Analysis of the possible cause of break up of PSLV-C3/PS4 stage

On 19t h December 2001 the orbiting spent PS4 stage of PSLV -C3 had undergone a break up. Following this event, the Two Line Element (TLE) sets of more than 300 debris pieces from the upper stage are available in public domain by January 2002. These TLE sets are the major input used in this study. Here the velocity components imparted on the fragments are evaluated by a new approach, which is less sensitive to the errors in the TLE sets. In Ref-1, the normal, radial and tangential components of fragment velocity additions are estimated from the differences in semi-major axis, eccentricity and inclination with respect to those of parent object. Unfortunately, when the parent orbit has small eccentricity or the break up occurs near either apogee or perigee, as it is likely in the case of PSLV-C3/PS4, the computation of radial component of velocity increment becomes close to a singular point and hence prone to errors because of imperfect orbital element data. In Ref-2, velocity increments are estimated from semi-major axis, eccentricity, inclination, and right ascension of ascending node and true anomaly of fragments as well as parent at the time of break up. It is very difficult to obtain true anomaly of fragments at the time of break up by propagating the element sets of debris pieces backward in time owing to uncertainties in orbital elements and drag parameters. Moreover, whenever the apogee of fragment orbit, computed from the TLE sets, becomes less than the perigee of parent orbit, this method does not yield any solution for radial component of velocity increment. The authors have estimated three components of velocity addition, utilizing relations involving the differences in semi-major axis, eccentricity and inclination and argument of perigee (Ref- 3) in a particular combination and sequence, which avoids the singularity in the computation. With this approach, the characteristics of velocity additions are similar in all the three directions and velocity addition histograms in these three directions are almost symmetric about zero. These results are pointer to the possibility of fragmentation from explosion in PSLV-C3/PS4 stage. It is also estimated that about 75 % of the total number of debris pieces from this break up would decay by the end 2002. References: (1) Nicholas L. Johnson &Darren S. McKnight, Artificial Space Debris, Orbit Foundation, 1987. (2) James G Miller, Velocity Distribution of Satellite Breakups, AAS 99-445, 1999. (3) Meirovitch L., Methods of Analytical Dynamics , McGraw Hill Company, 1970.