Nathan Reiland, University of Arizona; Aaron J. Rosengren, University of Arizona; Renu Malhotra, University of Arizona; Claudio Bombardelli, Technical University of Madrid;
Keywords: collision probability, collision prediction, mega-constellations, astrodynamics, orbital debris, space situational awareness
Abstract:
We aim to provide satellite operators and researchers with an efficient and effective means for evaluating collision risk during the design process of mega-constellations as well as insight into how the dynamical placement of orbiting systems can greatly reduce collision risk and the need for avoidance maneuvers. Current algorithms and software tools for assessing collision probabilities of satellites are not sufficiently robust for the forthcoming orbital environment with the deployment of many thousands of telecommunications satellites in low-Earth orbit(LEO). We report on satellite constellation configurations that take advantage of the natural dynamics of the Earth-Moon-Sun-satellite system in order to minimize the rate of satellite-satellite close encounters.
First we establish a baseline for evaluating various techniques (Hoots et. al. 1984, Jeong Ahn and Malhotra 2015, and Gronchi 2005) for the prediction of satellite-satellite close encounters by carrying out brute force numerical simulations. We integrate the equations of motion with a sufficiently-small time step, vis-à-vis the relative velocity of the satellites, and then compare their trajectories. Drawing inspiration from Hoots et. al. (1984), we implement a sequence of filters, so as to reduce the computational expense of the algorithm. Each subsequent filter consists of integrating the equations of motion with a smaller time step than the previous filter. We test the efficacy of this technique by creating a number of hard-to-detect collision events and propagating the trajectories of the involved objects backwards in time to an initial epoch.
The brute force approach is then applied to the anticipated orbital environment following the deployment of the OneWeb mega-constellation. Using the satellite-satellite close-encounter baseline, we evaluate the efficacy of the previously cited encounter-prediction and collision-probability algorithms. Of particular interest is a modern formulation of the classical collision probability technique of Öpik and Wetherill (JeongAhn and Malhotra 2015, 2017). This technique computes the collision probability per unit time of two objects in Keplerian orbits. We modify this technique to address the perturbed-Keplerian dynamics in the LEO environment. Following Jeong Ahn and Malhotra (2015), we create a distribution of clones to simulate the dynamical evolution of impacting objects having a distribution of initial conditions or of orbital parameters. Next, we compute the total collision probability by taking the sum of collision probabilities of the clones with the target satellites of interest with correction factors to account for the multiplicity of clones per target object in addition to the inflation of the collision radius. The greatest uncertainties in this approach are the generation of the distribution of clones as well as assumptions placed on the motion of the target objects. For various clone distributions and assumptions, we assess the validity of this fast method by means of a comparison with the brute force close-encounter baseline simulations.
As a further step, in order to respond to increasing space traffic rates in a more dynamical fashion, we investigate the efficacy of so-called Minimum Space Occupancy (MiSO) orbits. MiSO is a generalization of the well-known frozen orbits (in the natural dynamics of the Earth-Moon-Sun-satellite system) and are possibly the best solution to truly minimize collisions and/or avoidance maneuvers. Using the aforementioned techniques for collision probability calculation and close-encounter prediction, we evaluate the ability of MiSO configurations of the proposed OneWeb mega-constellation to reduce the risk of endogenous collisions. Preliminary results indicate that the application of the MiSO algorithm can significantly reduce this risk with very small adjustments to the nominal orbital elements of the constellation satellites.
Date of Conference: September 17-20, 2019
Track: Astrodynamics