Some numerical results of geocentric low thrust trajectory optimization
Determination of optimum, coplanar, circle-to- circle, transfer trajectories for low thrust space vehicles in strong central force field
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Determination of optimum, coplanar, circle-to- circle, transfer trajectories for low thrust space vehicles in strong central force field
A computer code has been developed for the analysis of SSME (Space Shuttle Main Engine) HPOTP (High Pressure Oxidizer Turbo Pump) nozzle plug trajectories in the turnaround duct downstream of the turbine. The algorithm is based on a combined Eulerian-Lagrangian analysis originally developed for the study of two-phase flows. The Lagrangian part of this analysis has been enhanced to include three-dimensional particle motion and the effect of particle-wall collisions in complex geometries (with a large number of boundaries). The sensitivity of the nozzle plug trajectories to a variety of parameters has been determined, via the qualitative analysis of a select number of computed trajectories. The results of extensive parametric studies have been reported in a companion paper.
Formulation of direct and adjoint methods of trajectory injection error in vector matrix notation and comparison
Nonaccelerated electron beam envelope trajectory equation reformulated and solved allowing for finite emittance, space charge and self- magnetostatic forces
Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.
Intense daytime surface heating over barren-to-sparsely vegetated surfaces results in dry convective mixing. In the absence of external forcing such as mountain waves, the dry convection can produce a deep, well-mixed, nearly isentropic boundary layer that becomes a well-mixed residual layer in the evening. These well-mixed layers (WML) retain their unique mid-tropospheric thermal and humidity structure for several days. To detect the SAL and characterize its properties, AIRS Level 2 Ver. 6 temperature and humidity products (2003-Present) are evaluated against rawinsondes and compared to model analysis at each of the 55 rawinsonde stations in northern Africa. To distinguish WML from Saharan air layers (WMLs of Saharan origin), the detection involved a two-step process: 1) algorithm-based detection of WMLs in dry environments (less than 7 g per kilogram mixing ratio) 2) identification of Sahara air layers (SAL) by applying Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) back trajectories to determine the history of each WML. WML occurrence rates from AIRS closely resemble that from rawinsondes, yet rates from model analysis were up to 30% higher than observations in the Sahara due to model errors. Despite the overly frequent occurrence of WMLs from model analysis, HYSPLIT trajectory analysis showed that SAL occurrence rates (given a WML exists) from rawinsondes, AIRS, and model analysis were nearly identical. Although the number of WMLs varied among the data sources, the proportion of WMLs which were classified as SAL was nearly the same. The analysis of SAL bulk properties showed that AIRS and model analysis exhibited a slight warm and moist bias relative to rawinsondes in non-Saharan locations, but model analysis was notably warmer than rawinsondes and AIRS within the Sahara. The latter result is likely associated with the dearth of available data assimilated by model analysis in the Sahara. The variability of SAL thicknesses was reasonably captured by both AIRS and model analysis, but the former favor layers than are thinner than observations. Finally, further analysis of HYSPLIT trajectories revealed that fewer than 10% and 33% of all SAL back trajectories passed through regions with notable precipitation (>100 mm accumulated along the trajectory path) or Aerosol Optical Depth (AOD greater than 0.4, 75th percentile of AOD) on average, respectively. Trajectory analysis indicated that only 57% of Saharan and 24% of non-Saharan WMLs are definitively of Saharan origin (Saharan requirement: Two consecutive days in Sahara and 24 or more of those hours within 72 hours of detection). Non-SAL WMLs either originate from local-to-regionally generated residual layers or from mid-latitude air streams that do not linger over the Sahara for a sufficient time period. Initial analysis shows these non-SAL WMLs tend to be both notably cooler and slightly moister than their SAL counter parts. Continuing analysis will address what role Saharan and non-Saharan air masses characteristics may play on local and regional environmental conditions.
Iterative guidance mode with application to three- dimensional upper stage vacuum flight
Designing interplanetary missions is an iterative process, with a tight coupling between mission analysis and vehicle design. The ability to simultaneously process both analyses early on can provide significant benefits in both the concept formulation and in overall mission feasibility. To implement such a simultaneous analysis process, there is a need to model interplanetary trajectories rapidly while maintaining an acceptable level of fidelity. Many simple patched conics tools make too many assumptions to satisfactorily address all relevant constraints and objectives, while full-fidelity trajectory design tools often require more time and expertise than is available in early conceptual studies. Hence, some form of middle-ground modeling tool would provide value. This paper introduces the development of such a tool using Python. This tool, Keplerian Analysis for Versatile Evaluation of Arbitrary Trajectories (KAVEAT), implements a patched conics method that enforces continuity of state (time, mass, position, velocity) through all transitions between various spheres of influence on the trajectory. The trajectory is constructed in an object-oriented manner, dynamically assembling unique maneuvers such as departure burns, heliocentric transfers (ballistic or with electric propulsion), and planetary flybys (powered or unpowered). Each maneuver has its own specific set of basic inputs needed to define it. The tool then takes these defined maneuvers, strings them together creating all the interdependencies required, and solves for the ideal trajectory using a gradient-based optimizer.
Single particle cryo-EM often yields multiple protein conformations within a single dataset, but experimentally deducing the temporal relationship of these conformers within a conformational trajectory is not trivial. Here, we use thermal titration methods and cryo-EM in an attempt to obtain temporal resolution of the conformational trajectory of the vanilloid receptor TRPV1 with resiniferatoxin (RTx) bound. Based on our cryo-EM ensemble analysis, RTx binding to TRPV1 appears to induce intracellular gate opening first, followed by selectivity filter dilation, then pore loop rearrangement to reach the final open state. This apparent conformational wave likely arises from the concerted, stepwise, additive structural changes of TRPV1 over many subdomains. Greater understanding of the RTx-mediated long-range allostery of TRPV1 could help further the therapeutic potential of RTx, which is a promising drug candidate for pain relief associated with advanced cancer or knee arthritis.
Trajectory optimization by explicit numerical methods
Two independent trajectory software systems are used to perform the TOPEX/Poseidon operational orbit determination and propagation: the Goddard Trajectory Determination System (GTDS) at the GSF/FDF and the Double Precision Trajectory System (DPTRAJ) at JPL. GTDS is used for operational tracking and TDRS-based orbit determination. DPTRAJ is used for ephemeris generation necessary to conduct day-to-day mission operations. This paper describes the DPTRAJ/GTDS trajectory comparison analysis conducted jointly by JPL and GSFC to ensure the compatibility of these two independent trajectory software systems.
Preliminary results are presented for two methods to approximate the mission performance of high specific impulse high specific power vehicles. The first method is based on an analytical approximation derived by Williams and Shepherd and can be used to approximate mission performance to outer planets and interstellar space. The second method is based on a parametric analysis of trajectories created using the well known trajectory optimization code, VARITOP. This parametric analysis allows the reader to approximate payload ratios and optimal power requirements for both one-way and round-trip missions. While this second method only addresses missions to and from Jupiter, future work will encompass all of the outer planet destinations and some interstellar precursor missions.
Minimization of total heat input for manned vehicles entering atmosphere at hyperbolic speeds
Various strategies are assessed by which the first two elements of Gateway could recover from missed thrust events during insertion into a Near Rectilinear Halo Orbit (NRHO). Recovery strategies are assessed in terms of their ability to maintain the desired NRHO insertion epoch ad well as their cost in terms of additional time and ∆v required to reach the NRHO. Strategies utilize a 50 kW Solar Electric Propulsion (SEP) system onboard the Power and Propulsion Element (PPE). Recovery solutions are found that, in the event of a missed thrust arc during the Insertion Phase of the Gateway Lunar Transit, deliver the space-craft into the NRHO within three additional revolutions (roughly 21 days) and 80 m/s ∆v.
This report presents data analysis results for a simulation-based approach named CASPEr (Characterization of Airplane State Prediction Error) to characterize the performance of onboard energy state and automation mode prediction functions for terminal area arrival and approach phases of flight over a wide range of conditions. In particular, the results include quantification of energy state (i.e., altitude and airspeed) prediction performance, models for prediction performance as a function of initial energy state (i.e., initial altitude, airspeed, and weight) and weather factors, and analysis of outlier prediction performance. Wind speed, wind direction, and wind gradient were found to be major factors in energy state prediction performance. Initial energy and gust intensity were also significant factors in airspeed prediction performance. Furthermore, the results suggest that errors in automation mode prediction may be a major contributor to outlier prediction performance.
Flight mechanics simulations are used to characterize the performance of Earth entry, descent, and landing vehicles. Atmospheric prediction models are often a key component of these simulations. Global atmospheric models are used for both engineering design due to their ability to define atmospheric properties over a large swath of locations and times as well as used for the availability of atmospheric uncertainties in the models that can be used in statistical performance analysis. However for day-of-flight operations, the use of forecast atmospheres based on more current measurements are beneficial to the accuracy of the performance prediction, including landing locations. Reanalysis of these forecasts can also be used for post-flight analysis, including trajectory reconstruction. This paper describes how forecast atmospheres can be beneficial for Earth entry, descent, and landing analysis and ways these models can be implemented in simulations.
Effect of thrust-weight ratios and specific impulses on trajectory parameters for earth orbit hyperbolic escape and entry
The atmospheric entry of meteoroids presents a rare and unpredictable phenomenon, posing challenges for systematic observation and detailed characterization. Such events are nonetheless critical for advancing understanding of acoustic wave propagation, atmospheric structure, and entry dynamics. In contrast, sample return capsules (SRCs) from space missions follow well constrained re-entry trajectories, enabling planned observations of shock wave generation and propagation under controlled conditions. This study compares two SRC atmospheric entries, Hayabusa2 in 2020 and OSIRIS-REx in 2023, to assess how different infrasound array configurations influence shock wave detection and trajectory validation. Hayabusa2’s re-entry was monitored using a distributed network of 28 portable infrasound sensors across seven arrays in Woomera, Australia, permitting three-dimensional reconstruction of the trajectory and analysis of wave characteristics. For OSIRIS-REx, a compact four-sensor array deployed near Eureka Airport provided trajectory confirmation through arrival-time differences and back-azimuth estimates. Spectral and waveform analyses revealed differences in signal properties associated with variations in entry angle and velocity. The results illustrate both the strengths and the limitations of the deployed array configurations. The dense and distributed arrays during Hayabusa2’s re-entry enabled detailed trajectory reconstruction, whereas the compact array at Eureka primarily provided confirmation of signal coherence and back-azimuth consistency. These case studies highlight that even relatively small arrays, if located close to the predicted ground track, can still capture useful information on arrival direction and timing. Such insights provide practical guidance for planning future observational campaigns of SRC returns and other controlled atmospheric entries, and may also inform approaches to opportunistic observations of meteoroid events and other atmospheric acoustic phenomena.