A.G.Kirichenko, L.M.Kizyun, M.I.Demchyk, V.U.Klimik, K.A.Kudak., G.M.Matso. CATALOGUE GOCKU(97-98) OF POSITIONS AND ORBITAL ELEMENTS OF GEOSYNCHRONOUS SPACE OBJECTS OBSERVED IN 1997- 1998. PROBLEM OF THE PASSIVE OBJECTS OBSERVATIONS

   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).

OBSERVATIONS AND SATELLITE IDENTIFICATION

   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


   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.


   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.

PROBLEM OF THE PASSIVE OBJECTS OBSERVATIONS

   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].

   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.

   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).

   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.

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