# Collision analysis and mitigation for distributed space systems

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## Abstract

Collision analysis and mitigation performed for the QB50 mission. The aim of this thesis report is to identify which mitigation strategies are most suitable for a network of uncontrollable satellites. Furthermore, the aim is to set-out a method to determine the collision probability for a network of uncontrollable satellites, and identify the parameters that influence the collision probability. These methods are applied to the QB50 mission; to find a scenario where the collision probability is lowest. An alternative method is developed by the author to calculate the Gaussian probability, which is applicable for small satellites. As the size of the satellites decreases relative to the error ellipsoid, the probability at a certain moment in time becomes more equal to the probability at the center of the combined sphere (assuming spherical satellites). Now, instead of dealing with a cumbersome volume integral through the combined error ellipsoid, the collision probability can be approached by a line-integral times the area of the combined satellites’ bodies. Four ideal deployment angles for the QB50 mission were found located in a plane of zero pitch and at yaw angles of 34?, 146?, 248?, 326? measured from velocity vector of the upperstage.Deploying at zero pitch has the effect that the phase between the cross-track and radial separation is half the orbital period. This has the consequence that, when either the cross-track separation is zero, the radial separation has its maximum and visa versa. This can also be identified as (anti-)parallel alignment of relative eccentricity and inclination vectors. Synchronization of the motion at times where the deployment is half or equal to the orbital period should be avoided. For these satellites the amplitude radial and cross-track separations are small. Furthermore, the relative perturbations between these satellites is large, decreasing the offset of the radial motion. This causes the radial and cross-track separation reach zero at equal time. Synchronized satellite increase the collision probability significantly. Both Patera’s method and the line-integral method are applied to a full-scale simulation for the QB50 mission. Multiple scenario’s are chosen for the full-scale simulation. The two scenario’s with the lowest probability are sequential deployment at one of the ideal angles and alternating deployment between two opposite ideal angles. These fall below the threshold value of 10?4, a value used by the German Space Operations Center (GSOC).