Identification of two collided objects from in-situ debris measurements

This paper proposes a method to estimate two sets of orbital parameters (inclination, right ascension of the ascending node, and nodal precession rate) of the collided objects from in situ measurements of sub-millimeter-size debris, using the first-ever accidental collision between US Iridium 33 and Russian Cosmos 2251 as an example. This collision released a large number of fragmentation debris and have had a tremendous impact on the environment around the Earth. Objects larger than 10 cm are cataloged and tracked, but it is difficult to observe sub-millimeter-size debris from the ground and predict their orbits accurately. Thus, this fact leads to insufficiently modelled sub-millimeter-size debris, despite their potential to space mission termination. Therefore, in situ debris measurements are essential to protect space systems against sub-millimeter-size debris. Previous studies assumed that an in situ debris measurements satellite records the position at the time of impact with sub-millimeter-size debris, and then demonstrated that it is possible to estimate the orbital parameters from in situ debris measurements when a single object is broken up. However, when two objects collide, measurements come from both objects, so the previous method cannot be simply applied. Besides, the inclination of the broken-up objects to which the previous method can be applied is constrained by the inclination of the measurements satellite. To solve this problem, this paper proposes using azimuth at the time of impact and applying the Lomb-Scargle Periodogram, a kind of frequency analysis. Finally, this paper demonstrates that it is possible to identify accidental collisions in space through in situ measurements.