Research On Several Issues Of Modelling Technology Of Space Debris Environment Engineering Model

Space debris environment is one of the major threats against on-orbit spacecrafts and human space activities.As one of the significant foundation works for space safety system,space debris environment engineering model is able to provide the description of space debris environment spatial-temporal distribution by probability and statistics methods.There are various foreign engineering models,serving the important space activities such as the ISS.The analysis of error sources and corresponding effects of engineering models can provide not only theoretical basis for model accuracy verification,but also technical route reference for model update and upgrade.Due to the lack of detection data of micro-scale space debris environment,cross-comparison is one of the accuracy validation methods.The analysis of error sources and corresponding effects provides important theoretical basis for accuracy verification during the cross-comparison process.On the other hand,the timeliness of space debris environment is strong,making it necessary to update and upgrade on time.Based on the modelling process,the study of analyzing error sources and their impacts,deepening the research of modelling theory,updating and improving engineering model on time is significant and urgent for improving the ability against space debris threat in order to guarantee on-orbit safety.The core content of the research of engineering models is: based on accessible modelling data,simulating the evolution of space debris environment,and evaluating its spatial-temporal distribution.Some of the urgent problems for the field of space debris environment modelling technology include: how to improve accuracy while maintaining high efficiency,how to build reasonable spatial density algorithm considering the spatial-temporal distribution characters of space debris environment,how to lower the influence of subjective factors during flux calculation process,and so on.The following research about modelling technology of the engineering model is carried out around the above problems.The main research is as follows:The error sources and corresponding effects of engineering models are analyzed.The analysis suggests that: 1)the balance between accuracy and efficiency of space debris orbital perturbation algorithm needs to be further improved;2)the temporal and spatial description of space debris varies in different orbital regions,the universality of spatial density algorithm to the whole debris environment and the pertinence to special orbital region need to be further analyzed;3)for spacecraft flux calculation,the outcome has direct connection with cube division process,the rationality needs to be further analyzed.The variable step-size orbital perturbation algorithm based on semi-major axis control is proposed.Space debris environment evolution simulation has multiple characters: the number of objects to be evaluated is significant,the time span is large,and the orbital region is wide.One of the urgent problems to be solved is how to improve the accuracy of the process while maintaining its efficiency.The orbital perturbation algorithm in current environment models is generally based on fixed time step-size.The accuracy is directly connected to the maximum value of semi-major axis variation during each interval step.Hence,based on the control of maximum variation range of semi-major axis in each step,the variable step-size orbital perturbation algorithm is proposed,which is able to improve the accuracy while the efficiency is guaranteed.Combined with space debris source models and event database,space debris environment evolution data from 1958 to 2050 is established,providing fundamental data base for engineering model.The spatial density algorithm based on the second zonal harmonic of non-spherical Earth gravity(J2)is proposed.The research in this paper suggests that for all the assumptions adopted by current spatial density algorithm,the error caused by “random” Right Ascension of Ascending Node(RAAN)is the most significant one,and it increases with the increase of orbital altitude.ORDEM 3.0 adopted the “fixed” RAAN assumption for GEO region,which successfully improved the accuracy in this area.However,appliance of “random” or “fixed” RAAN,the two extreme assumptions,is limited by orbital region.Hence,the “random” or “fixed” RAAN assumptions are replaced by RAAN “only affected by J2 factor”.Based on cataloged data,rationality of the new assumption is tested.Analysis suggests that compared with “random” or “fixed” RAAN assumptions,the assumption of RAAN “only effected by J2 factor” is more correspond to the real case.The spatial density algorithm based on Earth Centered Earth Fixed coordinate system(ECEF)is proposed.Synchronous orbital angular velocity is a unique feature of space objects in GEO region,which is embodied in relatively stable geographic longitude distribution of space objects in this region.Engineering model is more focus on space debris time-averaged distribution,instead of accurate orbital position of any particular moment.Due to the continuous rotation of ECEF against J2000 coordinate system,the synchronous orbital angular velocity and stable geographic longitude distribution of GEO objects cannot be deduced from spatial density under J2000.In order to improve the pertinence,spatial density algorithm based on ECEF is proposed.Spatial density output shows that cataloged objects are concentrated around the geopotential wells,which is in accordance with related researches.The target-centered spacecraft flux calculation method is proposed.During the flux calculation process in current engineering models,spatial cubes are generally pre-divided by equidistant dispersion.Orbital information of the target is not considered during this process,which is a typical un-supervised discretization method.This process is deeply influenced by subjective factors.Hence,by supervised discretization method,the target orbit is divided into a series of orbital positions based on target orbital elements.Spatial cubes are then defined centered around the orbital positions,and flux is presented accordingly.The target-centered spacecraft flux calculation method is not affected by the setup of orbital boundaries,therefore lowers the effect caused by subjective factors and improves the objectivity of the algorithm.Based on the above researches,Space Debris Environment Engineering Model(SDEEM)is built and the software SDEEM 2019 is made accordingly.The comparison against accessible international engineering models suggests that: 1)for small size debris in low Earth orbit,the variable step-size orbital perturbation algorithm is able to improve the accuracy while the efficiency is guaranteed;2)during the flux calculation process,the assumption of RAAN “only effected by J2 factor” is more corresponded to the real case for spacecraft in medium and high orbit;3)during the flux calculation process,the spatial density algorithm based on ECEF is more targeted for spacecraft in GEO region;4)during the flux calculation process,the target-centered spacecraft flux calculation method is more reasonable.In summary,the research on several issues of modelling technology of space debris environment engineering model is carried out in this paper.The modelling technology is optimized and improved from the following aspects: the simulation of space debris environment evolution process,the evaluation of space debris spatial-temporal distribution,the evaluation of space debris environment for particular spacecraft orbit,etc.On this basis,space debris environment engineering model SDEEM 2019 is established,as well as the corresponding software.Combined with the latest version of international engineering models available,SDEEM 2019 is verified and analyzed.The solution of related problems provides a theoretical foundation for the establishment of space debris environment engineering model.The corresponding software can provide data source for the risk assessment of space debris impact and spacecraft protection design.