It has been found that ballistic coefficient is a critical parameter in low Earth orbit(LEO) space debris orbit determination(OD) and orbit predication(OP) while using sparse tracking data. Ballistic coefficient of more than 2 000 space debris objects with perigee height below 850 km were estimated using the long-archived two-line elements(TLE) data and the drag perturbation equation of the semi-major axis of the orbit. Two applications of estimated ballistic coefficient values were discussed. In the first experiment, ballistic coefficient of 14 LEO space debris objects with high area to mass ratio(HAMR) were re-computed after TLEs of suspicious quality were removed through a TLE quality examination process in which the ballistic coefficient value was used to estimate a reasonable variation of the mean semi-major axis. Consequently, the errors of all the re-computed ballistic coefficient values were reduced. The newly estimated ballistic coefficient values were tested using a number of space debris objects with external ballistic coefficient values and agreements of about 20% were achieved. In the second experiment, ballistic coefficient of GRACE-B was used as initial value in the so-called TLE-OD/OP method. It is confirmed that the TLE-OD/OP method results have better OP accuracy than standard Simplified General Perturbations-4(SGP4).