Estimation of Orbital Parameters of Broken-Up Objects From In-Situ Debris Measurements

Abstract

This paper briefly introduces a new approach to estimate some orbital parameters of on-orbit satellite fragmentations (specifically, the direction of angular momentum at a specific time and the time change in direction of angular momentum) from in-situ debris measurements. This approach, as in previous studies, adopts a constraint equation derived from the fact that a piece of debris detected shares the geocentric position vector with an in-situ debris measurement satellite. However, unlike previous studies, this approach does not adopt a constraint equation that can be applied to the rate of change in right ascension of the ascending node of a broken-up object. Instead, this approach determines the inclination of a broken-up object from the maximum or minimum geocentric declination at the time of detection. Then, this approach finds out a candidate for the rate of change in right ascension of the ascending node of a broken-up object by assuming a circular orbit with a radius of the geocentric distance at the time of detection. Finally, using the constraint equation adopted, this approach estimates the right ascension of the ascending node at the time of breakup and calculates a correction for the rate of change in right ascension of the ascending node. This paper also verifies that this new approach works effectively under ideal conditions where all detections are assumed to be at the line of intersection of the two orbital planes of a broken-up object and an in-situ debris measurement satellite.