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.