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NASA NTRSDate not supplied

Setting the Bar for the Replacement of the Probability of Collision Metric

Recent research in satellite conjunction risk assessment has levelled a number of criticisms at the probability of collision (Pc) parameter as a durable statement of satellite collision likelihood, and a number of different alternatives to this calculation have been proposed. Many of these proposals, however, stop at the outlining of the theory and do not discuss the additional philosophical and practical issues that must be confronted in evaluating such proposals for adoption. The present work seeks to outline some of these philosophical and practical considerations, and therefore the kinds of analyses and profiling that will be needed before the Pc, which is at present nearly universally adopted in the conjunction risk mitigation community, can be replaced with a new (and superior) paradigm and associated metric.

conjunction assessment↗
NASA NTRS2006

Sense and Avoid Safety Analysis for Remotely Operated Unmanned Aircraft in the National Airspace System. Version 5

This document describes a method to demonstrate that a UAS, operating in the NAS, can avoid collisions with an equivalent level of safety compared to a manned aircraft. The method is based on the calculation of a collision probability for a UAS , the calculation of a collision probability for a base line manned aircraft, and the calculation of a risk ratio given by: Risk Ratio = P(collision_UAS)/P(collision_manned). A UAS will achieve an equivalent level of safety for collision risk if the Risk Ratio is less than or equal to one. Calculation of the probability of collision for UAS and manned aircraft is accomplished through event/fault trees.

Carreno, Victor↗
NASA NTRS2015

Total Probability of Collision as a Metric for Finite Conjunction Assessment and Collision Risk Management

On-orbit collision risk is becoming an increasing mission risk to all operational satellites in Earth orbit. Managing this risk can be disruptive to mission and operations, present challenges for decision-makers, and is time-consuming for all parties involved. With the planned capability improvements to detecting and tracking smaller orbital debris and capacity improvements to routinely predict on-orbit conjunctions, this mission risk will continue to grow in terms of likelihood and effort. It is very real possibility that the future space environment will not allow collision risk management and mission operations to be conducted in the same manner as it is today. This paper presents the concept of a finite conjunction assessment-one where each discrete conjunction is not treated separately but, rather, as a continuous event that must be managed concurrently. The paper also introduces the Total Probability of Collision as an analogous metric for finite conjunction assessment operations and provides several options for its usage in a Concept of Operations.

Conjunction Assessment↗
NASA NTRS1989

Charge exchange transition probability for collisions between unlike ions and atoms within the adiabatic approximation

A simple formula for the transition probability for electron exchange between unlike ions and atoms is established within the adiabatic approximation by employing the Linear Combination of Atomic Orbitals (LCAO) method. The formula also involves an adiabatic parameter, introduced by Massey, and thus the difficulties arising from the internal energy defect and the adiabatic approximation are avoided. Specific reactions Li(+++) + H to Li(++) + H(+) and Be(4+) + H to Be(3+) + H(+) are considered as examples. The calculated capture cross section results of the present work are compared with the experimental data and with the calculation of other authors over the velocity range of 10(7) cm/sec to 10(8) cm/sec.

Xu, Y. J.↗
NASA NTRS1974

Predicting the probability that earth-orbiting spacecraft will collide with man-made objects in space

A probabilistic approach to the problem of collisions is made possible by basing a model of the relevant characteristics of the total population on the known properties of a fraction of the total. A method of determining collision probability for objects in any two different but potentially intersecting orbits is derived. Collision probabilities for earth-orbital missions are investigated parametrically as a function of orbital characteristics and a hypothetical projection of the results to future orbital missions is discussed.

Brooks, D. R.↗
NASA NTRS2013

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Carpenter, J. Russell↗
NASA NTRS1992

Collision rates and impact velocities in the Main Asteroid Belt

Wetherill's (1967) algorithm is presently used to compute the mutual collision probabilities and impact velocities of a set of 682 asteroids with large-than-50-km radius representative of a bias-free sample of asteroid orbits. While collision probabilities are nearly independent of eccentricities, a significant decrease is associated with larger inclinations. Collisional velocities grow steeply with orbital eccentricity and inclination, but with curiously small variation across the asteroid belt. Family asteroids are noted to undergo collisions with other family members 2-3 times more often than with nonmembers.

Farinella, Paolo↗
NASA NTRS1987

Crater production on Venus and Earth by asteroid and comet impact

New calculations of the collision probabilities of asteroids and comets with Venus were carried out based on the orbits of the known Venus-crossing asteroids and comets. For comparison, asteroid and comet collision probabilities and cratering rates on the Earth and Moon were recalculated and the estimated cratering rates on Venus were normalized to those of the Earth.

Shoemaker, Eugene M.↗
NASA NTRS2016

A Numerical Approach to Estimate the Ballistic Coefficient of Space Debris from TLE Orbital Data

Low Earth Orbit (LEO) is full of space debris, which consist of spent rocket stages, old satellites and fragments from explosions and collisions. As of 2009, more than 21,000 orbital debris larger than 10 cm are known to exist], and while it is hard to track anything smaller than that, the estimated population of particles between 1 and 10 cm in diameter is approximately 500,000, whereas small as 1 cm exceeds 100 million. These objects orbit Earth with huge kinetic energies speeds usually exceed 7 kms. The shape of their orbit varies from almost circular to highly elliptical and covers all LEO, a region in space between 160 and 2,000 km above sea level. Unfortunately, LEO is also the place where most of our active satellites are situated, as well as, International Space Station (ISS) and Hubble Space Telescope, whose orbits are around 400 and 550 km above sea level, respectively.This poses a real threat as debris can collide with satellites and deal substantial damage or even destroy them.Collisions between two or more debris create clouds of smaller debris, which are harder to track and increase overall object density and collision probability. At some point, the debris density couldthen reach a critical value, which would start a chain reaction and the number of space debris would grow exponentially. This phenomenon was first described by Kessler in 1978 and he concluded that it would lead to creation of debris belt, which would vastly complicate satellite operations in LEO. The debris density is already relatively high, as seen from several necessary debris avoidance maneuvers done by Shuttle, before it was discontinued, and ISS. But not all satellites have a propulsion system to avoid collision, hence different methods need to be applied. One of the proposed collision avoidance concepts is called LightForce and it suggests using photon pressure to induce small orbital corrections to deflect debris from colliding. This method is very efficient as seen from theoretical simulations, even few continuous mode 10 kW ground-based lasers, focused by 1.5 m telescopes with adaptive optics, were enough to prevent significant amount of the debris collisions. Simulations were done by propagating all space objects in LEO by 1 year into the future and checking whether the probability of collision was high. For those space objects different ground-based lasers were used to divert them, afterwards collision probabilities were reevaluated. However, the actual accuracy of the LightForce software, which has been developed at NASA AmesResearch Center, depends on the veracity of the input parameters, one of which is the objects ballistic coefficient. It is a measure of bodys ability to overcome air resistance, which has a significant impact on the debris in LEO, and thus it is responsible for the shape of the trajectory of the debris. Having the exact values of the ballistic coefficient would make significantly better collision predictions, unfortunately, we do not know what are the values for most of the objects.In this research, we were working with part of LightForce code, which estimates the ballistic coefficient from ephemerides. Previously used method gave highly inaccurate values, when compared to known objects, and it needed to be changed. The goal of this work was to try out a different method of estimating the ballistic coefficient and to check whether or not it gives noticeable improvements.

Collisions↗
NASA NTRS2016

Bayesian Methods for Longitudinal Trending in Probabilities of Collision

Satellites have become an integral part of modern life, supporting phone communication, television and radio broadcasting, internet access, and military activities. Indeed, it is difficult to imagine modern society without many of these technologies, especially in an age when the world is increasingly interconnected via long-distance communications. As of 2013, there were over one thousand operational satellites in orbit about Earth. About half of these active satellites are in Low-Earth Orbit (LEO, meaning an orbital period less than 225 minutes), which is where the International Space Station (ISS) conducts operations, along with other commercial missions such as earth observation and satellite telephone communications. An increasing amount of attention is being placed on protecting satellites in LEO, as the frequency of object launches and satellite fragmentation events has contributed to the proliferation of space debris, resulting in increased congestion.

Conjunction↗
NASA NTRS2014

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.

Navigation↗
NASA NTRS1997

A Probability-Base Alerting Logic for Aircraft on Parallel Approach

This document discusses the development and evaluation of an airborne collision alerting logic for aircraft on closely-spaced approaches to parallel runways. A novel methodology is used when links alerts to collision probabilities: alerting thresholds are set such that when the probability of a collision exceeds an acceptable hazard level an alert is issued. The logic was designed to limit the hazard level to that estimated for the Precision Runway Monitoring system: one accident in every one thousand blunders which trigger alerts. When the aircraft were constrained to be coaltitude, evaluations of a two-dimensional version of the alerting logic show that the achieved hazard level is approximately one accident in every 250 blunders. Problematic scenarios have been identified and corrections to the logic can be made. The evaluations also show that over eighty percent of all unnecessary alerts were issued during scenarios in which the miss distance would have been less than 1000 ft, indicating that the alerts may have been justified. Also, no unnecessary alerts were generated during normal approaches.

Carpenter, Brenda D.↗
NASA NTRS2021

Expected Collision Rates for Tracked Satellites

This analysis estimates collision risks between tracked satellites based on the statistically expected collision rate _Nc and number of collisions Nc, which are closely related to the collision probability Pc. For isolated encounters, Nc equals Pc. For multi-encounter interactions, Nc can exceed Pc and is significantly easier to approximate semi-analytically. Estimating Nc requires integrating the collision rate over time throughout an interaction, with each required _Nc value calculated as a statistical expectation value based on the uncertainty distributions of initial orbital states. The uncertainty distributions are estimated from orbit determination analyses of satellite trajectory measurements. The formulation accounts for the nonlinear orbital motion of the satellites, and derives Nc and _Nc expressions for Monte Carlo simulations as well as semi-analytical approximations for single- and multi-encounter interactions.

Collision Rates↗
NASA NTRS1986

Head-on binary collisions in globular clusters

Collision probabilities between identical binaries of three different binding energies are computed for binaries in the cores of globular clusters. The more tightly bound a binary is, the smaller the chance is that it suffers a collision. It is found that a given binary in a globular cluster core probably does not suffer more than a very few collisions. If it is not broken up into single stars, it will become so tightly bound that collisions involving it are very rare. Since it is found that head-on collisions are so rare, the collisions which are probably more important in affecting the evolution of the cluster core are the long-range (large impact parameter) encounters.

Hoffer, James B.↗
NASA NTRS2001

A Decade of Growth

This paper examines the Space Surveillance Network catalog's growth in low Earth orbit (LEO) and the geosynchronous Earth orbit (GEO) over the decade 1990-2000. During this time, innovative space utilization concepts, e.g. the Iridium and Globalstar commercial communication satellite constellations, have increased the public's consciousness of space. At the same time, however, these constellations have increased spatial density per 10 km altitude bin by factors of two and three respectively. While not displaying as spectacular a growth in spatial density, other regions of space have grown steadily in terms of number, mass, size, and operational lifetime. In this work we categorize launch traffic by type (e.g. payload, rocket body, operational debris, fragmentation debris, or anomalous debris), mass, and size so as to present the observed growth numerically, in terms of mass, and in terms of cross-sectional area. GEO traffic is further categorized by operational longitude. Because growth itself defines only the instantaneous environment, we also examine the higher-order derivatives of growth. In addition, we compare the last decade's growth with modeling results to illustrate the subtle effects of inclination, eccentricity, and size, in addition to spatial densities, on estimating the collision probability. We identify those regions of space most subject to accidental collision.

Johnson, Nicholas L.↗