post of Atlanta approach control under time-based metering operations. Using trajectory-based decision-support tools, the participants worked the traffic under varying levels of wind forecast error and aircraft performance model error, impacting the ground automations ability to make accurate predictions. Results suggest that the controllers were able to maintain high levels of performance, despite even the highest levels of trajectory prediction errors.

trajectory prediction uncertainty↗

NASA NTRS2016

Deconflicting Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace

North Atlantic oceanic airspace accommodates more than 1000 flights daily, and is subjected to very strong winds. Flying wind-optimal trajectories yields time and fuel savings for each individual flight. However, when taken together, these trajectories induce a large amount of potential en-route conflicts. This paper analyses the detected conflicts, figuring out conflict distribution in time and space. It further describes an optimization algorithm aimed at reducing the number of conflicts for a daily set of flights on strategic level. Several trajectory modification strategies are discussed, followed with simulation results. Finally, an algorithm improvement is presented aiming at better preserving the trajectory optimality.

wind-optimal trajectories↗

NASA NTRS2016

Monte Carlo Analysis as a Trajectory Design Driver for the TESS Mission

The Transiting Exoplanet Survey Satellite (TESS) will be injected into a highly eccentric Earth orbit and fly 3.5 phasing loops followed by a lunar flyby to enter a mission orbit with lunar 2:1 resonance. Through the phasing loops and mission orbit, the trajectory is significantly affected by lunar and solar gravity. We have developed a trajectory design to achieve the mission orbit and meet mission constraints, including eclipse avoidance and a 30-year geostationary orbit avoidance requirement. A parallelized Monte Carlo simulation was performed to validate the trajectory after injecting common perturbations, including launch dispersions, orbit determination errors, and maneuver execution errors. The Monte Carlo analysis helped identify mission risks and is used in the trajectory selection process.

trajectory↗

NASA NTRS2016

Synchronized Lunar Pole Impact Plume Sample Return Trajectory Design

The presented trajectory design enables two maneuverable spacecraft launched onto the same trans-lunar injection trajectory to coordinate a steep impact of a lunar pole and subsequent sample return of the ejecta plume to Earth. To demonstrate this concept, the impactor is assumed to use the LCROSS missions trajectory and spacecraft architecture, thus the permanently-shadowed Cabeus crater on the lunar south pole is assumed as the impact site. The sample-return spacecraft is assumed to be a CubeSat that requires a complimentary trajectory design that avoids lunar impact after passing through the ejecta plume to enable sample-return to Earth via atmospheric entry.

impact plume↗

NASA NTRS2016

Monte Carlo Analysis as a Trajectory Design Driver for the Transiting Exoplanet Survey Satellite (TESS) Mission

monte carlo↗

NASA NTRS2017

A Time-Regularized Multiple Gravity-Assist Low-Thrust Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Kepler's equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight-suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Kepler's equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization↗

NASA NTRS2017

A Time-Regularized, Multiple Gravity-Assist Low-Thrust, Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Keplers equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Keplers equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization↗

NASA NTRS2017

NASA Double Asteroid Redirection Test (Dart) Trajectory Validation and Robustness

The Double Asteroid Redirection Test (DART) mission will be the first to test the concept of a kinetic impactor. Several studies have been made on asteroid redirection and impact mitigation, however, to this date no mission tested the proposed concepts. An impact study on a representative body allows the measurement of the effects on the target's orbit and physical structure. With this goal, DART's objective is to verify the effectiveness of the kinetic impact concept for planetary defense. The spacecraft uses solar electric propulsion to escape Earth, flyby (138971) 2001 CB21 for impart rehearsal, and impact the secondary body of the (65803) Didymos system. This work focuses on the interplanetary trajectory design part of the mission with the validation of the baseline trajectory, performance comparison to other mission objectives, and assessment of the baseline robustness to missed thrust events. Results show a good performance of the selected trajectory for different mission objectives: latest possible escape date, maximum kinetic energy on impact, shortest possible time of flight, and use of an Earth swing-by. The baseline trajectory was shown to be robust to a missed thrust with 1% of fuel margin being enough to recover the mission for failures of more than 14 days.

design↗

NASA NTRS2017

Trajectory Optimization of Electric Aircraft Subject to Subsystem Thermal Constraints

Electric aircraft pose a unique design challenge in that they lack a simple way to reject waste heat from the power train. While conventional aircraft reject most of their excess heat in the exhaust stream, for electric aircraft this is not an option. To examine the implications of this challenge on electric aircraft design and performance, we developed a model of the electric subsystems for the NASA X-57 electric testbed aircraft. We then coupled this model with a model of simple 2D aircraft dynamics and used a Legendre-Gauss-Lobatto collocation optimal control approach to find optimal trajectories for the aircraft with and without thermal constraints. The results show that the X-57 heat rejection systems are well designed for maximum-range and maximum-efficiency flight, without the need to deviate from an optimal trajectory. Stressing the thermal constraints by reducing the cooling capacity or requiring faster flight has a minimal impact on performance, as the trajectory optimization technique is able to find flight paths which honor the thermal constraints with relatively minor deviations from the nominal optimal trajectory.

electric propulsion↗

NASA NTRS2014

Three-Dimensional Trajectory Design for Reducing Climate Impact of Trans-Atlantic Flights

The impact of aircraft emissions and contrails on the environment adds an additional aspect to aircraft trajectory optimization. This study developed a three-dimensional trajectory optimization algorithm for trans-Atlantic flights in cruise to generate aircraft trajectories that minimize environmental impacts due to CO2 emissions and contrails in the presence of winds. The climate-optimal trajectory is developed using dynamic programming that adjusts a wind-optimal aircraft heading while determining the optimal locations, altitudes and times for en-route step climbs. Flying wind-optimal routes minimize aircraft travel time, fuel burn and associated emissions during cruise while adjusting aircraft heading and en-route step climbs at the optimal locations and times minimize climate impact of contrails. This capability integrates an air traffic management simulation with aircraft fuel burn and emissions models, contrail formation and dispersion models, simplified climate response models, and a common climate metric. A study was conducted to evaluate the potential cost and benefits of flying climate-optimal routes in North Atlantic Airspace and their impacts to the Organized Track System design based on the trans-Atlantic air traffic during a day, July 12, 2012. Results show eastbound flights achieved a larger environmental benefit with less additional fuel burn than westbound flights that operated in strong headwinds that caused more additional fuel burn and aircraft emissions to avoid traversing contrails favorable regions.

climate impact of aviation↗

NASA NTRS2014

Trajectory Prediction Accuracy and Error Sources for Regional Jet Descents: Results of a 2010 Flight Trial at Denver International Airport using a Global 5000 Test Aircraft - Part I

The Efficient Descent Advisor (EDA) controller automation tool generates trajectory-based speed, path, and altitude-profile advisories to facilitate efficient, continuous descents into congested terminal airspace. While prior field trials have assessed the trajectory-prediction accuracy for large jet (i.e., Boeing and Airbus) types, smaller (i.e., regional and business) jet types present unique challenges involving different descent procedures and Flight Management System (FMS) capabilities. A small-jet field trial was conducted at Denver in the fall of 2010 with the objective of measuring trajectory prediction accuracy and quantifying the primary sources of error. This paper uses data collected onboard a Bombardier Global 5000 test aircraft to quantify the size and sources of trajectory prediction error. Error sources were quantified for the 44 runs by incrementally replacing predicted data with data collected onboard the aircraft and measuring the effect on time error. Results for en-route descents, from prior to top of descent to the meter fix 60-120 nmi downstream, indicate that the aircraft arrived an average 15 seconds earlier than predicted, with a standard deviation of 10 seconds. Target Mach and CAS deceleration were found to be the two largest error sources. If CAS deceleration error was reduced using a typical, more predictable level flight deceleration then the arrival time prediction error in 2010 would be on par with a 2009 flight trial of Airbus and Boeing revenue flights. Four of the error sources, tracker jumps, CAS deceleration, target Mach, and path distance, lend themselves to significant reductions with modest to no changes to ATC automation andor procedures. Wind error and its impact on arrival time error was significantly reduced in 2010 compared to a 1994 flight test using NASAs Boeing 737 test aircraft.

Trajectory Prediction Error↗

NASA NTRSDate not supplied

Spatial and Temporal Deconfliction of Trajectories in the Presence of Uncertainties

Demonstration of conflict-free movement for multi-agent teams in challenging scenarios is crucial in developing trust and trustworthiness in an autonomous transport system. Tolerance verification queries are explored as a mechanism to enforce spatial and temporal deconfliction for a cooperating team of Unmanned Aerial Systems (UAS) with prescribed heterogeneous path-following performance. Obstacles in the environment are modelled as set of polyhedra, whereas each vehicle’s trajectory is represented as a sequence of polynomial curves with C2 continuity, expressed in a Bernstein basis. Each vehicle is modelled as a point mass and a safety distance, informed by the geometry of the UAS and the worst-case path-following error. This defines a tube around the trajectories where each UAS is most likely to fly through. In addition, obstacles in the environment have an associated safety buffer around them to account for the uncertainty in their location and geometric description. The tolerance verification queries explored in this paper combine the safety distance information from each UAS and environmental hazard to compute trajectories that are contained within the safe configuration space. Tolerance verification is also compared with other proximity queries to determine the suitability of each method along the different steps of the trajectory generation algorithm. This paper analyzes the fitness and performance of three proximity queries – collision, tolerance verification, and distance computations – between polyhedral and polynomial curves to ensure deconfliction between obstacles and vehicles, but also between polynomial curves to guarantee safe separation among cooperating UAS.

trajectory generation↗

NASA NTRS2020

Design and Implementation of a Scenario Development Process for a 2040 Trajectory-Based Operations Simulation

The National Aeronautics and Space Administration (NASA) is supporting research to transition from a legacy, air traffic management (ATM) system to Trajectory-Based Operations (TBO) environment targeting the 2035-2045 timeframe by creating simulation scenarios for current and future studies. TBO in the National Airspace System (NAS) focuses on modernizing the current operating paradigm to increase efficiency, predictability, resilience, and flexibility while migrating toward greater operational autonomy across the airspace. These simulation scenarios offer a wide dissemination and use of system-level constraints and aircraft state/intent data, routine use of data communications to request complex trajectory modifications and to receive clearances, and aircraft that are flying on 4-D trajectories with flexibility when desired, but structure where required. This report describes the end-to-end development of scenarios for the NASA Langley Research Center simulation environment to represent a 2040 Trajectory-Based Operations airspace for air transport operations research.

Trajectory-Based Operations↗