Colombo, C.

Frey, S.

Lemmens, S.

English

Archivio istituzionale della ricerca - Politecnico di Milano

Advancement of a density-based debris fragment model and application to on-orbit break-up localisationStefan Frey1, Camilla Colombo1, Stijn Lemmens21 Politecnico di Milano, 2 European Space Agency36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 Statistical collision risk estimation from objects down to very small sizes Inherently statistical (no need of Monte Carlo runs) Insight and fast propagation of cloud evolution in any orbital regime subject to major perturbations Application to criticality index computation Tracing newly observed fragments back to origin, possibly years awayBased on past work by Letizia, Colombo and Lewis @ Uni of Southampton Generalise the method (in LEO some parameter are randomly distributed) to any orbital region Remove some simplifying assumptions Broader application to space debris population propagationIntroductionWhy a density-based debris model?07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 2 The integrals can be approximated quickly numerically or analytically• E.g. Gauss-Legendre quadrature+ Flexible: can work with any drag model+ Valid for any eccentricity, i.e. series expansion avoided‒ Multiple density evaluations (usually 𝑁 = 33)• E.g. King-Hele (KH) method‒ Requires atmosphere to decay exponentially (next slide)‒ Series expansion in eccentricity (solved for low and high eccentricities by KH)+ Only one density evaluation at perigee+ Analytical estimation of the Jacobian availableForce modelOrbital contraction Liu, J. J. F., Alford, R. L., An Introduction to Gauss-Legendre Quadrature, Northrop Services, Inc., 1973. King-Hele, D., Theory of Satellite Orbits in an Atmosphere, London Butterworths, 196407/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 3 The King-Hele method assumes strictly exponential decaying density but in turn requires only one density evaluation at perigee Problem: Density decays slower with increasing altitude Solution: Smooth exponential atmosphere model Advantages• Fast: only p < 10 exponential evaluations required• Smooth: no problem for the integrator• Exact: each part is strictly decaying• Versatile: can be fit to any reference model Example: Fit to Jacchia-77 taking into account solar fluxForce modelAtmosphere density model𝜌 ℎ, 𝑇 =  𝑝𝜌0,𝑝(𝑇) exp−ℎ𝐻𝑝(𝑇) Jacchia, L. G., Thermospheric temperature, density, and composition: new models. SAO Special Report, 1977.07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 45DENSITY PROPAGATION07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 Fragments/debris modelled as a continuum Based on general continuity equation• 𝑛 density• 𝑡 time• 𝑭 dynamics• 𝑔 sources and sinks Can be turned into a PDE using method of the characteristics Requires Jacobian, which is obtainable using analytical formulated dynamicsDensity PropagationFormulation𝜕𝑛𝜕𝑡+ 𝛻 ∙ 𝑛𝑭 = 𝑔07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 6Population-driven forward propagationPropagate initial density of a cloud/many clouds/the whole population forward and interpolate where needed.Ideal if density needs to be known at many points07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 7Density PropagationTarget-driven backward propagationGiven a target location and time, propagate characteristics backward to initial density.Ideal if high accuracy in density is requiredPropagation method𝑡Area of interestInitial fragment distribution𝑡Point of interestInitial fragment distribution Curse of dimensionality workaround: • Sample initial distribution, e.g. few points where density low• Use combination of population-driven forward to identify the admissible region to be used for target-driven backward propagation07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 8Density PropagationInitial points selection𝑡Area of low informationInitial fragment distribution Initial condition for fragmentations from break-up models (e.g. NASA’s breakup model) Initial condition for background population from observations or space debris environmental tools (e.g. ESA’s MASTER) Dimensions• up to 5 states (𝑎, 𝑒, 𝑖, Ω, 𝜔)• physical properties (𝐴𝑚, 𝑐𝑑, 𝑐𝑟)07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 9Density PropagationBuilding of initial condition N. L. Johnson, P. H. Krisko, J.-C. Liou, and P. D. Anz-Maedor. NASA's new breakup model of EVOLVE 4.0. Advances in Space Research, 28(9):1377-1384, 2001. S. Flegel, J. Gelhaus, M. Möckel, C. Wiedemann, and D. Kempf. Maintenance of the ESA MASTER model. Final Report of ESA contract 21705/D/HK, 2010.Fragment distribution for break-up in GTO07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 10Density PropagationFrom Keplerian to spatial density1 January 20084607 objects1 January 20106047 objectsSpatial density from individual fragments in LEO From propagation, the density is given in Keplerian elements For collision risk calculation, a spatial density is required Not a point-to-point transformation, hence not straightforward  If anomaly, node and perigee are randomised, the density can be found as a function of radius and latitude Currently ongoing: transforming without assumptions07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 11BREAK-UP LOCALISATION Ever increasing observational capabilities will add small fragments of unknown origin to the catalogue (e.g. recent major fragmentation of Transtage 17 (1969-013B) in GEO)  Already now, almost 2500 unidentified objects are tracked, mostly non-LEO Due to lack of observations, origin can only be assigned probabilistically Application for density propagation, if number of objects with unknown origin is large However, at this point, number of fragments small enough for individual propagation07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 12Break-up localisationNeedObserved Fragments in LEO ESA Space Debris Office, ESA’s Annual Space Environment Report. Technical Note, May 2018. ROSCOSMOS IADC 2018, (WG 1) Recent major fragmentation of Transtage 17 (1969-013B) in GEO  Propagating back all fragments (individually) lead to peaks in the spatial density indicating break-up epoch and location However, ballistic coefficient estimation usually shows large variability, leading to inaccurate semi-major axis and eccentricity On the other hand, estimation of node and argument of perigee shown to be robust for several years Focusing (concentration) of node indicates break-up07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 13Break-up localisationMethodRAAN distribution, all fragments from 2010 backIridium 33Fengyun 1CKosmos-2251 Statistical interference for identification of sources and subsequent assigning of probability, e.g. Gaussian Mixture Model depending on “orbit similarity”07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 14Break-up localisationClustering, classification Density based propagation to estimate the evolution of the space debris environment allowing to adapt to new fragmentations easily Ideally, together with a criticality index, this method would be employed in rating future space missions towards their compliance with the mitigation guidelines This rating could lead to go/no-go decisions, or mandate a more effective post-mission disposal 07/06/2018 36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018 15OutlookAdvancement of a density based debris model and application to on-orbit break-up localisationStefan Frey1, Camilla Colombo1, Stijn Lemmens21 Politecnico di Milano, 2 European Space Agency36th IADC Plenary Meeting, Tsukuba, Japan, 5-8 June 2018This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 679086 – COMPASS)

Advancement of a Density-Based Debris Fragment Model and Application to On-Orbit Break-Up Localisation

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Advancement of a Density-Based Debris Fragment Model and Application to On-Orbit Break-Up Localisation

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