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DATABASE of JOINT PLATE ARCHIVE (DBGPA V2.0) |
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PROBLEM OF THE PASSIVE OBJECTS OBSERVATIONS54 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) Catalogues of Astrometric Positions and Photometric Stellar Magnitudes of SS Bodies (Каталоги астрометричних положень та фотометричних зоряних величин тіл Сонячної системи) Astrometric and Photometric Catalogues for research in stellar kinematics (Астрометричні та фотометричні каталоги для зоряно-кінематичних досліджень) Catalogues of Positions and Orbital Elements of Geosynchronous Space Objects (Каталоги положень та орбітальних елементів геосинхронних небесних об'єктів) |
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.
