Collision induced rotational transition probabilities in diatomic molecules
Explore the source record for details and available documents.
Pearson, W. E.↗
SEARCH · Search NASA
Results for “Probability of Collision”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Probable Disastrous Consequences of Collision Between Unknown Small (100 m) Asteroids with Known (Approximately 1 km) Near Earth Orbiting (NEO) Asteroids
The long-term stability of the Solar System is not well understood. Ironically its stability is taken for granted even though our knowledge of all the constituents [comets, asteroids. (The Asteroid Belt between Mars and Jupiter, Trojan Asteroids, Kuiper belt, Ort Cloud), planetoids, planets, moons, etc], and its long-term dynamics cannot be easily computed. At best one might say that the solar system is chaotic, but much of the time it seems to exists near a quasi-stationary state. An asteroid that passes near the Earth regularly returns with clock-like precision. Taking into account every known detail of its path through the solar system, its orbit is calculated forward thousands of years with no untoward calamity on the horizon. And then one day, this passive visitor slams into the Earth during a sunny afternoon picnic! Can this happen? Unfortunately, this is a real possibility in the ordinary history of the solar system. In fact our knowledge of the solar system in the small is sketchy, as will be pointed out. Events, which lie outside our awareness, can precipitate disasters that we may perceive when it's too late to launch effective counter measures. In this work, one such scenario is described and the direct consequences for the Earth are calculated.
Smalley, Larry↗
An Updated Process for Automated Deepspace Conjunction Assessment
There is currently a high level of interest in the areas of conjunction assessment and collision avoidance from organizations conducting space operations. Current conjunction assessment activity is mainly focused on spacecraft and debris in the Earth orbital environment [1]. However, collisions are possible in other orbital environments as well [2]. This paper will focus on the current operations of and recent updates to the Multimission Automated Deep Space Conjunction Assessment Process (MADCAP) used at the Jet Propulsion Laboratory for NASA to perform conjunction assessment at Mars and the Moon. Various space agencies have satellites in orbit at Mars and the Moon with additional future missions planned. The consequences of collisions are catastrophically high. Intuitive notions predict low probability of collisions in these sparsely populated environments, but may be inaccurate due to several factors. Orbits of scientific interest often tend to have similar characteristics as do the orbits of spacecraft that provide a communications relay for surface missions. The MADCAP process is controlled by an automated scheduler which initializes analysis based on a set timetable or the appearance of new ephemeris files either locally or on the Deep Space Network (DSN) Portal. The process then generates and communicates reports which are used to facilitate collision avoidance decisions. The paper also describes the operational experience and utilization of the automated tool during periods of high activity and interest such as: the close approaches of NASA's Lunar Atmosphere & Dust Environment Explorer (LADEE) and Lunar Reconnaissance Orbiter (LRO) during the LADEE mission. In addition, special consideration was required for the treatment of missions with rapidly varying orbits and less reliable long term downtrack estimates; in particular this was necessitated by perturbations to MAVEN's orbit induced by the Martian atmosphere. The application of special techniques to non-operational spacecraft with large uncertainties is also studied. Areas for future work are also described. Although the applications discussed in this paper are in the Martian and Lunar environments, the techniques are not unique to these bodies and could be applied to other orbital environments.
collision↗
Determining Appropriate Risk Remediation Thresholds from Empirical Conjunction Data Using Survival Probability Methods
Satellites sometimes maneuver before conjunctions to remediate the risk of an on-orbit collision. Many missions use probability of collision (P_c) thresholds to decide when such maneuvers should be performed. These thresholds tend to be conservative because of policies that require satellites survive their lifetimes without collision with high confidence (e.g., 99.9%). This study presents a semi-empirical method to estimate remediation P_c thresholds that satisfy such lifetime risk requirements. The formulation combines survival probability analysis with empirical conjunction histories to estimate remediation thresholds as a function of satellite size, remaining on-orbit duration, lifetime collision probability limit, collision consequence, and other parameters.
Risk Remediation↗
Comet and Asteroid Hazard to the Terrestrial Planets
We made computer simulations of orbital evolution for intervals of at least 5-10 Myr of N=2000 Jupiter-crossing objects (JCOs) with initial orbits close to those of real comets with period P less than 10 yr, 500 objects with orbits close to that of Comet 10P, and the asteroids initially located at the 3:1 and 5:2 resonances with Jupiter at initial eccentricity e(sub 0)=0.15 and initial inclination i(sub 0)=10(sup 0). The gravitational influence of all planets, except for Mercury and Pluto, was taken into account (without dissipative factors). We calculated the probabilities of collisions of bodies with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr, and then summarized the results for all bodies, obtaining, the total probability Psigma of collisions with a planet and the total time interval Tsigma during which perihelion distance q of bodies was less than a semimajor axis of the planet. The values of p(sub r) =10(exp 6)Psigma/N and T(sub r)=T/1000 yr (where T=Tsigma/N) are presented in a table together with the ratio r of the total time interval when orbits were of Apollo type (at a greater than 1 AU, q less than 1.017 AU, e less than 0.999) to that of Amor type (1.017 less than q less than 1.33 AU), r(sub 2) is the same as r but for Apollo objects with e less than 0.9. For asteroids we present only results obtained by direct integration, as a symplectic method can give large errors for these resonances.
Ipatov, S. I.↗
Constitutive Relation in Transitional Granular Flows
To study the constitutive behavior of granular materials, the presence of gravity is detrimental. Although empirical relations have been obtained for engineering designs to control granular flows on Earth, it is not known how well these Earthbound relations can be used in another gravity field. Fundamental understanding must be derived to reliably design for granular flows in space exploration. There are two extremes of granular flows of which significant amount of knowledge is available. One deals with a dense and quasi-static situation where the deformation rate nearly vanishes. The other deals with dilute and rapidly fluctuating grain velocities where particle inertia dominates. This project, funded by the NASA Microgravity Fluid Physics Program, aims to study this transitional regime via physical experiments and computer simulations. A conceptual model has been established as described below. There are two natural time scales in a granular flow. One is the travel time between two consecutive collisions and the other is the duration of a collision contact. At a very low shear-rate, the shear-induced particle velocity is low. Hence the travel time between collisions is longer than the contact time between colliding particles. Binary collisions prevail. As the shear-rate increases, the traveling time between collisions reduces and the probability of multiple collisions goes up. These particle groups disperse shortly after and new groups form. When shear-rate is further increased, clusters grow in size due to an increasing chance for free particles to join before groups have the time to disperse. The maximum cluster size may depend on the global concentration and material properties. As the solid concentration approaches zero, the cluster size goes to one particle diameter. The maximum possible cluster size under any condition is the container size, provided that the shear flow is inside a container. The critical shear-rates that dictate the initiation of the multiple contacts, and the size and lifetime of the collision clusters, are functions of the concentration also. A 'regime' theory has been proposed by Babic et al. This theory suggested that both the solid concentration, C, and the non-dimensional shear-rate, B, are important in determining the regimes of the granular constitutive law. Additional information is included in the original extended abstract.
Shen, Hayley H.↗
Multivariate Normality of Cartesian-Framed Covariances: Evaluation and Operational Significance
Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.
Lechtenberg, Travis F.↗
Multivariate Normality of Cartesian Frame Covariances: Evaluation and Operational Significance
Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.
Lechtenberg, Travis F.↗
Statistical Analysis of Deflation in Covariance and Resultant Pc Values for AQUA, AURA and TERRA
This presentation will display statistical analysis performed for raw conjunction CDMs received for the EOS Aqua, Aura and Terra satellites within the period of February 2015 through July 2016. The analysis performed indicates a discernable deflation in covariance calculated at the JSpOC after the utilization of the dynamic drag consider parameter was implemented operationally in May 2015. As a result, the overall diminution in the conjunction plane intersection of the primary and secondary objects appears to be leading to reduced probability of collision (Pc) values for these conjunction events. This presentation also displays evidence for this theory with analysis of Pc trending plots using data calculated by the SpaceNav CRMS system.
raw conjunction↗
Migration of Trans-Neptunian Objects to a Near-Earth Space
Our estimates of the migration of trans-Neptunian objects (TNOs) to a near-Earth space are based on the results of investigations of orbital evolution of TNOs and Jupiter-crossing objects (JCOs). The orbital evolution of TNOs was considered in many papers. Recently we investigated the evolution for intervals of at least 5-10 Myr of 2500 JCOs under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period P(sub alpha)less than 10 yr, and in the second series we took N=500 orbits close to the orbit of Comet 10P Tempel 2 (alpha=3.1 AU, e=0.53, i=12 deg). We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr, and then summarized the results for all time intervals and all bodies, obtaining the total probability P(sub sigma) of collisions with a planet and the total time interval T(sub sigma) during which perihelion distance q of bodies was less than a semimajor axis of the planet.
Ipatov, S. I.↗
Orbital Evolution of Jupiter-Family Comets
We investigated the evolution for periods of at least 5-10 Myr of 2500 Jupiter-crossing objects (JCOs) under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period less than 10 yr, and in the second series we took 500 orbits close to the orbit of Comet 10P Tempel 2. We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr and then summarized the results for all time intervals and all bodies, obtaining the total probability P(sub sigma) of collisions with a planet and the total time interval T(sub sigma) during which perihelion distance of bodies was less than a semimajor axis of the planet. The values of P = 10(exp 6)P(sub sigma)/N and T = T(sub sigma)/1000 yr are presented in Table together with the ratio r of the total time interval when orbits were of Apollo type (at e less than 0.999) to that of Amor type.
Ipatov, S. I.↗
An Investigation Into Transecting Satellites in Future Space Traffic Management Scenarios
The number of satellites expected to populate the near-Earth space environment is set to dramatically increase in the coming decade as new large constellations are approved and deployed. Current strategies for placing new batches of these satellites on orbit often involve launching into an initial orbit, and then performing apogee raising maneuvers to reach a target altitude. Similarly, end-of-life planning for these constellation satellites can consist of de-orbit burns that lower perigee to permit disposal via re-entry. Both the raising and de-orbiting maneuvers can result in the individual satellites traveling in high-eccentricity orbits that have the potential to transect other spacecraft trajectories. While individual large constellations may be able to coexist in separate altitude and inclination bands, having thousands of satellites moving between these bands as new satellites are replaced and old ones are removed could pose additional collision risks. Similar concerns have been raised regarding the impact that large numbers of university-class CubeSats might have in terms of their overall collision risk, especially as these satellites typically do not have propulsion systems for active maneuvering. To assess the impact that transecting satellites might have to future space traffic management strategies, this study explored a variety of future realistic scenarios using a high-fidelity simulation tool. The model can simulate the orbit of tens of thousands of resident space objects (RSOs) simultaneously, to include active satellites, debris, rocket bodies, or even future hypothetical scenarios, using a realistic force model that incorporates non-spherical gravity, atmospheric drag, solar radiation pressure, and more. As the model is run forward in time, various statistics and meta-data are gathered on any predicted conjunction event, providing insight into the nature and frequency of potential collisions, e.g., what size are the two satellites, who operates the satellites, are they active or passive objects, etc. Additional customization is available in terms of how probability of collision is computed, and how the probability ellipsoids and screening volumes are determined. The simulation tool also allows for rule-based maneuvers for active satellites, e.g, given an advance conjunction “warning,” one or both of the satellites can maneuver to a safe distance. A wide range of maneuvers can be implemented using impulsive or low-thrust methods, and the latencies can also be varied, e.g., using maneuver lead times of 48 hours, 24 hours, or 12 hours. Validation of the simulation results is performed against current and historical datasets available, to include comparisons to prior conjunction data messages (CDMs), object properties (mass, volume, etc.), and two-line-element records from both public and internal sources. Using the simulation environment, an assessment on the general risks that transecting satellites might pose for hypothetical future space object environments will be presented. This will involve the simulation of approximately 50,000 new large constellation satellites, in addition to the existing catalog of approximately 20,000 known resident space objects (RSOs), over propagation periods of one month to one year. A description of the simulation methodologies, scenarios evaluated, and validation methods will also be presented, as well as a preliminary assessment of the effectiveness of several candidate maneuver strategies that have the potential to reduce collision risk between active satellites.
Brian Gunter↗
Inefficacy of mallard flight responses to approaching vehicles
Vehicle collisions with birds are financially costly and dangerous to humans and animals. To reduce collisions, it is necessary to understand how birds respond to approaching vehicles. We used simulated (i.e., animals exposed to video playback) and real vehicle approaches with mallards (Anas platyrynchos) to quantify flight behavior and probability of collision under different vehicle speeds and times of day (day vs. night). Birds exposed to simulated nighttime approaches exhibited reduced probability of attempting escape, but when escape was attempted, fled with more time before collision compared to birds exposed to simulated daytime approaches. The lower probability of flight may indicate that the visual stimulus of vehicle approaches at night (i.e., looming headlights) is perceived as less threatening than when the full vehicle is more visible during the day; alternatively, the mallard visual system might be incompatible with vehicle lighting in dark settings. Mallards approached by a real vehicle exhibited a delayed margin of safety (both flight initiation distance and time before collision decreased with speed); they are the first bird species found to exhibit this response to vehicle approach. Our findings suggest mallards are poorly equipped to adequately respond to fast-moving vehicles and demonstrate the need for continued research into methods promoting effective avian avoidance behaviors.
60 APPLIED LIFE SCIENCES↗
Three CA-Related Covariance Issues and Their Solutions
This presentation addresses three issues that arise in the use of DoD-produced satellite state estimate covariances in the conjunction assessment process: the realism of the provided covariances, how to address correlated error between two satellites' covariance matrices, and how to proceed when a furnished covariance is non-positive-definite. To address the first, DoD has implemented a set of two "consider parameters" with which to alter/expand the covariance to account for atmospheric density forecast error and satellite frontal area uncertainty, the two largest sources of unmodeled position prediction error for LEO orbits; these values are governed by a satellite's orbital parameters and ballistic coefficient histories, as well as the current and predicted space weather situation. This approach substantially improves the realism of the covariance by accounting for expected prediction errors that are not part of the fit process that generates the covariance. The second issue of covariance correlation is a complicated one, but the main shared error source—global atmospheric density error that is common to both satellites can be characterized and, through sensitivity vectors, quantified at the conjunction's time of closest approach and removed from the joint covariance, which is used in the CA probability of collision (Pc) calculation. Finally, while according to the orbit determination theory a non-positive-definite (NPD) covariance is not possible, numerical truncation and covariance interpolation can conspire to produce NPD results, which render the covariance unusable for certain CA risk assessment calculations, such as Monte Carlo Pc determination. Three similar techniques are profiled and the simplest of them recommended as a reasonable remediation technique when NPD covariances are encountered by CA practitioners.
Dynamic Consider Parameter↗
Quantifying Shortcomings in the 2-D Pc Calculation
The probability of collision, Pc, between two Earth-orbiting satellites can often, but not always, be approximated adequately using the "2D-Pc" formulation. The objective is to find a set of "boundary conditions" that ensure the 2D-Pc approximation be sufficiently accurate, so that it may be determined when computationally-intensive Brute Force Monte Carlo1 (BFMC) Pc estimates are required. We critically examine the assumptions used in the formulation of the 2D-Pc approximation and then formulate 2D-Pc boundary condition tests to check if these assumptions are satisfied adequately.
Analysis↗
Trending in Pc Measurements via a Bayesian Zero-Inflated Mixed Model
Two satellites predicted to come within close proximity of one another, usually a high-value satellite and a piece of space debris moving the active satellite is a means of reducing collision risk but reduces satellite lifetime, perturbs satellite mission, and introduces its own risks. So important to get a good statement of the risk of collision in order to determine whether a maneuver is truly necessary. Two aspects of this Calculation of the Probability of Collision (Pc) based on the most recent set of position velocity and uncertainty data for both satellites. Examination of the changes in the Pc value as the event develops. Events should follow a canonical development (Pc vs time to closest approach (TCA)). Helpful to be able to guess where the present data point fits in the canonical development in order to guide operational response.
Conjuction Assessment↗
An Investigation Into Transecting Satellites in Future Space Traffic Management Scenarios
The number of satellites expected to populate the near-Earth space environment is set to dramatically increase in the coming decade as new large constellations are approved and deployed. Current strategies for deploying new batches of these satellites often involve launching into an initial orbit, and then performing apogee raising maneuvers to reach a target altitude. Similarly, end-of-life planning for these constellation satellites can consist of de-orbit burns that lower perigee to permit disposal via re-entry. Both the raising and de-orbiting maneuvers can result in the individual satellites traveling in transecting orbits that have the potential to cross other spacecraft trajectories. While individual large constellations may be able to coexist in separate altitude and inclination bands, having thousands of satellites moving between these bands as new satellites are added and old satellites are removed could pose additional collision risks. Similar concerns have been raised regarding the impact that large numbers of university-class CubeSats might have in terms of their overall collision risk, especially as these satellites typically do not have propulsion systems for active maneuvering. To assess the impact that transecting satellites might have on future space traffic management strategies, this study explored a variety of realistic future scenarios using a high-fidelity simulation tool. The model can simulate the orbit of tens of thousands of resident space objects (RSOs) simultaneously, to include active satellites, debris, rocket bodies, or even future hypothetical satellite constellations, using a realistic force model that incorporates non-spherical gravity, atmospheric drag, and solar radiation pressure, as well as station-keeping. The simulation can be customized to accommodate different methods of calculating the probability of collision, as well as the process for determining probability ellipsoids and screening volumes. This makes it possible to replicate, and compare, different processes used by different spacecraft operators and space situational awareness (SSA) providers. As the model is run forward in time, each conjunction event is recorded, allowing for the analysis of statistics and meta-data related to these events, providing insight into the nature and frequency of potential collisions, such as whether are they active or passive objects, what size are the two objects, and who owns the objects (if known). This information makes it possible to characterize how changes to the status quo affect the number and type of conjunctions that occur, as well as the distributional effects on various types of satellite operators. To assess the general risks that transecting satellites might pose for hypothetical future space object environments, approximately 60,000 new large constellation satellites were considered, in addition to the existing catalog of approximately 7800 known resident space objects (RSOs), over a simulation period of one year. The results indicate that the future space environment will introduce a non-linear increase in conjunction events as the number of RSOs also increase. This will require adjustments to spacecraft fuel budgets in order to conduct the avoidance maneuvers necessary to minimize collision risk, both for existing and new satellites. This increase is due in large part to the higher density of RSOs and the overlap between some constellation orbits. Current catalog objects were shown to require three times more ∆V for collision avoidance (CA) maneuvers in the simulated future environment, and some constellation spacecraft were estimated to devote the majority of their annual ∆V to CA. The impact of small satellites was found to be proportional for the current space environment, and actually decreased in terms of percentage for the future scenario, suggesting that small satellites do not pose an outsized collision risk. Lastly, transecting satellites were found to contribute thousands of additional conjunctions outside of their operational orbit, and may require up to an additional 5% in CA maneuver fuel allocation.
conjunction assessment↗
Investigating and implementing enhancements to the simulation of short-term collision hazards
A software tool, the Relative Collision Matrix (RCM), has been developed to provide a quick-look representation of the shortterm collision hazard to space systems from a fragmentation event in Earth orbit. The software performs multiple fragmentation simulations of space objects to quantify the probability of collision for a satellite or a constellation of satellites nearby. Previously, the results were displayed in a color matrix format which showed the relative hazard of each constellation. The RCM can be used for scientific research and operational assessments even though it was designed for test and evaluation applications. Because of its successful use as an analytical tool, the capabilities of RCM are being extended by enhancing the orbital hazard analysis routines, developing ballistic trajectory hazard analysis routines, and expanding the breakup modeling. Improvements are also being made to the RCM's usability and presentation quality by developing a graphical user interface and by providing graphical animated and nonanimated output.
Huth, Jeffrey S.↗