The orbital evolution of a passive high-orbit fragment with large surface area
A.A. Bazyey, N.V. Bazyey, V.I. Kashuba, S.G. Kashuba, V.V. Kouprianov, I.E. Molotov, Z.N. Khutorovsky, L.G Tsybizova
aa r X i v : . [ a s t r o - ph . E P ] A p r Astron. Nachr. / AN , No. , 0 – 3 (2014) /
DOI please set DOI!
The orbital evolution of a passive high-orbit fragment with large surfacearea.
A.A. Bazyey ,⋆ , N.V. Bazyey , V.I. Kashuba , S.G. Kashuba , V.V. Kouprianov , I.E. Molotov , Z.N.Khutorovsky , and L.G. Tsybizova Astronomical Observatory of I.I. Mechnikov Odessa National University, Marazlievska St. 1v, Odessa 65014, Ukraine The Main Astronomical Observatory of the Russian Academy of Sciences, Pulkovo, Pulkovo highway 65, Saint-Petersburg 196140, Russia Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Miusska square 4, Moscow 125047,Russia JSC Interstate joint-stock corporation Vympel, the 4th Vosmoye Marta St. 3, Moscow 125167, RussiaThe dates of receipt and acceptance should be inserted later
Key words methods: numerical – celestial mechanicsThe observation data for artificial celestial body 43096, which had been obtained during 2006-2012 within the frameworkof international project The Scientific Network of Optical Instruments for Astrometric and Photometric Observations- International Scientific Optical Network (ISON), were processed. The Keplerian elements and state vector as of 24November 2006 01:55:50.76 UTC were determined.The numerical integration of the motion equations was performed accounting for the perturbations due to the polar flat-tening of the Earth, Moon and Sun, as well as the solar radiation pressure.Based on the numerical model of a motion in the near-Earth space that accounts for only the most powerful perturbations,a new method for de-orbiting artificial celestial bodies from high altitudes is suggested.For the first time such a considerable amount of data over long time intervals was gathered for the objects with higharea-to-mass ratio that enabled to determine their specific characteristics. c (cid:13) Today there are tens of thousands of artificial celestial bod-ies in the near-Earth space. Most of them belong to thespace debris as such worn-out artificial satellites or theirfragments. Such celestial bodies can remain in high orbitsessentially indefinitely. Their motion is subjected to the per-turbations by the Moon and Sun, as well as by the asymme-try of the Earth’s gravitational field. The high-orbit objectsare monitored using optical telescopes. The internationalproject The Scientific Network of Optical Instruments forAstrometric and Photometric Observations - InternationalScientific Optical Network (ISON, Molotov et al. 2009)contributes the most.This paper describes the processing of the positional ob-servation data of one of passive high-orbit celestial bodies.Based on the obtained results, a new method for de-orbitingof worn-out artificial satellites from the geostationary orbitsin the near-Earth space to lower altitudes is proposed.
We selected fragment 43096, which was detected with theESA Space Debris 1-m Telescope located on the island ⋆ Corresponding author: e-mail: o.bazyey @ onu.edu.ua of Tenerife, Spain, by Thomas Schildknecht’s team dur-ing their cooperation with the ISON project (Volvach et al.2006). The fragment’s reference corresponds to the num-ber in the Keldysh Institute of Applied Mathematics of theRussian Academy of Sciences database. This fragment isinteresting by its high area-to-mass ratio (HAMR). Whendescribing changes in its orbiting, it is necessary to accountfor significant perturbations due to the radiation pressure inaddition to those by gravity. Perturbations due to the solarradiation pressure tend to be periodic.We processed observation data for the indicated fragment,which had been obtained by the ISON network during 2006-2012 within the framework of the Pulkovo Cooperation ofOptical Observers (PulCOO) programme in the followingobservation stations: Tenerife (Zeiss-1000), Zimmerwald(ZIMLAT), Crimean Astronomical Observatory (AT-64 andRST-220), Nauchniy village (Zeiss-600), Mondy village(infrared reflector ART-33), Mount Maydanak (Zeiss-600),Mayaki village (the Ritchey-Chretien telescope RC-600),Gissar (reflector ART-8), Terskol Peak (Zeiss-2000), Abas-tumani (AC-32), Andrushevka (S-600), Ussuriysk (ORI-50), Artem (ORI-25). c (cid:13) stron. Nachr. / AN (2014) 1 A total of 226 series of observations conducted from 18November 2006 to 16 June 2012 were processed. Eachseries averaged to 20-30 measurements of the topocentricright ascensions, declinations and UTC time references.The Keplerian elements were determined for each seriesby Laplace’s method with the subsequent refining by the6-parameter iteration method. The accuracy of the orbitalelements was estimated using the residual errors represent-ing differences of the observed positions of the fragmentfrom the predicted ones. The computation procedure isspecified in Bazyey et al. (2005) and Escobal (1970). Theleast errors in orbital element determination were obtainedfor the following series of observations:24 November 2006 01:09:56.87 (Tenerife) p = (6 . ± . equatorial radius e = (0 . ± . ω = (261 . ± . ◦ Ω = (321 . ± . ◦ i = (9 . ± . ◦ M = (242 . ± . ◦
08 February 2008 23:35:46.77 (Tenerife) p = (6 . ± . equatorial radius e = (0 . ± . ω = (295 . ± . ◦ Ω = (319 . ± . ◦ i = (8 . ± . ◦ M = (240 . ± . ◦ The state vector was determined as of 24 November2006 01:55:50.76 UTC:x = –2.28181 equatorial radiusy = 6.21066 equatorial radiusz = 0.54755 equatorial radiusVx = –0.0259860 equatorial radius per minuteVy= –0.0111238 equatorial radius per minuteVz = –0.00394734 equatorial radius per minuteThe indicated values were assumed to be the initial condi-tions for the fragment’s orbit integration.The area-to-mass ratio was assumed equal to Sm = 2 . sq.m/kg (Fr¨uh & Schildknecht, 2012). The acceleration dueto the direct solar radiation was estimated as follows: a = C Sm ( r r ) r − r S r (1)with C = P (1 + A ) , P = 0 . N/sq.m thesolar radiation pressure at the Earth’s orbit, A the electro-magnetic radiation reflection coefficient ( < A < ), r the average radius of the Earth’s orbit, r , r S - the fragment’sand the Sun’s positions in the Earth-centred coordinate sys-tem.As fragment 43096 is referred as a high-orbit artificialEarth’s satellites, the perturbations of its motion due tothe Moon and Sun are comparable to those by the Earth’s flattening (Borodovitsyna & Avdyushev, 2007). In turn,the perturbations due to the Earth’s flattening are consid-erably more powerful than any perturbations by all theother geopotential asymmetries (Borodovitsyna & Avdyu-shev, 2007). Therefore, when integrating the motion equa-tions, we accounted for the perturbations by the secondzonal harmonic of the Earth’s gravitational field, the Moonand Sun, as well as the solar radiation pressure. The Moon’sand Sun’s positions were adopted from the numerical the-ory DE405 . The integration was performed by the Runge-Kutta methods of the 10th order (Bazyey & Kara, 2005)during the period from 24 November 2006 to 31 July 2012.The results are presented in Figures 1 a-d. The orbital ele-ment observation values are marked as dots, the solid line isresulted from the integration.During the whole period the orbit’s semi-major axis hasnot been subjected to the secular perturbations. The eccen-tricity and argument of perigee are exposed to the periodicperturbations with duration of some 370 days. The eccen-tricity varies from 0.017 to 0.071. The apse line oscillateswith amplitude of about 80 ◦ and slowly rotates with the an-gular velocity of 0.020 ◦ /day. The longitude of the ascend-ing node and inclination of the orbit decrease at the rateof 0.0028 ◦ /day and 0.0016 ◦ /day, respectively, within thewhole observation interval.Therefore, the 43096 fragment orbit periodically changesthe shape and position of the apse line, leaving its size un-altered. Besides, the apse line, longitude of the ascendingnode and inclination change monotonically.The numerical integration shows that the periodic perturba-tions in the eccentricity and argument of perigee are due tothe solar radiation pressure: assuming P = 0 , those pertur-bations disappear. Those orbital elements computed by theobservations with the least absolute errors of ∆ e < . are presented in Figure 2. The dashed line corresponds tothe values computed with allowance for all above-indicatedperturbations. The solid line represents the same orbital el-ements computed not accounting for the radiation pressure.That fact can be used to purposely change orbits of the geo-stationary objects and their de-orbiting to lower altitudes asdown as the Earth’s atmosphere.Let us explain that by exemplifying simulation of the 43096fragment motion. Using the eccentricity variation curve, itis easy to detect that the eccentricity was increasing from05 May 2007 to 13 November 2007, from 08 May 2008to 19 November 2008, from 15 May 2009 to 26 November2009, from 22 May 2010 to 03 December 2010, and from 29May 2011 to 04 December 2011. During those periods theperigee distance decreases due to the radiation pressure withthe semi-major axis remaining altered. The eccentricity wasdecreasing from 13 November 2007 to 08 May 2008, from19 November 2008 to 15 May 2009, from 26 November2009 to 22 May 2010 and from 03 December 2010 to 29 ssd.jpl.nasa.gov c (cid:13) Bazyey et al.: The orbital evolution of a passive high-orbit fragment S e m i m a j o r ax i s ( E a r t h r a d i u s ) Date E cce n t r i c i t y Date A r g u m e n t o f p er i g ee ( d e g ree ) Date A s ce nd i n g n o d e ( d e g ree ) Date I n c li n a t i o n ( d e g ree ) Date
Fig. 1
The orbital elements of fragment 43096 in 2006-2012. The observed values are marked as dots, and the solidline represents the computational simulation solution.
Date E cce n t r i c i t y A r g u m e n t o f p er i g ee ( d e g ree ) Date
Fig. 2
A selection from the orbital elements of fragment43096. The values with the least absolute error in the eccen-tricity determination (less than 0.002) are marked as dots.The orbital element changes, which were obtained by thenumerical integration of the motion equations, are repre-sented as the solid line for the case of not allowing for thesolar radiation pressure and as the dashed line when the ra-diation pressure is taken into account.May 2011. If the solar radiation pressure force is stronger,while the eccentricity increases comparing to those time in-tervals when it decreases, then it is possible to determinegeneral secular increase of the orbital eccentricity. The sameeffect can be reached, for instance, by increasing the area-tomass ratio of the fragment while the eccentricity increases.We conducted the numerical experiment on the simulationof the 43096 fragment orbit with the same initial condi-tions as of 24 November 2006 01:55:50.76 UTC, but withalternating radiation pressure. It was assumed that P =0 . N/sq.m for the increasing eccentricity and P = 0 for the decreasing eccentricity. The result is shownin Figure 3. The eccentricity increased from 0.02 as of 08May 2007 to 0.30 as of 31 July 2012. And the semi-majoraxis remained unaltered at that. At the end of the integra-tion interval the perigee distance decreased down to 29000km (the Earth’s equatorial radius 4.54). Such a considerablechange in the fragment’s orbit was successfully attained justby changing the solar radiation pressure force two times peryear.Colligating the result obtained, it should be noted thatsuch method of changing the celestial body orbit in thenear-Earth space can be applied to solve problems of thenear-space ecology. Provided the capabilities to control the c (cid:13) stron. Nachr. / AN (2014) 3 Date E cce n t r i c i t y E a r t h r a d i u s Date
Fig. 3
The change in the orbital elements of the celestialbody subjected to the alternating radiation pressure.changes in the area-to-mass ratios of worn-out satellites, itis possible to solve the problem of cleaning up the near-Earth space from the space debris of artificial origin usingthe solar radiation pressure exclusively.Thus, we processed the positional observation datafor the artificial celestial body 43096, which had beenobtained during 2006-2012 by the network of observationstations participated the ISON project. The Keplerianelements were determined for each series of observations,and the errors in those determinations were estimated. Thestate vector for fragment 43096 was determined as of 24November 2006 01:55:50.76 UTC, and that value served asinitial condition for the integration of differential motionequations in Cartesian coordinate system. The numericalintegration was performed accounting for the perturbationsdue to the polar flattening of the Earth, Moon and Sun, aswell as the solar radiation pressure. The received numericalsolution is in good agreement with the observation data andrepresents periodic and secular changes of the orbit in thenear-Earth space.Based on the numerical model of motion in the near-Earthspace that accounts for only the most powerful pertur-bations, a new method for de-orbiting artificial celestialbodies from high altitudes is suggested.
For the first time such a considerable amount of dataover long time intervals was gathered for the objects withhigh area-to-mass ratios that enabled us to determine and estimate their observation and orbital characteristics.Altogether the Keldysh Institute of Applied Mathematicsof the Russian Academy of Sciences database containsdata for 247 geostationary and geostationary transitingobjects with high area-to-mass ratios, as well as for 23objects in the high-elliptic orbits (only objects with theresults of observation for more than 2 nights were takeninto account). The number of detected relatively brightobjects (which are brighter than magnitude 15.5) has beencontinuously increasing, and that is a rather surprisingfact with regard to the continuous series of geostationaryobservations, which have been conducted by the ISON net-work for several years already. It is about 5-10 new objectsdiscovered every month. Many of those new objects crossthe GEO protected zone thereby increasing the predictedhazard for the working satellites. It is very important todetect as many space debris as possible to determine thesources of its origin. It is anticipated that there are at leastseveral hundreds of space debris fragments brighter thanmagnitude 18 in the geostationary ring. Meanwhile, thenumber of weaker (and correspondingly smaller) objectscan not be correctly estimated.Described here method of the celestial body orbit changingin the near-Earth space can be useful in solution of thenear-space ecology problem, namely in the cleaning up thenear-Earth space from the artificial space debris using thesolar radiation pressure only.
Acknowledgements.
The authors express their gratitude to S.M.Andrievsky, the Director of the Astronomical Observatory ofI.I. Mechnikov Odessa National University, for his valuableassistance in performing this study.
References
Bazyey, A. A., Kara, I. V.: 2005, Odessa Astron. Publ. 18, 14Bazyey, A. A., Sibiryakova, E. S., Shulga, A.V.: 2005, Odessa As-tron. Publ. 18, 8Borodovitsyna, T.V., Avdyushev, V.A.: 2007, The Theory of theEarth’s Artificial Satellites’ Motion. Analytic and NumericalMethods, Tomsk University Publishing HouseEscobal, P.: 1970, Methods of Orbit Determination. Moscow: MirFr¨uh, C., Schildknecht, T.: 2011, Mon. Not. R. Astron. Soc., 419,3521Molotov, I.E., Agapov, V.M., Kouprianov, V.V. et al.: 2009, TheProceedings of Central Astronomical Observatory of the Rus-sian Academy of Sciences at Pulkovo, No. 219, Edition 1, 233Volvach, A.E., Roumyantsev, V.V., Molotov I.E. et al.: 2006, SpaceScience and Technology 12, No. 5/6, 50 c (cid:13)(cid:13)