A TLE-based Algorithm for Correcting Empirical Model Densities during Geomagnetic Storms

Neutral densities increase up to 800% during geomagnetic storms. Satellite two-line element sets (TLEs) show increased orbital decay during geomagnetic storms from increased drag

Effects of Uncertainties in the Atmospheric Density on the Probability of Collision Between Space Objects

The rapid increase of the number of objects in orbit around the Earth poses a serious threat to operational spacecraft and astronauts. In order to effectively avoid collisions, mission operators need to assess the risk of collision between the satellite and any other object whose orbit is likely to approach its trajectory. Several algorithms predict the probability of collision but have limitations that impair the accuracy of the prediction. An important limitation is that uncertainties in the atmospheric density are usually not taken into account in the propagation of the covariance matrix from current epoch to closest approach time. The atmosphere between 100 km and 700 km is strongly driven by solar and magnetospheric activity. Therefore, uncertainties in the drivers directly relate to uncertainties in the neutral density, hence in the drag acceleration. This results in important considerations for the prediction of Low Earth Orbits, especially for the determination of the probability of collision. This study shows how uncertainties in the atmospheric density can cause significant differences in the probability of collision and presents an algorithm that takes these uncertainties into account to more accurately assess the risk of collision. As an example, the effects of a geomagnetic storm on the probability of collision are illustrated.Plain Language SummarySpacecraft collision avoidance is particularly challenging at low altitudes (below  700 km). One of the main reasons is that, at these altitudes, satellite trajectories are strongly perturbed by atmospheric drag, a force particularly hard to model. The sources of errors mostly come from the complex coupling between the Sun and the Earth’s environment. This system drives the density of the Earth’s atmosphere on which the atmospheric drag directly depends. In other words, uncertainties in the atmospheric density result in large uncertainties in the satellite trajectories. The probability of collision, which is computed from the prediction of the satellite trajectories, thus cannot be predicted perfectly accurately. However, mission operators decide whether or not a collision avoidance maneuver has to be carried out based on the value of the probability of collision. Therefore, it is essential to characterize the level of uncertainty associated with the prediction of the probability of collision. The research presented here offers an approach to determine the uncertainty on the prediction of the probability of collision as a result of uncertainties in the atmospheric density. The ultimate goal is to assist mission operators in making the correct decision with regard to potential collision avoidance maneuvers.Key PointsUncertainties in the atmospheric density result in uncertainties in the probability of collisionProbability distribution functions of the probability of collision resulting from uncertainties in the atmospheric density are derivedMonte Carlo procedures are used to compute the probability of collisionPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144643/1/swe20687_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144643/2/swe20687.pd

A Simple Method for Correcting Empirical Model Densities During Geomagnetic Storms Using Satellite Orbit Data

Empirical models of the thermospheric density are routinely used to perform orbit maintenance, satellite collision avoidance, and estimate time and location of re- entry for spacecraft. These models have characteristic errors in the thermospheric density below 10% during geomagnetic quiet time but are unable to reproduce the significant increase and subsequent recovery in the density observed during geomagnetic storms. Underestimation of the density during these conditions translates to errors in orbit propagation that reduce the accuracy of any resulting orbit predictions. These drawbacks risk the safety of astronauts and orbiting spacecraft and also limit understanding of the physics of thermospheric density enhancements. Numerous CubeSats with publicly available ephemeris in the form of two- line element (TLEs) sets orbit in this region. We present the Multifaceted Optimization Algorithm (MOA), a method to estimate the thermospheric density by minimizing the error between a modeled trajectory and a set of TLEs. The algorithm first estimates a representative cross- sectional area for several reference CubeSats during the quiet time 3- weeks prior to the storm, and then estimates modifications to the inputs of the NRLMSISE- 00 empirical density model in order to minimize the difference between the modeled and TLE- provided semimajor axis of the CubeSats. For validation, the median value of the modifications across all CubeSats are applied along the Swarm spacecraft orbits. This results in orbit- averaged empirical densities below 10% error in magnitude during a geomagnetic storm, compared to errors in excess of 25% for uncalibrated NLRMSISE- 00 when compared to Swarm GPS- derived densities.Plain Language SummaryEmpirical atmospheric density models underestimate the increase in thermospheric density observed during times of intense solar and geomagnetic activity. This demonstrates our limited understanding of the physics of the thermosphere during these times and limits our ability to accurately predict the orbits of both operational satellites and space debris. We present a method to correct these density underestimations by using an orbital propagator and correcting the inputs to the NRLMSISE- 00 density model to minimize orbit error. We apply medians of these adjustments along the orbit of the Swarm spacecraft and compare resulting corrected densities to GPS- derived densities collected by Swarm.Key PointsEmpirical atmospheric models exhibit significant density underestimation during geomagnetic stormsA simple algorithm presents a new way of obtaining improved density model estimates from two- line elements describing satellite orbitsThe technique is validated against Swarm GPS- derived densities during geomagnetic quiet and active timesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163957/1/swe21072_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163957/2/swe21072.pd