Effects of atmospheric density uncertainties on the probability of collision for the CYGNSS constellation.

The number of objects in space has dramatically increased in the past decade, significantly increasing the risk of collisions with operational satellites. Collision avoidance has thus become a major component of mission operations. Predicting a collision requires a perfect knowledge of the current positions and velocities of the two objects, as well as the forces acting on them, so that their future trajectories can be modeled accurately. Since this is not possible in reality, mission operators evaluate the risk of collision by calculating the probability of collision, and from it make a decision with regard to a potential avoidance maneuver. Unfortunately, the computation of the probability of collision comes with uncertainties. For satellites in low orbit (below 1,000 km), subject to drag, errors in the forecast of the atmospheric density are one of the main sources of uncertainties in the probability of collision. In order to evaluate the true risk of collision, a method is presented that computes probability distribution functions of the probability of collision from a modeling of the forecast errors in the solar irradiance flux F10.7 and geomagnetic index Ap, which are two main drivers of the atmospheric density. The algorithm is applied to different encounter geometries and used to investigate historical conjunctions of the CYGNSS constellation. Errors in the forecast of the two solar proxies are shown to cause large uncertainties in the probability of collision, which, if ignored, can lead mission operators into making unnecessary collision avoidance maneuvers, or in the worst case, in missing a collision. The proposed method can assist them in the determination of the true risk of collision in the presence of atmospheric density errors.