The long-term evolution of geostationary satellite fragments after an explosion

Transcription

1 The long-ter evolution of geostationar satellite fragents after an explosion E.D. Kuznetsov Astronoical Observator of the Urals State Universit Ekaterinburg Russia The odel of the sphericall setric explosion of the geostationar object is constructed. The evolution of the fragent's cloud is siulated b the Nuerical Model of Artificial Satellite Motion. The densitand axiu and iniu initial velocities are deterined for the fragents cloud. The collision velocities of the fragents with the satellites and the collision energies are calculated. The dnaical evolution of geostationar satellite fragents after low energ explosion is investigated. The nuerical odelling of the fragents otion on tie-scales 1 das and 1 ears are ade. It is the drawn conclusion on the considerable role of the libration resonance due to the ellipticit of the Earth's equator on the fragents cloud evolution. The expansion of the cloud along to the explosion object orbit and closing one to the torus is the result of the fragents oving in circular odes onl. The libration resonance leads to the fact that the inner structure of the cloud will sta heterogeneous on a long-ter interval. Peculiarities of evolution of the node longitudes of the fragents orbits evolve into regions where the particle flow is axiu. These regions are the best to search for the explosion fragents and on the other hand are regions of highest eergenc for active geostationar objects. Introdution The ballistic life-tiea of geostationar satellites are estiated as illions of ears. Fast increases in the quantit of satellites in geostationar orbit lead to increases of space debris particles in the geostationar region. The nuber of geostationar objects increases not onl due to the launch of new satellites but also the destruction of objects in geostationar orbit. In this case the nuber of sall sized fragents is increasing considerabl. It represents serious daage for satellites. However ost large fragents are observed onl singl. One source of an-caused particles on geostationar orbit is the explosion of satellites. Several rando explosions of satellites and upper stages in the geostationar ring are detected [4 6 7]. Investigation of the dnaical evolution of the fragent cloud can help to estiate the danger of the fragents to the geostationar satellites. The odelling results are where the densit of flow is high whereever the region of space is ore dangerous and where it is necessar seek the explosion fragents. Short-period evolution gives the description of the debris torus foration along the exploding object orbit. Long-period evolution gives the prediction of distant consequences of the explosion. In the present work we investigate the kineatical and dnaical paraeters of the fragent cloud due to a sall power explosion. Dnaical evolution of the fragent cloud after an explosion of a geostationar satellite with asses of 1 and kg is considered. Model of explosion The odel of the sphericall setric explosion of the geostationar object is based on the results of the works [ 3 5]. Model input paraeters are the satellite orbital eleents (the sei-ajor axis a the eccentricit e the inclination i the longitude of ascending node Ω the arguent of pericentre g and the ean anoal M ) the satellite ass sp the relation of the satellite iddle section area A to the its ass γ = A / and the axiu and iniu asses in and ax of the fragents. sp

2 Model output paraeters are the nuber of fragents N the asses of the fragents n the area-to-ass relations γ = A / the velocit vector v = v v v ) and the orbital n n n n ( xn n zn eleents a n e n i n Ω n g n M n. The odelling of explosion is in following. Geocentric coordinates x z and velocities w x w w z of a satellite at the explosion oent are calculated fro the orbital eleents of a satellite. Nuber N() of fragents with asses less than N ( sp ) = 4. e 5756 sp e 1936g < 1936g. Here in is the iniu ass of a fragent asses are in gras. The distribution function of the fragent asses 1 η F( ) = 1 s η ax s 1 η = s =. 83. in Calculation of fragent asses for the liit ass is ade a few ties. On the first step =1 g on the next =1 g and so on while the total ass of fragents is equal to sp. Diaeters d of fragents are deterined fro d = ( ) 4 ( ) 1/.6 1/ 3 > c1ρ = c 1 ρ=699 kg/ 3 c 1 =.1664 c =.6. Here asses are in kg diaeters are in eters. Middle area of fragents are found fro the assuption of its spherical shape A = πd 4 A γ =. A ean value of the velocit increent Δ v (k/s)is calculated fro log Δv =.676 log d.84 log d The velocit increent Δ v is founded fro triangular distribution 5 (5x x +.5).1 x 1 = 7 Δv G ( x) x =. 5 ( 15x + 39x 19.95) 1 < x 1.3 Δv 7

3 are Velocit vectors are isotropicall distributed. Distribution functions for angles Φ and Τ F ( Φ) = Φ π 1 cost F( T) =. Coponents of relative velocit Δv x Δv Δv z are Δv = Δv cost Δv = Δv cosφsin T Δv = Δvsin Φsin T. z x Coponents of geocentric velocit are w x = w + Δv w = w + Δv wz = w + Δv x x z z. Orbital eleents of fragents are calculated fro the initial position x z and velocit w w w. x z The kineatical and dnaical paraeters of the fragent cloud Using the odel of the object explosion on a geostationar orbit the kineatical and dnaical paraeters of the fragent cloud are investigated. The initial orbital eleents of the explosive object are chosen as follows: sei-ajor axis is equal to 4 k eccentricit is equal to inclinations are equal to 1. Input paraeters of the odel are used as following: the initial ass of object is equal to 1 and kg iniu ass of fragents is equal to 1 g. Two tpes of explosions are considered. The first tpe explosion produces one fragent of a big ass..3 sp and a few nuber of sall ass fragents (fro 9 to 6). The second tpe explosion produces greater fragents (fro 3 to 31) and the ass of the biggest fragents are less than. sp. Table 1 gives soe paraeters of fragents for sall power explosions. Table 1. Paraeters of fragents for two tpes of sall power explosions. Description First tpe explosion Second tpe explosion Miniu ass of fragents g Diaeters of fragents Relation of iddle area to ass /kg Initial velocit /s To siulate the evolution of the fragent's cloud the nuerical odel of artificial satellite otion [1] was used. Evolution of orbital eleents of the fragents and 48 geostationar satellites (a=4165 k e=.1 i= 15 Ω= 5 g= 7 M = sp = kg) was ade on a tie interval of 1 das.

4 The results of odelling show that the ipact velocities essentiall depend on the utual inclination I of orbits of the fragent and the geostationar satellite. Table gives axiu ipact velocities V ax and correspond to the asses of ipactors li depending on the angle of utual orbit inclination I for the geostationar satellite of ass 1 5 kg. In this case the axiu increent of sei-ajor axis Δ a of the geostationar satellite is equal to 4 k. The ass li corresponds to the axiu ass of the ipactor for non catastrophical ipact. Ipact is catastrophical if the energ densit exceeds 45 kj/kg [5]. Catastrophical ipacts destro the satellite. Table. Maxiu ipact velocities V ax that correspond to asses of ipactors li depending on theangle of utual orbit inclination I for geostationar satellite of ass 1 5 kg. I V ax /s li kg Ipacts of geostationar object with the fragents are generated b low power explosion and do not destro objects generall. First tpe explosions can generate a few nuber of fragents that ipact catastrophicall. Short-periodic evolution of the fragent cloud To investigate short-periodic evolution of space debris particles after an explosion of the geostationar object the odelling of the fragents otion is taken on 1 das interval. The Nuerical Model of a Artificial Satellite Motion [1] is used. Main perturbations due to the Earth's gravit odel EGM-96 (up to order and degree) Moon and the Sun attraction tides and solar radiation pressure are taken into account. 84 explosions are considered. Initial values of the orbital eleents span the geostationar region copletel: sei-ajor axis is equal to and 41 k eccentricit is equal to and.1 inclination is equal to 1 and. Analsis of the results shows that the fragents cloud resulting fro sall power explosions exceed along the sei-ajor axis the libration region (fro 413 to 4 k) and close-fitting regions of rotation otion. It leads to a significantl different evolution of the subsatellite points longitudes of fragents even on short-tie intervals. The fragents ove in the regions with different odes of otion: circulation on the east or westand libration near one or two stable libration points. The longitudes drift relative to the parent object (exploded satellite) essentiall depends on the sei-ajor axis of the fragent orbit. On 1 das intervals the range of subsatellite point longitude is changed fro 5 near stable libration point to 1 6 for particles oving in circulation ode. The fragent cloud is propagated along the orbit due to the particles oving in circular ode high and low of the libration otion region. Moving near one stable libration point particles influence the foration of the inner regions of the debris torus in this libration region onl. Long-periodic evolution of the fragent cloud The long-periodic evolution of the fragent cloud after an explosion of the geostaionar object was investigated nuericall. The otion of the fragents on the 11 ears tie interval

5 was studied for 1 sall power explosions. Initial values of the orbital eleents correspond to the geosnchronous satellite: sei-ajor axis is equal to 4165 k eccentricit is equal to inclination is equal to and 1. The satellite was situated near the stable libration point 55. Analsis of the odelling results shows that ore than 95% of the particles arising after an explosion of the libration satellite are oved in a circular ode. If at the oent of explosion the satellite is situated near the stable libration point then on the phase plane ''subsatellite point longitude sei-ajor axis'' near the other stable libration point the fragents will be absent. ''Slow diffusion'' of a sall nuber of the fragents to the region near the other stable libration point is possible for fragents which oved in libration ode near two stable points due to the luni-solar and light pressure perturbations (in one particle for 4 explosions fro 11 ones). In the phsical space this effect is evinced ore weakl due to nonzero inclinations and eccentricities of orbits of particles oving in the neighboring regions of circular otion. Libration resonance leads to the debris ring staing heterogeneous on long-ter interval. Fig. 1 gives the fragent cloud structure. Positions of all particles of the cloud are shown at the initial oent (vertical line on longitude 5 ) 1 da after an explosion (slanting line for longitude range fro 3 to 315 ) and further with 4 das step on a tie interval of 4 das. Size of the fragent cloud with respect to sei-ajor axis is larger than the size of the libration otion region. 45 a k Fig. 1. The fragent cloud structure. Fig. shows the fragent cloud structure near the region of the libration resonance. In the present explosion odel several fragents oving near the stable libration point 55 and one particle librating with respect to the two stable libration points are generated. In the libration region near the stable point 75 fragents of the explosion are absent. Tpical trajectories of the fragent cloud particles are given on fig. 3: circulation to the east or west libration near the stable point 55 and libration with respect to the two stable libration points. λ

6 43 4 a k Fig.. The fragent cloud structure near the region of the libration resonance. λ a k λ Fig. 3. Tpical trajectories of the fragent cloud particles.

7 Dnaical evolution of the fragents cloud leads to the foration of two regions with sall cross-sections. These regions correspond to situations of the fragent orbits nodes with respect to the orbital plane of the exploded satellite. Position and shape of these regions are changed due to perturbations with tie. Iediatel after an explosion the nodes of the particles orbits are collected at the explosion point and along a line crossing the antipode line (fig. 4a). In the first tie nodes of the fragents orbits are situated in a sall neighborhood. After a short tie period (less than.5 ears) nodes of orbits are distributed along the orbit of the parent bod (fig. 4b). Further evolution leads to closings in the node lines of the fragent orbits and decreased distances between the orbital nodes (fig. 4c d). The ean distance between nodes is a easure of nodes closeness. Initiall the ean distance between the nodes aounted to approxiatel 6 k then increased up to 3 k and 11 ears after an explosion decreased to k. Several ears after an explosion the neighborhood of the nodes of the fragents orbits densit of the particle flow is a axia.???the fragents of the explosion necessar to seek in neighborhood of nodes of the fragents orbits.??? k k x k а) -4-4 x k б) k -1 k x k в) x k г) Fig. 4. Evolution of nodes. Conclusion Modelling of kineatical and dnaical properties of the fragent's cloud arising fro an explosion of an object shows that the nuber of fragents andtheir velocit are changed in

8 wide intervals. In spite of the fact that the initial increents of velocit are less than several tens of /s for low energ explosions ipact velocit on orbits with big utual inclinations can exceed 1 k/s. Ipacts with assive fragents can be catastrophic soeties. Resonance due to ellipticit of Earth's equator influences significantl the dnaical evolution of the fragents cloud. The propagation along orbit and close in torusis the result of the otion of particles in circular ode. Libration resonance leads to the inner structure of the fragents cloud staing heterogeneous on long-ter interval. Features of the orbital nodes evolution eliinates regions where flow of particles is axia. These regions are the ost convenient to search for fragents of explosions. On the other hand these are regions of higher danger for geostationar satellites. Acknowledgeents This work was supported b the Ministr of Industr Science and Technolog of Russian Federation (Contract ). References 1. Bordovitsna T.V. Sharkovskij N.A. Yandul'skij G.I. et al. Nuerical odel of artificial satellite otion // Observations of Artificial Celestial Bodies P.1. P Bordovitsna T.V. Druzhinina I.V. Siulation of dnaic paraeters of fragent streas originated after desintegration of space objects in near-earth orbit // Near-Earth Astrono (Space Debris). Moscow: Kososinfor P Bordovitsna T.V. Druzhinina I.V. The progra coplex for the deterination dnaic paraeters of breakup aking orbital particle strea // Astrono and Geodes. Tosk: Tosk State Universit P Kasienko T.V. Mikisha A.M. Rkhlova L.V. Sirnov M.A. Explosions of the geostationer orbits // Collisions in the Surrounding Space (Space Debris). Moscow: Kososinfor P Pardini C. Anselo L. Rossi A. et al. AAS/AIAA Space Flight Mechanics Meeting Montere CA USA 9 11 Feb // 6. Sirnov M.A. Mikisha A.M. Kasienko T.V. Rkhlova L.V. Space debris and explosion of near Earth objects // Near-Earth Astrono of the XXI Centur. Moscow: GEOS 1. P Vershkov A.N. Grigoriev K.V. Kiladze R.I. Sochilina A.S. Model of a geostationarobjects explosion and coparison with observations // Near-Earth Astrono of the XXI Centur. Moscow: GEOS 1. P