Научная статья на тему 'Analysis of spacecraft orbital motion stability of Gonets-M No 37152'

Analysis of spacecraft orbital motion stability of Gonets-M No 37152 Текст научной статьи по специальности «Физика»

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КОСМИЧЕСКИЙ АППАРАТ / ПАРАМЕТРЫ ОРБИТЫ / ЭКСЦЕНТРИСИТЕТ / АРГУМЕНТ ПЕРИГЕЯ / ДРАКОНИЧЕСКИЙ ПЕРИОД ОБРАЩЕНИЯ / БАЛЛИСТИКА / SPACECRAFT / ORBITAL PARAMETERS / ECCENTRICITY / PERIGEE ARGUMENT / NODICAL PERIOD / BALLISTICS

Аннотация научной статьи по физике, автор научной работы — Kolovsky I.K., Shmakov D.N., Podolyakin V.N.

In the present investigation we envisage the spacecraft motion of Gonets-M (Gn-M) orbit group which is located in a circular orbit at a height of 1500 km with an inclination of 82.5 degrees. Its movement is measured based on the current navigation parameters which reveal its orbital motion analysis. Gn-M has a special characteristic feature of rotation with apsidal motion in frozen orbit. Based on this fact, the present study was carried out with the conception of a frozen orbit of Gn-M by investigating eccentricity parameter e and perigee argument w. The comparative analysis is presented as graphs which indicates the variation in the values of eccentricity parameters e and the perigee argument w which is calculated based on the current navigation parameters and the predicted motion of Gn-M. An orbital measurement was carried out by studying three Gn-M of the same orbital plane over a period of one year. The study insight on the complete analysis of specific changing revolution of the nodical period of Gn-M staying at frozen orbit. The amplitude vibrations of an orbital nodical period are calculated and compared with the orbital parameters of Gn-M which are in the same orbital plane. Overall the results obtained in the present investigation are promising enough which can aid in improving the calculation accuracy of orbit correction parameters of Gn-M.

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Текст научной работы на тему «Analysis of spacecraft orbital motion stability of Gonets-M No 37152»

UDC 629.78.015

Siberian Journal of Science and Technology. 2018, Vol. 19, No. 1, P. 76-81 ANALYSIS OF SPACECRAFT ORBITAL MOTION STABILITY OF GONETS-M NO 37152 I. K. Kolovsky*, D. N. Shmakov, V. N. Podolyakin

JSC "Academician M. F. Reshetnev" Information Satellite Systems" 52, Lenin Str., Zheleznogorsk, Krasnoyarsk region, 662972, Russian Federation

Е-mail: kolovigor@mail.ru

In the present investigation we envisage the spacecraft motion of Gonets-M (Gn-M) orbit group which is located in a circular orbit at a height of 1500 km with an inclination of 82.5 degrees. Its movement is measured based on the current navigation parameters which reveal its orbital motion analysis. Gn-M has a special characteristic feature of rotation with apsidal motion in frozen orbit. Based on this fact, the present study was carried out with the conception of a frozen orbit of Gn-M by investigating eccentricity parameter e and perigee argument w. The comparative analysis is presented as graphs which indicates the variation in the values of eccentricity parameters e and the perigee argument w which is calculated based on the current navigation parameters and the predicted motion of Gn-M. An orbital measurement was carried out by studying three Gn-M of the same orbital plane over a period of one year. The study insight on the complete analysis of specific changing revolution of the nodical period of Gn-M staying at frozen orbit. The amplitude vibrations of an orbital nodical period are calculated and compared with the orbital parameters of Gn-M which are in the same orbital plane. Overall the results obtained in the present investigation are promising enough which can aid in improving the calculation accuracy of orbit correction parameters of Gn-M.

Keywords: spacecraft, orbital parameters, eccentricity, perigee argument, nodical period, ballistics.

Сибирский журнал науки и технологий. 2018. Т. 19, № 1. С. 76-81

АНАЛИЗ СТАБИЛЬНОСТИ ДВИЖЕНИЯ КОСМИЧЕСКОГО АППАРАТА «ГОНЕЦ-М» № 37152 ПО ОРБИТЕ

И. К. Коловский , Д. Н. Шмаков, В. Н. Подолякин

АО «Информационные спутниковые системы» имени академика М. Ф. Решетнёва» Российская Федерация, 662972, г. Железногорск Красноярского края, ул. Ленина, 52

Е-mail: kolovigor@mail.ru

Исследуется движение космических аппаратов орбитальной группировки «Гонец-М». Орбитальная группировка «Гонец-М» представляет собой космические аппараты на круговой орбите с высотой 1500 км и наклонением 82,5°. Для анализа движения по орбите используются измерения текущих навигационных параметров космических аппаратов «Гонец-М». Рассмотрены особенности изменения параметров орбиты космических аппаратов «Гонец-М». После анализа орбитального движения была отмечена особенность во вращении линии апсид космического аппарата «Гонец-М» на замороженной орбите. Раскрывается понятие «замороженная орбита». Приведены значения параметров орбиты эксцентриситета е и аргумента перигея w, характеризующие подобные орбиты. Построены сравнительные графики изменения значений параметров орбиты эксцентриситета е и аргумента перигея w, полученных с помощью измерения текущих навигационных параметров, и соответствующих значений, рассчитанных через прогнозирование движения космического аппарата «Гонец-М». Рассмотрено и приведено на одном графике вековое изменение периода обращения в течение года у трех космических аппаратов «Гонец-М» одной орбитальной плоскости. Выявлена особенность изменения величины драконического периода обращения космического аппарата на замороженной орбите. Вычислена величина амплитуды колебания драконического периода обращения. Проводится сравнительный анализ параметров орбиты космических аппаратов «Гонец-М», которые находятся в одной орбитальной плоскости. Полученные результаты могут способствовать повышению точности вычисления параметров коррекции орбиты космического аппарата «Гонец-М».

Ключевые слова: космический аппарат, параметры орбиты, эксцентриситет, аргумент перигея, дракони-ческий период обращения, баллистика.

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 parameters e and w of Gn-M. A frozen orbit is an orbit whose mid elements, particularly the eccentricity e and the perigee 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 parameters 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 behavior of the considering orbital motion elements according 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 resistance 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 Тм, 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 ТпсЬ 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

A2 ™A5

A3 mf/ ■

u\ 1 Д1 jj

■ A4

0,00090 0,00095 0,00100 0,00105 0,00110 0,00115 0,00120 0,00125 0,00130 0,00135

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

е

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 на интервале одного года

At the fig. 1, 2 and 3 it can be seen that the values obtained 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 significant 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 perturbation 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 sidereal period in orbit. The long-period component is generated by the long-period oscillations of the nodical period, which have an amplitude [9-11]

^t = 3-C2,0'(RJa)2-Tnd'(2 - (5-sin2(i))/2)-e, (2)

where C20 = -1082.627T0-6 - dimensionless constant characterizing the shape of the Earth; R3 = 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 following 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 (Tnd)db с 1/2-(Tndk, 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 (Jn^dh с 1/2'(Tndk, 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 (Jn^dh с 1/2'(Tndk, 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)A at the time of equator passing take the following form [9-11] in the turn

(Tnd)dk = -AT-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 AT is 0.007-0.030 s according to the formula (3).

If Gn-M No 37152 is moving along frozen orbit, its AT 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 calculations (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.

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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 calculation 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 reduction of SC retention area at the necessary points of standing, i. e., in connection with the requirements increasing to the structural stability of the orbital group.

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© Kolovsky I. K., Shmakov D. N., Podolyakin V. N., 2018

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