### About accuracy of the INTERBALL spacecraft motion calculation and orbital elements modification

Dear colleagues!
Let us draw your attention to the following:
• The accuracy of calculation of both INTERBALL spacecraft (SC) motion has been estimated at the IKI. For this estimation, we used the initial orbital elements, determined at the Keldysh Institute of Applied Mathematics (KIAM) of Russian Academy of Sciences during the treatment of the inflight SC trajectory measurements. The 30 days measuring intervals were used during the Tail probe (TP) orbital data treatment, and 15 days intervals - during the Auroral probe (AP) orbit determination. Obtained orbital elements are presented as a state vectors, which include the SC Cartesian coordinates and velocity components in the J2000 reference. These state vectors correspond to the last points of measuring intervals. The orbit determination mean square error of 30-40 km inside the measuring intervals was estimated by KIAM.
• During the forward in time extrapolation of SC motion outside the measuring interval the additional error appear as the SC orbiting period error. The mean square error of TP orbiting period is 13.6 s. In one month it leads to the mean square errors of 550 km at the SC position near the perigee region, and of 80 km near the apogee. For the AP, these values respectively are 0.91 s, 550 km and 145 km, but in the 15 days. The reason of these errors is the non-determined character of the orbit perturbation, caused by the attitude control system outside the measuring interval.
• During the aposteriory orbital calculations, there is a possibility to completely avoid the methodological errors described above, using the interpolation of the SC motion inside the measuring interval only. For this purpose, it is necessary to perform integration of the SC position backward in time. In this case we obtain as a result the accuracy of SC position calculation of 30-40 km. This accuracy corresponds to the one obtained during orbit determination.
• The same effect may be achieved using the standard procedure of integration forward in time, but taking as an input the new modified orbital elements produced at IKI, which now correspond to the initial points of the measuring intervals. These modified orbital elements were obtained by means of backward integration of the both probes motion from now up to the launch.
• The modified orbital elements, as well as the original ones, are available now in the same format from IKI Satellite Situation Center (SSC) Web site. Please use the following URLs:
• The aposteriory orbital calculations based on the modified orbital elements are available now via INTERNET:
• The ballistic center at KIAM continue its efforts to improve the orbit determinations accuracy by the after-flight reconstruction of the INTERBALL orbits on the basis of the full set of the performed orbital measurements. The accelerations caused by the attitude control system and thus impossible to model before the flight are now being included into consideration. This will allow to significantly improve the accuracy of the INTERBALL SC motion calculations and reduce the errors down to only several kilometers.
The first results of the orbit reconstruction are being added to the test IKI database. Presently, testing and comparisons of this new dataset with the existing data are on the way. After this strict analysis, if necessary, we will need to make a decision on the aposteriory calculations modification.
 Scientific Coordinator of the INTERBALL Project Prof. Lev Zelenyi lzelenyi@iki.rssi.ru 25 July 1999 IKI Satellite Situation Center Prof. Ravil Nasirov, rnazirov@rssi.ru Dr. Victoria Prokhorenko, vprokhor@iki.rssi.ru