Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth_Moon.pdf

(https:/creativecommons/licenses/by/4.0/)CThe Author(s)2023.This is an open access article under the CC-BY 4.0 LicenseScience,2023,43(4):724-735.D0I:10.11728/ss2023.04.2022-0065FENG Shuai,WANG Ronglan.Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth/Moon.Chinese Journal of SpaceChin.J.SpaceSci.空间科学学报0254-6124/2023/43(4)-0724-12Meteoroid and Space Debris Risk Assessment forSatellites Orbiting the Earth/MoonFENG ShuaiWANGRonglan(National Space Science Center,Chinese Academy of Sciences,Beijing 100190)(University of Chinese Academy of Sciences,Beijing 100049)(State Key Laboratory of Space Weather,National Space Science Center,Chinese Academy of Sciences,Beijing 100190)(Key Laboratory of Science and Technology on Environmental Space Situation Awareness,Chinese Academy of Sciences,Beijing 100190)Abstract Interplanetary meteoroids and space debris can impact satellites orbiting the Earth or spacecraft trav-eling to the Moon.Targeting China Space Station(CSS),7 satellites selected from the constellation of Beidou Nav-igation Satellite System Phase III(BDS-3),and 3 spacecraft orbiting the Moon,we have adopted in the paper theMeteoroid Engineering Model 3,Divine-Staubach meteoroid environment model,and Jenniskens-McBride mete-oroid steam model to analyze the meteoroid environment with the mass range of 10-10 g.Orbital Debris Engi-neering Model 3.1 space debris model is used to analyze the orbital debris environment faced by these satellites.The flux of space debris with a size larger than 100 m is compared with that of the meteoroids.The results showthat the space debris flux encountered by China Space Station is much higher than that of the meteoroids with sizesin the above range.And quite the opposite,the meteoroids flux impacting the 7 satellites from the BDS-3 is higher.Upon adopting the double-layer Whipple protection measure,the catastrophic collision flux of these satellites en-countering meteoroids is about 10-times of that without protection,or even less,implying that the Whipple pro-tection effectively guarantees the safety of the satellites in orbit.Besides,it is also found that the flux of the high-density meteoroid population encountered by each satellite is greater than that of the low-density population,whereas the impact velocity is lower for each satellite.These results can aid the orbit selection and the protectiondesign for satellites and spacecraft.Key words Meteoroid environment model,Space debris model,Ballistic limit equation,Impact risk assessmentClassified index P2230IntroductionIn the Earths orbit space,the spacecraft is impacted byboth meteoroids and space debris,while in the Moonsorbit space,it is mainly impacted by the meteoroids.Theflux of meteoroids is relatively stable over time,and theamount of space debris increases with the increasing hu-man space activities,especially the deployment of largeconstellations in recent yearsl European Space Agen-cy(ESA)estimates that the number of flying objects in*Supported by the National Natural Science Foundation of China(42074224),Key Research Program of the ChineseAcademy of Sciences(ZDRE-KT-2021-3)and Pandeng Program of National Space Science Center,Chinese Academy ofSciencesReceived November3,2022.Revised June 25,2023E-mail:725FENG Shuai et al.:Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth/Moonouter space can be about 130 million in 20192,and withthe current space debris status and scheduled space mis-sions,fragmentations increase the cross-section of satel-lites on orbit3,and the collision probability will rapidlyrise every 7 years14.Thus,to ensure the sustainable de-velopment of the space environment,meteoroid andspace debris mitigation measures are needed to take,andthe impact risk of meteoroids and space debris alsoneeds to be assessed5.Currently,the meteoroid and space debris modelsor software tools that are widely used include MeteoroidEngineering Model(MEM),Bumper,Orbital Debris En-gineering Model(ORDEM),Meteoroid and Space De-bris Terrestrial Environment Reference(MASTER),andDebris Risk Assessment and Mitigation Analysis(DRA-MA).Cooke et al0 used MEMR2 and ORDEM 3.0models to analyze the flux of meteoroids and space de-bris penetrating 1 mm thick aluminum plates in 6 direc-tions of spacecraft in the Earth orbit space.They foundthat the penetrating flux of meteoroids on the surfacefacing the zenith is greater than that of space debriswhile,the penetrating flux of space debris on the sur-face facing the ram,port and starboard is higher thanthat of meteoroids between 250 km and 2500 km.Moor-head et al.7l used the later models,i.e.MEM 3 and OR-DEM 3.1,addressing a similar problem and found thatthe penetration rate of meteoroids varies by an order of 2in magnitude whereas the space debris penetration ratechanges by an order of 7 in magnitude between the or-bits from 100 km to 100 000 km.Krag et al.8 investigated the impact of micro-mete-oroid and orbital debris onto a solar array in 2017.Hoff-man et al.9 used the Bumper-3 code to assess the fail-ure of Extravehicular Mobility Unit(EMU)for Extrave-hicular Activity(EVA)on International Space Station(ISS)caused by meteoroids and space debrisiol.Further,they employed MEM 3 and ORDEM 3.1 to assess thedamage risk of EMU,and found that for a period of 6.5h EVA,the impact damage risk is rather small.Evans etal.ll provides an overview of the modeling theory andfunctionality of the Manned Spacecraft Crew Survivabil-ity software code,which is used to predict the probabili-ty of several outcomes of micrometeoroid and orbital de-bris penetration for ISS.Actually,according to the mea-sured value,the damage found in post-flight inspectionof the Pressurized Mating Adapter cover and the re-turned airlock shield panels of ISS is consistent with thepredicted results of the Bumper 3 risk assessment codeusing the ORDEM 3.0 and MEMR2 modelsl12.Addi-tionally,Lorenzo Olivieri et al3 prformed the spacedebris assessment for the large constellations in Low-Earth Orbit,and found that reducing the lifetime of indi-vidual satellites in a constellation would cause an over-all increase in the total number of uncontrolled residentobjects.Currently,few researchers have systematically as-sessed meteoroid risk for satellite constellations.There-fore,operational satellites and spacecraft including theChina Space Station(CSS)in Low Earth Orbit(LEO),7satellites in the satellite constellation of Beidou Naviga-tion Satellite System Phase III(BDS-3),and 3 satellitesorbiting the Moon orbit are tested against a variety ofmeteoroid and space debris models in this paper.MEM3,Divine-Staubach meteoroid environment models,andJenniskens-McBride meteoroid stream model are used tocompute the meteoroid flux encountered by each satel-lite.The double-layer Whipple protective structures areconsidered.ORDEM 3.1 model is used to generate thespace debris environment for the 8 satellites orbiting theEarth.Both the fluxes of meteoroids and space debrisand the impact risk assessments are compared and ana-lyzed,which can provide support for spacecraft struc-ture and orbit design as well as on-orbit maintenance.One application is the installation of the ISS protectiveshields based on the calculated risk assessment data tohelp enhance spacecraft protection in the maximum risk14zonest1Meteoroid Environment Model andImpact Risk Analysis MethodIn this section,we briefly discuss the meteoroid environ-ment models that we have adopted to analyze the envi-ronments faced by the 8 satellites in the Earths orbitspace and the 3 satellites in the Moons orbit space.Allthe satellites are developed in China,and the 8 satellitesorbiting the Earth are currently in operation.1.1MeteoroidEnvironmentModelMeteoroids are granular particles in the interplanetaryspace orbiting the Sun,generally including sporadic me-7262023,43(4)Chin.J.SpaceSci.空间科学学报teoroids,meteoroid streams,etc.A complete meteoroidenvironment model includes:(1)mass-density distribu-tion,(2)velocity distribution,and(3)flux-mass/diame-ter distribution.The meteoroid flux F is defined as thenumber of particles with mass greater than m passingthrough any configuration surface per square meter peryear generally(m-.al),which refers to the average ac-cumulation number of sporadic meteoroids and mete-oroid steam.In this paper,MEM 3 and Divine-Staubachmeteoroid environment models are selected.MEM 3 canbe used to analyze the flux and impact velocity varia-tions of meteoroids in all directions of the spacecraft andthe Divine-Staubach model can be used to calculate thecatastrophic collision flux and penetrating flux of mete-oroids.The results are compared to those obtained fromthe Jenniskens-McBride meteoroid stream model.The MEM developed by NASA is based on meteorradar observations,lunar impact craters and zodiacallight observations.Its a parametric model of the spatialdistribution of sporadic meteoroids in the solar systemfrom 0.2 to 2.0 AU.NASA released MEM 3.0 in2019l15,which models meteoroids with mass rangingfrom 10-to 10 g.MEM 3 divides the meteoroid envi-ronment into two populations:the high-density popula-tion consisting of helion and anti-helion meteoroids witha density of about 3.8 gcm-,and the low-density popu-lation with a density of about 0.85 gcm,with the lat-ter composed of toroidal and apex meteoroids 16.Ac-cording to the output results of MEM 3,this paper main-ly discusses 9 directions:ram,wake,port,starboard,zenith,nadir,Earth/Moon,Sun,and anti-Sun.ESAs MASTER assesses the influence of theseparticles on space missions by simulating known debrisand meteoroids in the Earth spacel17.ESA releasedMASTER v8.0.3 in April 2022,which improves the au-tomation significantlyl1s,and embeds both the Divine-Staubach meteoroid environment model(denoted byD-S)and Jenniskens-McBride meteoroid stream model(denoted by J-M)19 Jenniskens and McBride estab-lished the J-M meteoroid stream model based on naked-eye and photographic observations of amateuras-tronomers around the world from 1981 to 199 20.In theD-S model,the average density of meteoroids originat-ing in asteroids is about 3.5 gcm-,and the density p ofmeteoroids originating in other parent bodies is given by2.0,m10-2.Here unit of p is gcm,and m is the mass of the mete-oroid(unit g).NASAs ORDEM can be used to describe the spacedebris environment faced by spacecraft and can give theflux data of space debris at 6 different sizes.NASA re-leased ORDEM 3.1 in December 2019 which uses thelatest and highest-fidelity datasets derived from radarand optical detections and in situ detections21.Themodel uses state-of-the-art analytical techniques to up-date the model population2 ORDEM 3.1 categorizesspace debris into 5 types:intacts,low-density fragments,medium-density fragments and microdebris,high-densi-ty fragments and micro debris,and sodium-potassiumeutectic coolant droplets for Radar Ocean Reconnais-sance Satellite reactors.The densities are about 2.8,1.4,2.8,7.9 and 0.9 gcm-3,respectively.In fact,meteoroids with a masmaller than 10-ghave a very small possibility of causing damage tospacecraft in orbit.According to the limiting conditionsof the mass of the meteoroid in each model,the mete-oroid environment with mass ranging from 10-to 10 gwill be discussed in the risk assessment of the space-craft.And based on the output results of each model,theparticle velocities discussed in this paper are relative tothe spacecraft unless otherwise specified.1.2Ballistic Limit EquationThe expected damage on a satellite surface as the resultof a meteoroid or space debris impact can be assessedthrough empirically derived design equations by provid-ing crater depths or diameters as a function of the parti-cle properties23 The Ballistic Limit Equation(BLE)de-fines the failure limit of the spacecraft structure on thebasis of the properties of the particles,and is used to cal-culate the critical particle diameter(that is,particles withthe velocity u,the impact angle,and the diametergreater than de colliding with the protective layer willpenetrate,24.BLE can be divided into single-layer BLEand multi-layer BLE.In this paper,the satellite protec-tion type is set as double-layer Whipple plate protection,and its BLE uses the Christiansen equation 21:727FENG Shuai et al.:Meteoroid and Space Debris Risk Assessment for Satellites Orbiting the Earth/Moon1819+ts40Un3;250.6VPpU3(cos)32131.071tSUCOSa0.757041118do19+t40UcOSQ1.248VPpcos43 Un7;113.9183S3370Un7.Ppe(ucos a)工2(2)Where d.is the critical particle diameter in cm;the sub-scripts p,s,and b denote the parameters of the particle,the first protective layer,and the second rear wall(bulk-head),respectively;t is the thickness of the plate in cm;p is the density in gcm;o is the yield strength of therear wall in MPa;is impact angle,in degree;is theimpact velocity in kms-and Un=vcosa;S is the dis-tance between the first protective layer and bulkhead,incm.Some of the above models use size as one of the pa-rameters,while others use mass.In order to facilitate thecomparative analysis,this paper assumes that the shapeof the meteoroid is spherical,so the mathematical ex-pression of the relationship between the mass and diam-eter of the meteoroi is s fllows 2a.pd3m=(3)6Therefore,the critical particle mass me can be calculatedaccording to Eq.(2)and(3).Similar to de,m means thata particle with mass greater than or equal to me will pen-etrate when impacting the protective layer with the ve-locity v and the impact angle.1.3ImpactRiskAnalysisMethodParticles with high velocities,when colliding withspacecraft produce large impact energy.For instance,theenergy of a particle with a mass of 1 g,whose speed is10 kms,is equal to the load energy of a mass of 1 ton,falling from a height of 5 m for Css 27.When assess-ing the risk of spacecraft caused by meteoroids or spacedebris,the Energy-to-Mass Ratio(EMR,the symbol E isemployed as a representation for the acronym EMRhere)can be used to measure whether or not an impact isa catastrophic collision event.If the value of EMR isgreater than 40 000 Jkg,it is considered that the im-pact event is a catastrophic collision.The mathematicalexpression of EMR is given byes.E=mpu2(4)2msHere mp is the mass of the particle;v is the velocity ofthe particle impacting the spacecraft;ms is the mass ofthe spacecraft;the unit of EMR is J-kgl.It is assumed that the probability of the spacecraftexperiencing particle impact follows Poisson distribu-tion 29,i.e.the probability P of the spacecraft encoun-tering n times of collision is given byNnN(5)Pn！andN=FAT.(6)Here N is the average number of collisions betweenspacecraft and particles;F is the flux of spacecraft en-countering particle impacts;A is the impact cross-sec-tional area of the spacecraft;T is the operating time ofthe spacecraft.For the convenience of comparison,thispaper assumes that the impact cross-sectional area A ofthe spacecraft with the meteoroids or space debris is 1m,and the time T of the spacecraft is 1 year.Thus,the probabil