APPLICATION OF SPACE TETHERED SYSTEMS FOR SPACE DEBRIS REMOVAL

Transcription

1 APPICATION OF SPACE TETHERED SYSTEMS FOR SPACE DEBRIS REMOVA Dakov P.A, Malashn A.A., Srnov N.N oonosov Moscow State Unversty (MSU Faculty of Mechancs and Matheatcs, 999, Man Buldng, GSP-, ennskye Gory, Moscow, Russa, wll not be dangerous for actve space ssons or they Abstract Ipleentaton of space tethered systes s an nterestng and portant scentfc and techncal proble. Tethered systes ay be used for a wde range of purposes, for exaple, to execute orbtal aneuvers, to establsh "orbt-al", to clean up space debrs and for any other purposes whle alost no fuel s requred. Ths paper deals wth an applcaton of space tether systes for cleanng of eleents of space debrs or another unwanted waste fro orbts or space statons []. We consder a space tethered syste whch conssts of a bg satellte wth a counterweght ass ( sall satellte attached to t by eans of a flexble tether. The syste oves n the gravtatonal feld along a crcular Earth orbt. A sall load (a contaner wll burn up on enterng the Earth's atosphere. We propose to arrange a counterweght as follows. It conssts of a few loads that are fastened together wth a specal devce. Ths devce s a trpod wth elastc legs. If the collected ass less than a certan value the legs are unfolded (Fg.(a. At a certan nuber of collected contaners at the counterweght when new cong load pacts the upper contaner, under ths pact the legs fold and the lower contaner can be released. It starts ovng. The ntal speed s deterned by the pact that transts fro the ncong load (Fg. (b. The lt of collected ass and the ass rato between the lads and the counterweght s deterned by the elastc ateral propertes of the legs. After releasng the load, the legs return to the unfolded poston (Fg. (c. can ove (transpor along the tether n the drecton fro the bg satellte to the sall one. oads are openng capsules wth space debrs eleents or other objects nsde. When a load reaches the sall satellte t stops and specal devces can easure change of ass. Wth the accuulaton of a certan crtcal ass (few loads at the end of the tether, the collected loads are released and can ove to a lower orbt where they Fgure.The prncple schee of devce of loads collecton and releasng. Proc. 7th European Conference on Space Debrs, Darsta, Gerany, 8 Aprl 07, publshed by the ESA Space Debrs Offce Ed. T. Flohrer & F. Schtz, ( June 07

2 At certan relatonshps between asses of the S s a agrange coordnate of an eleent of the tether. load and counterweght the veloctes of contaners and counterweght can be sall and ther oton s stable and t can be consdered as quazstatc. In ths case the nfluence of dynac effects n the tether s neglgble n copare wth the nfluence of ass forces (Corols force, nertal forces, Earth s gravty. In ths approach we consder the proble of stable loads transportng x s, t,, y s t are dsplaceents n OX andoy drectons respectvely. Х ( s, and Y( s, area Cartesan coordnates of a partcle of a part of the tether (Fg..Pont Х ( s, Х (0, 0 s the pont where the tether leaves the bg satellte. along the tether. Ths proble was set and solved. The nuercal results confred analytcal conclusons and show the strong dependence of stablty of oton of loads along the tether on the relaton between the asses and ntal velocty of a load.. Matheatcal stateent of the proble. et us assue that a bg satellte oves along a crcular orbt of radus R wth constant angular velocty. Then t releases a sall satellte wth ass at ts end. The coordnate syste s connected wth the bg satellte. At the ntal te we assue that the syste s stablzed as t shown n []. et us drect the OX axs towards the Earth and the OY axs along the trajectory of the bg satellte. In ths syste of coordnates external forces nclude the force of gravtatonal attracton to the Earth, the centrfugal force and the Corols force. In ths paper we consder that the tether s not electrcally conductve, so, the forces of electroagnetc nteracton are ssed. The total agrange length of the tethers. Fgure..Choce of the coordnate syste. We got equatons of oton of deforable strngs fro [3]. In case when the tethered syste oves along a crcular orbt these equatons can be wrtten n the followng way [4]: x y ( ( T cos ( 3 ( s x s y x ( ( T sn ( s Here s the densty of the tether, T s tenson s an angle deforng part of tether and OX axs. Index represents parts of the tether before or after the load ( or. We can express the deforaton of the eleent as:

3 And for cosnes and snus we have the followng forulas: ( x y x y ( ( cos s ;sn s. Dependence of tenson on relatve deforaton s consdered as a lnear functon: T E Where E s Young s odulus constant of ateral. At the pont s s, Cartesan coordnates x ( s,, y ( s, of attachent to the load we have such dynac boundary conons for connectng two parts of tether: dx x s,0 0; (0,0 V dy y( s,0 0; (0,0 0 ( 0. Nuercal calculatons The analyss shows that the behavor of the syste s hghly dependent on the ass rato and ntal speed of load. Trajectores of loads at dfferent asses ratos shown n Fgure.Trajectores of sall satellte at dfferent asses ratos shown n Fgure 3. We take = rad/s (angle velocty n the GEO, M =4 kg, l =30000 as paraeters of the syste. And ntal speed of the load s /s. Curve corresponds to the ass rato of loads and sall satelltes :0, curve corresponds to ass rato :5 and curve 3 d x d y T T cos T sn T dy cos dx sn 3 ( s s to : (Fgure. Curve 4 corresponds to the ass rato x :0, curve 5 corresponds to :5 and curve s to 6 : accordngly (Fgure 3. At the pont s of attachent to the sall satellte wth ass M we have such dynac boundary conons: d x d y T T dy cos dx sn 3 ( x Fgure.3. Trajectores of loads at dfferent asses ratos And ntal conons are consdered as follows

4 Fgure.4.Trajectores of sall satellte at dfferent asses ratos As we can see n Fgures and 3, the ost realstc conons for stable and controllable transportaton of loads when the asses rato s :0 and ore (curves and 4. Also n ths case the assuptons about sallness of veloctes and deforatons n tether are perfored. In the other cases we can see strong devatons of the tether fro the local vertcal and large dsplaceents of a sall satellte. In the conon of real space operaton t eans the falure of the sson. Fgure 4 shows the trajectory of a load (contaner at dfferent ntal veloctes. It can be seen that by ncreasng the ntal velocty (curve 7 corresponds ntal speed of 4 /s and curve 8 5 /s there s a large dsplaceent of the load, there are loops of trajectory. In the conon of the real space operaton t also eans the falure of sson. loads speed /s. All subsequent calculatons were perfored wth these paraeters. It should be entoned that the oveent of the tether n the syste s drectly dependent on velocty of transverse waves n tether. It s portant that the velocty of the transverse waves n the tether ust be greater than the speed of oveent of the load along the tether. Otherwse, undesrable overlaps of the tether and the load can occur. Fg. 5 shows that at ass rato :0 and ntal velocty of the load /s the velocty of transverse waves (curve 0 s greater than the velocty of loads (curve 9. A sall ncrease n wave velocty ndcates sall relatve deforatons n the tether. Fgure.6. Veloctes of loads descent (9 and transverse waves(0 3. Conclusons Fgure.5.The trajectory of loads at dfferent ntal veloctes We can conclude that the ost realstc conons for stable are the rato of asses :0 and ntal A certan schee s proposed for transportaton of loads fro one orbt to another wth the help of a space tether syste. The analyss shows strong dependence of transverse dsplaceents of a load on ts ass, ntal speed and the ass of counterweght.. In space such devatons can play a ajor role n the loads oveent and subsequently stablzaton of the whole syste. It s necessary to chose carefully the paraeters of syste (ass of the load, ntal velocty of the load, ass of the "sall" satellte. One soluton of the

5 proble s proposed based on the results of nuercal calculatons. References. [] V.A. Chobotov, Dsposal of geosynchronous satelltes by Earth- orented tethers// 55th Internatonal Astronautcal Congress 004, Vancouver, Canada. [] Dynac control of the space tethered syste / A. A. Malashn, N. N. Srnov, O. Y. Bryukvna, P. A. Dyakov // Journal of Sound and Vbraton. 07. Vol P [3] Kh. A. Rahatuln, Uy. A. Deyanov. Prochnost pr ntensvnyh kratkovreennyh nagruzkah. (Strength n ntense pulse loadng, 96, Moscow, (n Russan [4] N.N.Srnov, Yu.A.Deyanov, A.V. Zvuagun, A.A. Malashn, A.A. uzhn, Dynacal sulaton of tether n orbt deployent, Acta Astronautca 67(00, 3-4, p.p