Reentry Time Determination Analysis for 99058E Satellite. Yurasov Vasiliy S. 1 SRC Kosmos. Nazarenko Andrey I. 2 Center for Program Studies

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1 Reentry Time Determination Analysis for 99058E Satellite Yurasov Vasiliy S. 1 SRC Kosmos Nazarenko Andrey I. 2 Center for Program Studies Abstract This paper describes the work done and the results obtained during the international reentry prediction campaign for Russian Soyuz (SL-4) upper stage (COSPAR ID E, NORAD catalog number is 25947). The order of organization and realization of activities is considered. The reentry predictions obtained by various authors are analyzed. Introduction During the last ten years regular practice became the international cooperation for the monitoring of space objects nearing the end of their orbiting. The examples of such works were the reentry of Salyut-7/Kosmos-1686 in 1990 [1], the reentry of Cosmos-398 in November- December 1995 and the reentry of Chinese descent capsule FSW-1-5 in February-March 1996 [2]. Inter-Agency Space Debris Coordination Committee (IADC) carried out the last reentry test campaign in February-March For this campaign a Russian Soyuz (SL-4/A-2) upper stage was adopted. On 18-Oct-1999 it delivered four Globalstar constellation satellites into orbits of 950 km x 892 km at deg inclination. The upper stage was registered under CO- SPAR ID E and NORAD catalog number It has a cylindrical shape of 2.7 m diameter and 8.2 m length, with an empty mass of 2.7 tons. Each of participants of test campaign was calculated your own re-entry prediction results, which can then be entered into the ESOC database, in order to make them accessible to the other campaign participants. This paper describes the work done and summarizes the results obtained by participants of the international reentry prediction campaign for SL-4 upper stage. Organization and realization of activities The authors of the given paper were connected to this international test campaign independently as unofficial participants after the appropriate reference to its organizers. All activity was conducted on the computer of the authors, on which there were installed the Internet and services. The own software realized on PC and available information sources was used for calculations. The theoretical and methodical fundamentals of the realized methods for satellite orbit determination and prediction are explained in a number of the papers [1-11] and were proved in the similar activities carried out earlier. Therefore there is no necessity here to consider these questions. Let's mark here only some nodal moments of adopted calculation process. 1. For satellite motion prediction the numerical and semi-analytical methods were used [2,4]. The numerical method was applied only at the last phase of satellite lifetime, 3 day prior to its reentry. 1 Magadanskaya str, 10-59, Moscow, Russia, , vyurasov@chat.ru 2 Profsoyuznaya str, 84/32, Moscow, Russia, , nazarenko@iki.rssi.ru

2 2. We have used prediction methods implementing 8x8 Earth s gravity model and GOST atmosphere density model [13]. 3. The current and forecasting values of solar and geomagnetic indices were used as input data for calculation the atmospheric density by GOST model. 4. As the initial data for reentry calculation were used the orbital parameters and ballistic factors obtained by joint processing by a least square method of the orbital data of Russian and US Space Surveillance System in 1-2 day interval (depending on a remaining lifetime). Figure 1 illustrates the scheme of information flow during our activities for determination of reentry time for SL-4 (99058E) upper stage. It is seen that for calculation of reentry time for SL-4 satellite were not used direct measurements obtained by space surveillance sensors. Instead of them were used orbital data obtained by Russian and US SSS. The US orbital data in the Two-Line Element Set Format (TLE-format) were accessible on Web-page of NASA Orbital Information Group (OIG). These data were updated in near-real time. As a rule their delay with respect to a current moment did not exceed several hours. In this connection US SSS data was the main source for estimation of decay time. 2 Internet (OIG) Internet (Solar and geomagnetic indices) Satellite Measurements TLE TLE F10.7 and Kp Measurements US SSS Prediction results My computer TLE, Prediction results RSSS Internet (Results of reentry time calculation) Prediction results TLE, Prediction results Prediction results Prediction results Orbital elements MCC Reentry mail list Figure 1. Scheme of information flow

3 The Russian data were transferred by from Russian Mission Control Center (MCC), where Dr. Kalyuka Yu.F. executed a role of Russian contact points for reentry. These data were presented also in TLE-format. They were not used for calculations at first because of the delay in obtaining of these data reached 1-2 day at the beginning of campaign. However at the last stage of campaign the Russian data came faster. Besides they were obtained on those revolutions, on which US SSS did not observe the SL-4 satellite. Therefore information of RSSS represented doubtless value from a point of view of purposes of this experiment. The experiment has confirmed once again an importance of cooperation of efforts and information capabilities of international community at the solution of the problem of uncontrolled satellite reentering. Our predictions of reentry time calculated for a SL-4 satellite were delivered by as the bulletins to 9 participants of campaign, including Russian Mission Control Center, and were simultaneously placed on our Web page The first outcomes were obtained by February 16, messages with the predictions of other participants of campaign come to us from MCC with delay of 1-2 day. The solar and geomagnetic indices for calculations of atmospheric density are available in the Internet (see gopher://solar.sec.noaa.gov). The present activity has shown that the information on indices is updated now every day and can be used in near-real time calculations. The plots for changing of indices of solar and geomagnetic activity, appropriate to campaign period are shown in Figures 2 and 3. It is seen that helio-geomagnetic conditions in the specified period was dynamical that should introduce additional errors to the solution of a posed problem. 3 Solar flux F Solar flux 14:02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :03: :03: :03: :03: :03:2000 Date Figure 2. Indices of solar activity

4 4 4 Planetary index Kp 3 Planetary index Kp :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :02: :03: :03: :03:2000 Date Figure 3. Indices of geomagnetic activity The main results of calculation Tables 1 and 2 generalized all set of prediction data obtained during test campaign. Here t 1 is preparation time of the prediction, t 2 is the time of last orbit used for calculations and t 3 is reentry time estimate. The first table contains the outcomes of calculations of the official participants of campaign received by from Dr. Kalyuka Yu.F., MCC. The second table composed by using our bulletins. The time format in these tables is identical to that used in the Two-Line Element Set Format. The copy of our bulletins is submitted in Table 3. Table 1. The results of official participants # Authors i k t 1, days t 2, days t 3, days ε i 1 Bain Bain Bain Klinkrad Pardini Pardini Xinying Ivanov Ivanov Bain Klinkrad

5 # Authors i k t 1, days t 2, days t 3, days ε i 12 Xinying Ivanov Ivanov Xinying Xinying Bain Klinkrad Pardini Ivanov Bain Pardini Xinying Ivanov Bain Ganeshan Klinkrad Xinying Ivanov Bain Ganeshan Ganeshan Klinkrad Konno Pardini Xinying Ganeshan Ganeshan Klinkrad Klinkrad Klinkrad Konno Pardini Pardini Xinying Xinying Ivanov Ivanov Ganeshan Klinkrad Xinying Pardini Bain Ivanov Ganeshan Johnson Klinkrad Pardini Soula Xinying

6 # Authors i k t 1, days t 2, days t 3, days ε i 61 Bain Bain Ganeshan Johnson Klinkrad Klinkrad Klinkrad Konno Pardini Pardini Soula Xinying Ivanov Ivanov Alwes Alwes Alwes Alwes Alwes Bain Ganeshan Ganeshan Johnson Johnson Klinkrad Klinkrad Klinkrad Konno Pardini Pardini Pardini Soula Soula Xinying Ivanov Ivanov Ivanov Ivanov Ivanov Ivanov

7 7 Table 2. Our results i k t 1, days t 2, days t 3, days ε i Table 3. Reentry time for SL-4 upper stage (NORAD #25947, COSPAR E) Bull # Preparation time Last orbit Decay time Decay window Measurement interval, days/source /US TLE 08:00:00 22:03:34 00:01: /US TLE 07:40:00 20:48:44 10:36: /US TLE

8 Bull # Preparation time Last orbit Decay time Decay window 8 Measurement interval, days/source 07:00:00 21:03:37 12:13: /US TLE 06:18:00 21:39:37 00:51: /US TLE 07:00:00 03:50:34 05:10: /US TLE 07:00:00 05:21:02 18:30: /US TLE 18:40:00 05:27:43 16:19: h -48h 2/US TLE 16:40:00 08:35:36 15:49: h -48h 2/US TLE 5:40:00 02:35:56 17:25: h -24h 2/US TLE 6:28:00 20:54:49 06:15: h -24h 2/US TLE 6:28:00 03:07:50 05:33: h -24h 2/US TLE 18:25:00 12:57:10 05:35: h -24h 2/US TLE 18:25:00 14:26:42 06:06: h -15h 2/US TLE 7:25:00 17:25:45 07:31: h -15h 2/US TLE 7:25:00 20:24:46 07:34: h -15h 2/US TLE 7:25:00 22:21:58 07:36: h -15h 2/US TLE 10:50:00 03:52:02 05:53: h -15h 2/US TLE 10:50:00 05:21:27 05:43: h -10h 2/US TLE 14:10:00 10:00:05 03:51: h -10h 2/US TLE 14:10:00 08:08:24 03:33: h -10h 2/US TLE 18:30:00 14:04:47 04:16: h -10h 2/US TLE 18:30:00 15:59:55 04:15: h -8h 2/US TLE 08:10:00 04:54:19 02:02: h -8h 2/US TLE 13:30:00 09:20:44 01:40: :00: :18:12 00:56:34 +5h -8h 2/US TLE

9 9 Bull # Preparation time :00: :20: :20: :20: :20: :50: :50: :00:00 Last orbit :46: :50: :03: :21: :49: :18: :47:49 02:32:23 Decay time 01:06:43 04:01:46 04:17:33 04:47:25 04:56:19 05:06:46 04:50:00 05:32:00 Decay window Measurement interval, days/source +5h -8h 2/US TLE +5h -5h 1/US TLE +5h -5h 1/US TLE +3h -3h 1/US+RSSS TLE +3h -3h 1/US+RSSS TLE +3h -3h 1/US+RSSS TLE +3h -3h 1/US+RSSS TLE +40m -30m 0.6/US+RSSS TLE Reentry time determination analysis In Table 4 are submitted the last estimations of reentry time for all participants of campaign. These data are taken from the message of Dr. Kalyuka, sent March 3 at 22 hours 04 min. Table 4. Last estimations of reentry time # Authors Last orbit time, mm/dd hh:mm UTC Estimation of reentry time, mm/dd hh:mm UTC 1 Ganeshan 03/03 12:08 03/04 04:54 2 Ivanov 03/03 16:48 03/04 06:59 3 Xinying 03/01 00:00 03/04 08:04 4 Pardini 03/03 15:11 03/04 04:42 5 Bain 03/02 00:00 03/04 04:10 6 Klinkrad 03/03 15:11 03/04 05:13 7 Konno 03/03 03:03 03/04 03:55 8 Johnson 03/03 00:00 03/04 05:33 9 Soula 03/03 03:03 03/04 05:47 10 Alwes 03/03 15:11 03/04 06:28 11 Yurasov 03/03 16:47 03/04 04:50 Only six participants from 11 ones have presented estimation data calculated by using orbits updated after afternoon of March 3. These most reliable data are marked with a bold font. The time spread of estimations for reentry is equal 6 h 59 m -4 h 42 m =2 h 17 m. Mean value for decay time is equal 5 h 30 m UTC (t r =64.212). This is the most reliable estimation of

10 the reentry time obtained by the participants when satellite was in orbit. It was obtained an additional orbit from US SSS after 3 days of SL-4 decay. The reentry time calculated by us using this orbit is equal 5 h 32 m. It confirms also the previous mean estimate. In Figure 4 the track of SL-4 upper stage at the final stage of its flight appropriate to the given decay time is plotted. 10 Satellite # Irkutsk Latitude, deg Decay:04/03/ :32:39 H=101.7km 04/03/ :14: Longitude, deg Figure 4. The track for final stage of SL-4 flight The additional analysis have shown also that if the reentry time of a satellite was equal 5 h 50 m UTC, it would be observed by Russian radar located near Irkutsk at 5 h 43 m UTC on an elevation about of 9.2 degrees and range about of 493 km. If the reentry time of a satellite would make 6 h 30 m UTC it would be observed by this sensor on an elevation of about 13 degrees at range of 502 km. The absence of the radar observations allows to assert with sufficient reliance that the satellite was decayed earlier, at least, before 5 h 50 m. For all of tabulated in Tables 1 and 2 estimations were calculated the relative errors by using the mean evaluation of an reentry time (t r =64.212): ( t3 tr ) i ε i = ( t2 t r ) i These data are presented in the last columns of Tables 1 and 2. The mean M( ε i ) and root-mean-square RMS( ε i ) values of the relative errors ( ε i ) are calculated for everyone of authors. These results are presented in Table 5. All participants are break down here into 2 groups. Into the first group are included those who has received more than 10 estimations of the reentry time. The number of such participants was equal seven. All of them worked on an interval more than 10 days. Second group included those who have executed 4-5 estimations. These participants worked only at the last stage of campaign (4-5 days). Among the presented assessments of M( ε i ) and RMS( ε i ) the most reliable are the data of the participants of the first group, as these evaluations are obtained for a number of predictions more than 10 and in the greater temporary interval. For the participants of the second

11 group the statistical characteristics of εi are less reliable. Therefore the comparative analysis of average assessments we shall conduct only for the participants of the first group. Figure 5 illustrates the relative errors of reentry time determination obtained by the participants of the first group. These data are covering a 22-days interval before SL-4 reentry. This figure supplement materials of a Table 5. In particular, the presence of significant biases in estimations of Chinese (Xinying) and Russian (Ivanov) participants is precisely visible Relative errors Ganeshan Yurasov Ivanov Xinying Pardini Bain Klinkrad Interval before SL-4 reentry, days Figure 5. Relative errors of reentry time determination for participants of the first group Table 5. Statistical characteristics of relative errors # Authors Number of predictions M( ε i ) RMS( ε i ) 1 Pardini Yurasov Ganeshan Klinkrad Xinying Ivanov Bain Alwes Johnson Konno Soula The considered seven participants are divided into 3 subgroups by RMS values. In the first group are included Pardini, Yurasov and Ganeshan. They have the least level of errors. RMS values are about of 4-5% for this group. For these participants the systematic errors have also the small values. They do not exceed 1%. The greatest RMS values of errors have the predictions of Xinying, Ivanov and Bain. The RMS( ε i ) values for these participants are two times

12 more than for the participants of the first group and are equal 9-10%. And, for the latter from the abovementioned participants the greatest value reaches the random subcategory of error (biases has a level of 1 %). Intermediate levels of errors have the estimates of Klinkrad (RMS( ε i )=7.3%). Figure 6 shows the RMS-values for the last 4 days of SL-4 lifetime. They concern to all participants of campaign. It is necessary to note that at the last phase of a satellite lifetime the role of a possible error of "true" decay time adopted in calculations (t r =64.212) is increased. At intervals more than 5 days before reentry the 1-hour error of this parameter results to changing of a relative error no more than 1%. The same error results to changing of a relative error about of 10% if the remaining lifetime is less than 0.5 day. Therefore we add the data of a Figure 6 by possible spreading of values ε i caused by possible ±1-hour error for t r value. The appropriate results of calculations are presented in Table relative errors Ganeshan Yurasov Ivanov Xinying Pardini Bain Klinkrad Konno Johnson Soula Alwes Interval before SL-4 reentry, days Figure 6. Relative errors of reentry time determination for last 4 days By the bold font are marked the maximum absolute values of relative errors for participants. The data of Table 6 are arranged in ascending order of these errors. Besides in the last two columns are adduced the interval between the moments of preparation data and last orbit s update and also the interval between the moments of adopted decay time and last orbit s update. The important future of these results is that the minimum interval between a moment of the last update of orbital elements and a moment of a satellite reentry is equal day. Five participants could operatively receive and process the last data: Ivanov, Yurasov, Alwes, Klinkrad and Pardini. From the remaining participants the length of interval less than one day has only Ganeshan. It is necessary to note also that the Russian SSS was executed the last observation of SL-4 (0.53 day before the reentry). The results of first three rows in Table 5 are characteristic not only by minimum level of maximum relative errors (5%-8%) but also by minimum quantity of the predictions and by maximum values of intervals t1 t and 2 t r t. This circumstance hampers objective ranking 2 of this prediction results by its accuracy. For the remaining eight participants the maximum values of relative errors are in range of 9%-19%. The lower boundary of this range is reached by Klinkrad s and Ganeshan s predictions, upper one by Ivanov's and Soula s estimates. Table 6. Prediction characteristics for last 4 days

13 13 # Author Number of predictions t, days ε min ε max 1 t2 t r t 2, days 1 Xinying Bain Johnson Klinkrad Ganeshan Konno Pardini Alwes Yurasov Ivanov Soula The histogram in Figure 7 presents the distribution of relative errors for abovementioned 132 estimations obtained by all participants. It is visible that the distribution of relative errors is close to normal with a standard deviation of σ 7% and rather small bias (+2.1%). Such level of errors is normal. It corresponds to preceding practice of satellite reentry time and its impact area determination Number of predictions <= -.2 (-.15,-.1] (-.05,0.] (.05,.1] (.15,.2] (-.2,-.15] (-.1,-.05] (0,.05] (.1,.15] Relative errors Figure 7. Distribution of relative errors >.2 From these results of analysis it is possible to make the following conclusion: though the mean accuracy of the considered above reentry time predictions is normal, for the separate participants it differs by times. This is explained by using of various data processing technology and software. It is required an additional analysis for finding-out the reasons of these differences. The organization of arguing of techniques used by various participants can promote to develop the recommendations for reaching maximum accuracy. In particular, the rec-

14 ommendations can be reduced to implementing the concrete software. Apparently, on this basis can be reached the increase of accuracy by times on a comparison with mean current accuracy level (7%-10%). During SL-4 reentry test campaign were not used all known reserves for accuracy increasing. First of all it concerns to operative determination and account of variations of atmospheric density. Other known capability consists of application of methods of processing of the measuring information permitting to inspect change of the ballistic characteristics of a satellite. Apparently, there are also other possibilities, for example, more accurate forecasting of indices of solar and geomagnetic activity. The expected effect of application of listed measures is an additional increase of accuracy by times. Thus, RMS of errors of reentry time determination about of 2.5%-3.5% from the remaining lifetime is accessible in the near-term outlook. Besides this experiment have confirmed once again the known fact that for increase of accuracy of reentry time determination it is very important to obtain measurements on last satellite revolutions. In this case reduction of the time interval t r t from 0.5 to 0.1 day would 2 allow to increase accuracy of reentry time determination of a satellite not less than by 5 times. For example, if RMS of relative errors is equal σ ( ε) = 7% then the confidence interval of decay time window will be equal ± 3 σ ( ε) ( t r t2 ) = ± 150 min. If the size of t r t interval will 2 be reduced five times then the confidence interval would decrease to ±30 m. However, the regular practical reaching of such level of errors is improbable because of an existing Russian and US space surveillance network cannot supply now the global observation of reentry satellites. More realistic prospect is now perfecting of methods for processing of the information and for satellite motion prediction. In this case for conditions of the given activity on SL-4 satellite the confidence interval of decay time in the future could make ±25 m. It is natural, that this prospect will not come itself. It is necessary to note, that the carried out analysis is not full. A number of the important problems were not considered. In particular, they are: the analysis of quantity and accuracy of Russian and US SSS orbital elements; the analysis of the ballistic coefficients obtained by SSS and by the participants of campaign; the analysis of influence of variability of solar and geomagnetic activity on results of the predictions. Conclusions 1. The international campaign has confirmed once again the importance of cooperation of efforts and information capabilities of world community at the solution of a problem of reentry time and impact region determination of uncontrollable dangerous space objects. The existing telecommunication and information resources, in particular and Internet, allow to decide this problem for anyone and in any site of the world. 2. The experiment has shown that only Russian and US SSS can supply with the regular real information the solution of the given problem. 3. About of 10 representatives of various space agencies and countries have taken part in fulfillment of the predictions of the reentry time of SL-4 upper stage. The participation of representatives of the various countries has allowed to estimate quality of methods used by them. However, this demonstrating was not full, as the outcomes of a number of participants were not sufficiently representative. Nevertheless, for a number of the participants the information exchange will allow to develop the recommendations for improving used methods. 4. The last near-real time update of test satellite orbit were obtained by Russian SSS for 12 h 45 m before the most probable moment of its reentry. The last US SSS important data with 14

15 binding of orbit for 3 h before the satellite reentry were announced after some days after real satellite decay. Calculated by the participants of campaign the confidence interval for reentry time was equal ±3 h and more. Thus, the results of activity were not sufficient for acceptable determination of possible impact region of a satellite. 5. Since February 14 till March 3, 2000 by participants of campaign were executed 132 predictions of the reentry time for chosen satellite. RMS of prediction errors is equal 7% of the remaining lifetime. Such level of errors is normal. It is even a little bit lower, than the usually received average level of errors (RMS=10%) in spite of the solar and geomagnetic activities during the experiment were not quiet. 6. The maximum difference of accuracy of predictions obtained by the different participants reaches times. The correct comparative analysis for a number of the participants of activity could not be executed because of insufficiency of a number of realizations. Nevertheless, the detail arguing of methods, used by the participants, can promote development of the recommendations for their perfecting. In particular, the recommendations can be reduced to application of particular software. 7. Actual direction of the further activities is the evaluation of capabilities of accuracy increasing for the considered task solution and development the realistic recommendations directed to reaching the best possible accuracy. Apparently, in the near future it is possible really to come nearer to relative errors at a level of 2.5%-3.5% of the satellite remaining lifetime. 8. The experiment has shown, that at realization of similar experiments in the future it is necessary to be aimed, that the information from Russian and US SSS and from other sources was accessible to the participants with the minimum delay and without participation of the additional intermediaries (such as MCC, ESOC etc.). It can be, for example, direct publication of the available information on beforehand opened theme Web page or organization of operative dispatch the data by to the participants of experiment. Acknowledgement The authors would like to acknowledge Dr. Ken Seidelmann (U.S. Naval Observatory) and Dr. Felix Hoots (General Research Corporation) for supporting the regular US/Russian Space Surveillance Workshops. The authors would like to thank Dr. Yuri Kalyuka for providing prediction data of official participants of test campaign. The first author would like to acknowledge the lasting attention to his research of Drs Valery Shishkin, Viktor Karelin and Alexander Vorobyov. References 1. Nazarenko, A.I. Determination and Prediction of the Satellite Motion at the End of the Lifetime, Proceedings of International Workshop on Salyut-7/Kosmos-1686 reentry, ESOC, Darmstadt, 9 April 1991, pp Andrewshchenko, V., Batyr, G., Bratchikov, V., Dicky, V., Veniaminov, S., Yurasov, V. Reentry time determination analysis for "Cosmos-398" and FSW-1-5, Proceedings of U.S.- Russian Second Space Surveillance Workshop, Poznan, Poland, 1996, pp Yurasov, V.S. Universal Semianalytic Satellite Motion Propagation Method, Proceedings of U.S.-Russian Second Space Surveillance Workshop, Poznan, Poland, 1996, pp Amelina, T., Batyr, G., Dicky, V., Tumolskaya, N., Yurasov, V. Comparison of atmosphere density models, Proceedings of U.S.-Russian Second Space Surveillance Workshop, Poznan, Poland, 1996, pp Nazarenko, A.I. Technology of evaluation of atmosphere density variation based on the 15

16 space surveillance system's orbital data, Proceedings of U.S.-Russian Second Space Surveillance Workshop, Poznan, Poland, 1996, pp Nazarenko, A.I., Kravchenko, S.N., Tatevian, S.K. The space-temporal variations of the upper atmosphere density derived from satellite drag data, Adv. Space Res., Vol. 11, #6, Nazarenko, A.I. A priori and a posteriori orbit prediction error evaluation of LEO artificial Earth satellites, Journal of Cosmic Research, vol. 29, #4, Nazarenko, A.I., Cherniavskiy, G.M. Evaluation of the accuracy of forecasting satellite motion in the atmosphere, Proceedings of U.S.-Russian Second Space Surveillance Workshop, Poznan, Poland, 1996, pp Batyr, G., Bratchikov, V., Kravchenko S., Nazarenko A., Veniaminov, S., Yurasov, V. Upper atmosphere density variation investigations based on Russian Space Surveillance System data, Proceedings of the First European conference on space debris, Darmstadt, Germany, Anisimov, V.D., Bass, V.P., Komissarov, I.N., Kravchenko, S.N., Nazarenko, A.I., Pyatnitskiy, Yu.S., Rychkov, A.P., Sych, V.I., Tarasov, Yu.L., Fridlender, O.G., Schackhmistov, V.M., Yurasov, V.S. Results of investigations of aerodynamic characteristics and density of upper atmosphere with the help of passive "PION" satellites, Observation of artificial celestial objects, #86. USSR Academy of Sciences Astrocouncil, Moscow, Nazarenko, A.I., Amelina, T.A, Gukina, R.V., Kirichenko, O.I., Kravchenko, S.N., Markova, L.G., Tumolskaya, N.P. and Yurasov, V.S. An estimation of efficiency of various ways of atmosphere density variations accounting at satellite motion prediction during geomagnetic storms, Observation of artificial celestial objects, #84. USSR Academy of Sciences Astrocouncil, Moscow, The upper atmosphere of the Earth. Model of density for ballistic maintenance of the Earth artificial satellite flights. GOST , Publishing House of the Standards, Moscow,