Abstract. Catalogue GOCKU(97-98) (Geosynchronous Objects Catalogue:Kyiv-Uzhgorod 1997-1998) containing topocentric equatorial coordinates and orbital elements of geosynchronous satellites obtained by photographic methods at the Main Astronomical Observatory of the National Academy of Sciences of Ukraine ( MAO NASU ) and at the Space Research Laboratory of Uzhgorod State University (SRL USU) in 1997-1998 is presented. Results of identification of 2129 observations of 246 objects among the total 2609 observations of 334 objects are given. The problem of observations of passive geosynchronous space objects is considered. The evolution of the orbital elements by different revolting forces during the 2836 days is investigated using the free librating object Cosmos 1738 (86027A).


Photographical observations of geosynchronous satellites were performed at MAO NASU and SRL USU in 1997-1998 following the previous surveys (Demchyk et al. 1996; Kizyun et al.1998). Total number of identified and unidentified objects for each station is summarized in Table 1. The satellite right ascensions RA and declinations D obtained using the observations at MAO NASU reduced using the PPM Star Catalogue in J2000.0 reference frame( Table 2 ,2a). Time instants are given in the UTC scale. Table 3 presents the satellites positions obtained at SRL USU and reduced using the SAO Star Catalogue in B1950.0 reference frame. Time instants are given in the UTC(SU) scale. Beginning from 1998 SRL USU presents the satellite positions reduced using the PPM Star Catalogue in J2000.0 reference frame (Table 3a). The object name,its COSPAR designation, the object motion type ((c)-controlled satellites,(d)-drifting objects and (l)-librating ones), objects subsatellite longitude L (degree),longitude drift Lt (degree/day), time in MJD scale, i- orbital inclination, W- longitude of the ascending node (degree), u -argument perigee (degree) are provided for the identified objects. There are W(lap),i(lap) for the active satellites with a large orbital inclination (i) and for the passive objects with a large longitude drift (Lt). TABLE 1. NUMBER OF GEOSYNCHRONOUS OBJECTS DERIVED BY OBSERVATIONS IN KYIV AND UZHGOROD IN 1997-1998 ______________________________________________________ Object type Kyiv Uzhgorod ______________________________________________________ Identified controlled 114 114 librating - 7 drifting - 11 Unidentified controlled - 6 librating - - drifting - - unknown type 45 37 Totally 159 175 ___________________________________________________________ The identification has been pursued by the orbital inclination, longitude of the ascending node, both reffered to the Laplace plane, objects Greenwich longitude and longitude drift using the method (Kirichenko & Klimik 1994). The photographic surveys are performed without using ephemeris - the instruments are equiped in equator using the time angles (declination from -7 degr to -7.5 degr),where as usual the active geostationare objects are founded (longitude drift is equal zero). A distribution of the geosynchronous objects on the drift and orbit inclination to the equator depending on the subsatellite longitude is shown for 1998 in Fig.1,2 Fig.1 The position and drift of geostationary objects with subsatellite longitude on January 14, 1999. Fig.2 The position and orbital inclination of geostationary objects with subsatellite longitude on January 14, 1999. It is necessary to note that the satellites not always are observed and depended on the satellite zenith distance. This distance must to be no more than 70 degr. The Sun must be under the horizon at the angle distance no less than 12 degr, only then the faint objects might be observable. Besides the satellite should not to be in the Earth's shadow. For an example was determined the time of being the satellite in the Earth's shadow for Uzhgorod station (geocentric distance of the satellite is 42164 km). In Fig.3 the time of the evening twilight for Uzhgorod is limited by the curves 3,4, the morning twilight - 1,2.
  • Fig.3 Moments of the beginning and the end of the evening and morning twilights (1, 2, 3, 4) and the shadow regions (5,6) of the geosynchronous objects of zone -10 degr < t < 65 degr, -10 degr < d < -4 degr for Uzhgorod. The curves 5 and 6 are selected two regions according to UT time (vertical coordinate axis) and period of the year (horizontal axis), when the geosynchronous objects which are in zone -10 degr < t < 65 degr, -10 degr < d < -4 degr (d-declination),may be in the shadow. These time regions are received as a sum of the shadow regions for each point of zone.


    54 years libration period caused by lunisolar perturbations is a feature pecularity of evolution of some orbital elements (inclination and longitude of an ascending node) reduced ("classical" geostationary satellite) to the equatorial plain. That's why a satellite inclination is changes from 0 degr up to 15 degr and node - from 270 degr up to 90 degr [Sochilina 1985]. But today so-called "unknown" geosynchronous objects are already observed: minimum orbital inclination to the equatorial plain amount to 3 degr - 4 degr, maximum - 18 degr - 20 degr, the longitude of a node is changes from 270 degr through 180 degr once to 270 degr [Grigoriev 1996].These objects influence the shape and sizes of the geosynchronous objects spatial region of motion. That's why the catalogization of these objects is an actual problem. The space objects with observed satellites longitudes from -60 degr to +60 degr are shown in Fig.4,5,6 for Uzhgorod and Kyiv, obtained for 1997 on the base of our calculations using the catalogue [Sochilina 1986] and it electronic version [Vershkov 1996]. Fig.4.The position and drift of uncontrolled geostationary satellites on December 25, 1997 for Uzhgorod and Kyiv Fig.5.The position and inclination of uncontrolled geostationary satellites on December 25,1997 for Uzhgorod and Kyiv Fig.6.The position of controlled geostationary satellites with a zero drift on December 25, 1997 for Uzhgorod and Kyiv The calculated positions of passiv objects are given on December 25,1997. We have limited by +- 28 degr/day longitude maximum drift of subsatellite point and 15 degr maximum orbital inclination for these object. Controlled (active) geostationary objects with identical longitudes are located in column (Fig. 6), a longitude drift is almost zero for these objects. The observations and identifications of geosynchronous objects in Uzhgorod and Kyiv [Demchyk 1996; Kizyun 1998] also analysis of Fig 4-6 have shown still unused possibilities of passive objects observations at these stations. The height upon horizon of active objects amount to 15 degr in the time angles +- 60 degr, that's why the active objects need for fine transparency and also high-quality emulsions. But it is also necessary to calculate the ephemerides for passive objects. Some limits of geosynchronous objects appearance declinations (d) with an angle of orbital inclination i to equator not equal to zero are calculated for Uzhgorod and Kyiv : i = 5 degr - 12.8 degr< d < -1.7 degr i = 10 degr - 18.1 degr< d < 3.9 degr i = 15 degr - 23.4 degr< d < 9.6 degr It is seen that the changes of declinations depends on an angle of orbital inclination of the satellite. Dependence of satellite height upon the horizon from a time angle for two station [Uzhgorod, Kyiv] for different orbits are shown in Fig. 7, 8. Here: f-geografical latitude of the station in degrees, d-declination in degrees. Fig.7.Dependence of satellite height on the time angle for seven different declinations for Uzhgorod Fig.8.Dependence of satellite height on the time angle for seven different declinations for Kyiv One can see that for large negative meanings of declinations the possibility of observations limits by the time angle up to 36 degr because of small satellites height. It is necessary to know a period of libration in longitude caused by resonance perturbations for the satellites with a large positive drift. There are histograms of resonance periods for three types librating and drifting satellites shown in Fig.9(a,b,c), 10(a,b,c). Fig.9a.Histograms of resonant periods for geostationary satellites l1 Fig.9b.Histograms of resonant periods for geostationary satellites l2 Fig.9c.Histograms of resonant periods for geostationary satellites l3 Fig.10a.Histograms of resonant periods for geostationary satellites d1 Fig.10b.Histograms of resonant periods for geostationary satellites d2 Fig.10c.Histograms of resonant periods for geostationary satellites d3 It is seen from histograms that the more part of satellites of a type d have the period from 14 to 190 days and the librating one - from 700 to 2900 days.We use designation for librating objects according to [Sochilina et al.1996]: l1 - libration around the stable point with a longitude 75(E) degr, l2 - around point 255(E) degr, l3 - around both points ; for drifted satellites : d1 - with a large negative rate of drift, d2 - with a rate of drift no more than 2.5 degr/day, d3 - with a large positive drift. It is necessary to know the orbital elements in some initial instant for the passive objects observations.From the motion theory of artificial Earth satellites the problem is known, which consist of that knowing initial or mean values orbital elements using the motion theory, by means of an elimination a short and sometimes long periodical terms, it is possible to obtaine all components - secular, long-periodical and short-periodical terms. Each orbital element E can be represented as a time function t: E = Eo + Èo (t-to) + A + B, (1) where A - sum of the long periodical terms (function of t, geopotential harmonics, solar radiation pressure, gravitational attraction by the Moon and Sun,lunar and Sun tides and so on), and B - sum of short periodical terms (function of t,J2, J3). Eo and Èo -initial meaning of a selected element E and it velosity in initial instant to, J2,J3 - second and third zonal geopotential harmonics. As an example we consider the satellite Cosmos 1738 (86027A), which from MJD= 47617.0 has ceased to be active object and now is librating satellite of a type l2 . Electronic catalogue [Vershkov 1996] was used to derive the orbital elements of this satellite from MJD 48741.3214 to 51577.3842 in each 25-30 day. The mean ratio of meadel section to satellite mass is 0.0092 m 2/kg for this object. The system of 100 equations were solved for the unknowns Eo and Èo by the least square methods and the mean orbital elements of Cosmos 1738 (86027A) were derived a = 42189.92 - 1.40013*10-2 (t - to) [km] e = 0.108548*10-2 + 0.203047*10-6(t-to) i = 4.587863 + 1.855241*10-3 (t-to)  (2) W = 73.487290 - 0.110948*10-1 (t-to) u = 155.0332 - 0.216810*10-1 (t-to) n = 1.001818 - 0.501602*10-6 (t-to) [circ/day] , where t is given in modified days (MJD) and to=48741.3214 MJD. It is necessary to pay attention to elements a,e,i, which should not have the secular terms. It is possible to explain the appearance of these terms by the methodical errors and empirical braking (Sorokin 1996). The long-periodical perturbation called by zone geopotential harmonics have period of about 50 years which follows from a change of an element u. These perturbations are represented as secular changes for all elements. To determine of the long periodical terms the value obtained from (2) was excluded from each sets of orbital elements. As a result we obtained the sets of small values, which include the long-periodical variation from listed effects. These sets of data are an initial material for search of the longe periodicals. The hidden periodicity was calculated by the least square method (Kirichenko 1993). Proceeding from an essence of physical process it is may be stated that each orbital element can include a periodical term (as a function of time) and unperiodical one. From the analysis of the whole spectrum of harmonics of each satellite elements the amplitudes and periods of geopotential resonance harmonics of perturbations of a geopotential (Table 4), perturbation by the Moon and Sun (Table 5),the solar radiation pressure (Table 6) are precisely looken through. Not all amplitudes and periods give in to an identification. There are periods T (in days) and amplitudes A of the first main harmonics for orbital elements e, a (km), i,u,W (all in degrees) and n(circ/day) in Tables 4-6. ------------------------------------------------------------------------------------ TABLE 4. PERIODS AND AMPLITUDES OF LONG-PERIODICAL PERTURBATIONS BY RESONANCE HARMONICS OF A GEOPOTENTIAL ------------------------------------------------------------------------------------ Ta,days Aa,km Tu,days Au,grad ------------------------------------------------------------------------------------ 1216.9 6.324 3003.4 4.9311 1443.1 5.180 809.61 1.4864 ------------------------------------------------------------------------------------ Te,days Ae TW,days AW,grad | ------------------------------------------------------------------------------------ 1099.4 0.57659*10-4 1018.4 0.35628 2495.3 0.17207*10-3 1502.8 0.41475*10-1 ------------------------------------------------------------------------------------ Ti,days Ai,grad ------------------------------------------------------------------------------------ 834.45 0.57139*10-1 1198.9 0.61326*10-1 ------------------------------------------------------------------------------------ TABLE 5. PERIODS AND AMPLITUDES OF SHORT AND LONG-PERIODICAL PERTURBATIONS BY THE MOON AND SUN ------------------------------------------------------------------------------------ Ta,days Aa,km Ti,days Ai,grad ------------------------------------------------------------------------------------ 38.04 2.6285 44.21 0.37013*10-1 142.06 0.9948 42.68 0.41842*10-1 570.19 6.3210 90.12 0.66502*10-2 ------------------------------------------------------------------------------------ Te,days Ae Tu,days Au,grad ------------------------------------------------------------------------------------ 43.78 0.33554*10-4 43.18 0.12774 36.24 0.70452*10-5 36.22 0.92395 802.89 0.46109*10-4 123.36 0.20934 ------------------------------------------------------------------------------------ TW,days AW,grad ------------------------------------------------------------------------------------ 44.38 0.27672 41.514 0.18781 91.63 0.41527*10-1 ------------------------------------------------------------------------------------ TABLE 6. PERIODS AND AMPLITUDES OF LONG-PERIODICAL PERTURBATIONS BY THE SOLAR RADIATIONS PRESSURE ------------------------------------------------------------------------------------ Ta,days Aa,km Tu,days Au,grad ------------------------------------------------------------------------------------ 355.96 3.5982 332.30 0.46941 ------------------------------------------------------------------------------------ Te,days Ae TW,days AW,grad ------------------------------------------------------------------------------------ 338.79 0.15953*10-4 381.32 0.10831 297.69 0.11809*10-4 ------------------------------------------------------------------------------------ Tn,days An,circ/day ------------------------------------------------------------------------------------ 334.44 0.9162*10-1 379.93 0.3344*10-4 ------------------------------------------------------------------------------------ The more effective observation of the passive geosynchronous satellites will require a further research of orbital elements evolution of different types of the satellites (l1,l2,l3,d1,d2,d3) and calculation of their ephemeris. Part 1.Table 2.(28.6Kb) Results of geosynchronous satellites observations in Kyiv in 1997 Part 2.Table 2a.(41.1Kb) Results of geosynchronous satellites observations in Kyiv in 1998 Part 3.Table 3.(33.2Kb) Results of geosynchronous satellites observations in Uzhgorod in 1997 Part 4.Table 3a.(77.2Kb) Results of geosynchronous satellites observations in Uzhgorod in 1998 References: 1.Sochilina A.S. Lunisolar perturbations and movements of the high satellites. Bjuleten Instituta teor. astronomiji. AN USSR.- 1985. - N 7 (170). - P. 383-395. 2.Grigoriev K.V. The unknown geostationary satellites.// Observations of natural and artificial of the Solar system bodies (Thezis to report.). S.-Petersburg, ITA RAN. - 1996. - P. 51-52. 3.Sochilina A.S., Kiladze R.I., Grigoriev K.V., Vershkov A.I. (1996) Catalog of orbit of geostationary satellites. S.-Petersburg, ITA RAN. 104 p. 4.Vershkov A. I. (1996) Electronic version of the Catalog of orbits of geostationary satellites, Observations of natural and artificial bodies of the Solar System, Book of Abstracts, S.- Petersburg, ITA RAN. (In Russian). 5.Demchyk M.I., Kirichenko A.G., Kizyun L.N., Klimik V.U., Kudak K.A.,Matso G.M., Starodubtseva O.E. (1996) Some results of observation and identification of geosynchronous space objects. /Kosmichna Nauka I Tekhnologija, Dodatok do Zhurnalu (Space Science and Technology, Supplement), Kyiv, 2 , N1, 52 p.(In Ukrainian and Russian). 6.Kizyun L.M., Kirichenko A.G., Rudenko S.P., Demchyk M.I., Klimik V.U., Starodubtseva O.E. (1998) Catalogue GOCKU96 of positions and orbital elements of geosynchronous space objects observed in 1996. // Kosmichna Nauka I Tekhnologija, Dodatok do Zhurnalu (Space Sciense and Technology, Supplement), Kyiv, 4, N 1, 52 p. 7.Sorokin I.A. Some problems of a research of satellite perturbed movement.// Kosmicheskaja geodezija i sovremennaja geodinamika (Space geodesy and modern geodinamics),(Zbornik nauchnikh Trudov. M., IA RAH, 1996. - P. 134-169.(In Russian). 8.Kirichenko A.G., Klimik V.U. Use of a method of least squares for a solution of some problem of an astronomy. - Dep. In GNTBUkr/, 14.07.1993, N 1487-Uk93. - 16 p. Kirichko A.G. and Klimik V.U. (1994) Method of determination of osculating orbital elements of geostationary objects by observations from one station,Nabljudenija Iskustvennikh nebesnykh Tel (Observation of Artificial Celestial Bodies), Moscow, N 88, pp.36-38. (In Russian). 9.Arnold K.(1973) Metodi sputnikovoj geodezii. M., "Nedra", 224 p. (In Russian).

  • Photographic Survey of the Northern Sky (Фотографічний огляд Північного неба - ФОН)

    Astrometric and Photometric Catalogues for researches in stellar kinematics (Астрометричні та фотометричні каталоги для зоряно-кінематичних досліджень)

    Catalogues of Astrometric Positions and Photometric Stellar Magnitudes of SS Bodies (Каталоги астрометричних положень та фотометричних зоряних величин тіл Сонячної системи)

    Catalogues of Positions and Orbital Elements of Geosynchronous Space Objects (Каталоги положень та орбітальних елементів геосинхронних небесних об'єктів)

    L.Pakuliak. Questions, remarks and propositions are welcome.