ANALYSIS OF SPACECRAFT ORBITAL MOTION STABILITY OF GONETS-M NO 37152

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Introduction. The flatness of the Earth leads to the displacement of the satellite orbit perigee [1]. However, after consideration of the orbit group parameters of Gn-M, it was observed that the orbit apsidal line of SC No 37152 vice versa practically retains its position. Despite the fact that the orbital plane inclination of Gn-M is different from the critical value (the critical inclination equal to 63.43 degrees and 116.57 degrees). It was found out that after the reduction correction Gn-M No 37152 hit the target orbit at a height of 1500 km with an inclination of 82.5 degrees with special laws changes in the orbit parameters - frozen orbit. The study of the evolution of the orbital parame- ters e and w of Gn-M. A frozen orbit is an orbit whose mid elements, particularly the eccentricity e and the peri- gee argument w, for a long period of time can take almost constant or within a limited range enclosed values [2-4]. Analysis was studied by measurements of current navigation parameters (MCNP) of SC’s No 37152, No 38736, No 38734 which are located in the same orbital plane. Special attention was paid to the following SC orbit parameters: e, w and the nodical period Tnd. Due to the analysis it turned out that the parameters, obtained after processing MCNP of SC’s No 38736, No 38734 behave in the following way: w changes in the range from 0 degree to 360 degrees, i. e., it has secular changes, e changes in the range from 0.001 to 0.003. The nodical period Tnd in addition to the secular component has got a long-period one. On the other hand, orbit pa- rameters w and e of SC No 37152 change in a completely different way (tab. 1). It must be noted that SC No 37152 is different in be- havior of the considering orbital motion elements accord- ing to its own points A1-A5 (tab. 1) in comparison with parameter values at points B1-B5 and C1-C5 of other SC’s and in addition to this its secular component of the perigee argument change disappeared. Therefore, further for the study, we take the values obtained by MCNP, orbit parameters e and w of SC’s No 37152, No 37836 and No 38734 over a period of one year (tab. 1) and compare these values with the predicted values of e and w. The forecast will be carried out taking into account the influence of the Sun, moon and the resis- tance of the atmosphere over a period of one year. All the corresponding values will be presented in one graph (fig. 1-3). Table 1 The MCNP results of SC’s No 37152, No 38736, No 38734 SC No 37152 № Date Тnd, с e w, ° i, ° А1 04.06.16 6955.066 0.0010284 67.778 82.460 А2 06.07.16 6955.067 0.0011624 73.497 82.460 А3 06.11.16 6955.046 0.0009379 73.050 82.459 А4 06.03.17 6955.042 0.0012092 61.417 82.461 А5 07.07.17 6955.019 0.0012199 75.115 82.463 SC No 38736 № Date Тnd, с e w, ° i, ° B1 29.06.16 6955.032 0.0032782 70.250 82.484 B2 22.09.16 6954.957 0.0010319 238.830 82.484 B3 16.11.16 6954.955 0.0028615 107.508 82.487 B4 17.03.17 6954.950 0.0011888 197.741 82.488 B5 17.07.17 6954.914 0.0019047 349.824 82.486 SC No 38734 № Date Тnd, с e w, ° i, ° С1 29.06.16 6954.913 0.0030670 69.888 82.479 С2 21.08.16 6954.883 0.0017654 177.554 82.475 С3 26.11.16 6954.899 0.0028563 91.390 82.482 С4 27.03.17 6954.905 0.0014133 163.996 82.484 С5 05.05.17 6954.892 0.0027339 99.380 82.483 Fig. 1. e, w orbit parameters change of SC No 37152 over a period of one year Рис. 1. Изменение параметров е, w на орбите КА № 37152 на интервале одного года Fig. 2. e, w orbit parameters change of SC No 38736 over a period of one year Рис. 2. Изменение параметров е, w на орбите КА № 38736 на интервале одного года Fig. 3. e, w orbit parameters change of SC No 38734 over a period of one year Рис. 3. Изменение параметров е, w на орбите КА № 38734 78 на интервале одного года At the fig. 1, 2 and 3 it can be seen that the values ob- tained by MCNP are in good agreement with the values calculated by the forecast of SC orbit motion. Looking at tab. 1 and fig. 1 it can be concluded that in a frozen orbit parameters e and w of SC No 37152 are changing in the following intervals of values 0.0009 ≤ e ≤ 0.0013; 60.0° ≤ w ≤ 80.0° (1) The obtained inequalities of e and w changes are assumed as a condition for SC being in a frozen orbit at an orbit height of 1500 km with an inclination of 82.5 degrees. The orbit period changes of Gn-M. Consideration should be given to the nodical period Tnd of Gn-M. The observation of the Tnd secular changes according to the NORAD database [5] shows that SC No 37152 has sig- nificant decreasing of the amplitude of the long-period component in the nodical period, compared to SC No 38736 and SC No 38734 of the same orbital plane and of the same location in a non-frozen orbit (fig. 4). It is necessary to pay attention to one more feature of carrying out calculations by Tnd using. It is talked about the influence of TGF tesserial harmonics on the average anomaly. These harmonics cause secular perturbation in the average anomaly, what corresponds to the SC secular drift along the trajectory. This secular drift should be taken into account in project calculations where the initial conditions are the use of the sculating orbital elements at some point. If Tnd is used as initial conditions, this pertur- bation should not be taken into account, since it is included as a component of nodical period initial value [6; 7]. The analysis of the secular change in Tnd circulation period by all three SCs Gn-M shows that every SC Tnd value over a period of one year, starting since 01.06.2016, decreased an average of ~ 0.04 s. Considering fig. 4 in greater detail, the significant amplitude decreasing of the long-period component can be noted in the nodical period of Gn-M No 37152. The changing nature of treatment period became smooth over time. The difference in Tnd values changes of SC No 37152 and Tnd of other orbit group SCs can be explained due to the influence of long-period perturbations [8]. The oscillation amplitude changes of Gn-M side- real period in orbit. The long-period component is gen- erated by the long-period oscillations of the nodical pe- riod, which have an amplitude [9-11] АТ = 3·C2,0·(Rэ/a)2·Tnd·(2 - (5·sin2(i))/2)·e, (2) where C2.0 = -1082.627·10-6 - dimensionless constant characterizing the shape of the Earth; Rэ = 6378.16 km - the equatorial radius of the Earth [12; 13]; e - the eccentricity of orbit turn; a = 7878.16 km - a large orbit axis; Tnd = 6955.0 s - the initial value of Gn-M orbit nodical period [14]; i = 82.5 degrees - the inclination of orbital plane. On substituting values into expression (2), the follow- ing formula is obtained АТ = 6.8·e. (3) Fig. 4. Tnd change of SC No 37152, SC No 38736 and SC No 38734 Рис. 4. Изменение Тдр КА № 37152, КА № 38736 и КА № 38734 Table 2 AT, (Tnd)dk calculations results following MCNP data SC No 37152 Date e w, ° АТ (Тnd)dk, с 1/2·(Тnd)dk, с 04.06.16 0.0010284 67.778 0.00699 -0.00265 -0.00133 06.07.16 0.0011624 73.497 0.00790 -0.00225 -0.00113 06.11.16 0.0009379 73.050 0.00638 -0.00186 -0.00093 06.03.17 0.0012092 61.417 0.00822 -0.00394 -0.00197 07.07.17 0.0012199 75.115 0.00830 -0.00214 -0.00107 SC No 38736 Date e w, ° АТ (Тnd)dk, с 1/2·(Тnd)dk, с 29.06.16 0.0032782 70.250 0.02229 -0.00755 -0.00377 22.09.16 0.0010319 238.830 0.00702 0.00364 0.00182 16.11.16 0.0028615 107.508 0.01946 0.00584 0.00292 17.03.17 0.0011888 197.741 0.00808 0.00770 0.00385 17.07.17 0.0019047 349.824 0.01295 -0.01274 -0.00637 SC No 38734 Date e w, ° АТ (Тnd)dk, с 1/2·(Тnd)dk, с 29.06.16 0.0030670 69.888 0.02086 -0.00718 -0.00359 21.08.16 0.0017654 177.554 0.01200 0.01199 0.00600 26.11.16 0.0028563 91.390 0.01942 0.00046 0.00023 27.03.17 0.0014133 163.996 0.00961 0.00923 0.00462 05.05.17 0.0027339 99.380 0.01859 0.00301 0.00151 In this case, the long-period oscillations of nodical period (Tnd)dk at the time of equator passing take the following form [9-11] in the turn (Тnd)dk = -АТ·cos(w), (4) where w is the value of the orbit perigee argument in the turn. Following MCNP data the Gn-M orbits eccentricity is being ranged between 0.001 and 0.004. It follows that the long-period component amplitude of the nodical period АТ is 0.007-0.030 s according to the formula (3). If Gn-M No 37152 is moving along frozen orbit, its АТ change is different. To check this situation actual values obtained by MCNP, w and e parametres results are taken out of the tab. 1, formulas (3), (4) are used for calcu- lations (tab. 2). In tab. 2 parameter 1/2 · (Tnd)dk means the semirange of Tnd long-period oscillations. It must be noted that the value (Tnd)dk depends on time. Comparing presented in tab. 2 parameter 1/2·(Tnd)dk with the values of the Tnd. behavior by its real observations (see fig. 4) it can be seen that in both cases the semirange of the long-period oscillations of Tnd period is about 0.001 s in magnitude. In the tab. 2 t SC No 37152 eccentricity changes from 0.0009 to 0.0013, thus the long-period component amplitude of the nodical period changes in closer limits from 0.007 to 0.009 s. Conclusion. Presented data point to a potentially promising application area of orbits as a frozen orbit. The detection of the nature changes in the motion of SC Gn-M No 37152 in such an orbit can aid in improving the calcu- lation accuracy of orbit correction parameters, which will be relevant by increasing the number of Gn-M orbit groups, as is proposed in [15], and by a significant reduc- tion of SC retention area at the necessary points of stand- ing, i. e., in connection with the requirements increasing to the structural stability of the orbital group.

作者简介

I. Kolovsky

JSC “Academician M. F. Reshetnev” Information Satellite Systems”

Email: kolovigor@mail.ru
52, Lenin Str., Zheleznogorsk, Krasnoyarsk region, 662972, Russian Federation

D. Shmakov

JSC “Academician M. F. Reshetnev” Information Satellite Systems”

52, Lenin Str., Zheleznogorsk, Krasnoyarsk region, 662972, Russian Federation

V. Podolyakin

JSC “Academician M. F. Reshetnev” Information Satellite Systems”

52, Lenin Str., Zheleznogorsk, Krasnoyarsk region, 662972, Russian Federation

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