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).
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
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:
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.