GSLV-D2/CS1 Lifetime Estimation by Genetic Algorithm with Response Surface Approximation
- Paper number
IAC-06-B6.2.11
- Author
Mr. Priyankar Bandyopadhyay, Indian Space Research Organisation (ISRO), India
- Coauthor
Dr. V. Adimurthy, Indian Space Research Organisation (ISRO), India
- Year
2006
- Abstract
Any launch vehicle upper stage becomes space debris following the completion of its mission. A spent stage in GTO orbit is unique in the sense that its collision threat potential spreads across the gamut of operational orbit regimes- from LEO to GEO. So minimization of spent stage lifetime is one of the important objectives for space debris mitigation efforts. Unfortunately, some of the measures like de-boosting following the completion of mission, which have been contemplated for LEO lifetime reduction, may not be very suitable for GTO owing to its higher velocity magnitude. Also, any measure for de-boosting compromises the payload capacity of the launch vehicle. Fortunately, interplay of natural forces like drag and lunar-solar perturbations can give rise to favorable conjunctions when the lifetime in GTO may be reduced to a level much lower than the one, which can be attained under the sole influence of drag. Against this backdrop, the monitoring of accelerated decay from GTO orbit under those favorable conditions is an important activity to gather valuable knowledge so that for future missions, it can be incorporated into the planning of GTO spent stage lifetime reduction without jeopardizing operational requirements. In order to extract information on the lifetime of a GTO object from its orbital data, the estimation of ballistic coefficient and initial eccentricity is performed. For orbital propagation, initial conditions are obtained from the observed orbital elements at a chosen epoch. The estimation of the initial eccentricity is required to compensate for measurement error. The estimation of ballistic coefficient is carried out to know the effect of drag on trajectory propagation. While estimation involves minimization of a cost function straightforward integration of a numerical orbital propagator to an optimizer may be impractical for several reasons. The repeated evaluation of cost function for the purpose of minimization with an embedded numerical orbital propagator is computationally expensive. Also, the optimizer and propagator may have to be executed on different hardware platform, in diverse operating systems, with incompatible computer languages and etc. For these reasons, it is advantageous that the estimation of ballistic coefficient and initial eccentricity be performed with the coupling of an optimizer to easy–to–calculate approximations of the cost function. The optimizer evaluates the minimum value of this approximate cost function and then the numerical orbital propagator with estimated ballistic coefficient and initial eccentricity updates the approximation and this process is repeated. Finally, the numerical orbital propagator with estimated ballistic coefficient and initial eccentricity also makes the prediction of reentry date once the minimization process is over. One of the approximation approaches that are suitable for the estimation of ballistic coefficient and initial eccentricity is the response surface technique. This technique replaces the cost function with simple functions, which are fitted predictions made with numerical orbital propagator at a set of observation points. The apogee values predicted by numerical orbital propagator with different values of ballistic coefficient and initial eccentricity at a set of time instants for observed apogee are fitted to make the response surfaces, which in this case literally, are apogee surface in initial eccentricity and ballistic coefficient phase space. It may be noted that the temporal variations of the apogee surface reflects the dynamics of orbital motion. This methodology has been applied to predict the reentry date of GSLV-D2 Rocket Body, which put the GSAT-2 satellite on 08th May 2003. Shortly after the launch it was predicted that it would reenter during the end of 2004 and the beginning of 2005. The GSLV-D2 Rocket Body reenters on 24th February 2005 and the final predicted reentry time matches very well with those from USAF Space Command and Aerospace Corporation.
- Abstract document