Colombo, C.

Del Campo, B.

Frey, S.

Giudici, L.

Gonzalo Gómez, J. L.

Lemmens, S.

Letizia, F.

Muciaccia, A.

Trisolini, M.

English

Archivio istituzionale della ricerca - Politecnico di Milano

Credit: iStock.com/slavemotionTHEMIS: Tracking the health of the environment and missions in spaceCamilla Colombo 1, Andrea Muciaccia1, Mirko Trisolini 1, Lorenzo Giudici 1, Juan Luis Gonzalo 1, Stefan Frey 2, Borja del Campo 3, Francesca Letizia 4, Stijn Lemmens 41 Politecnico di Milano, 2 Vyoma, 3 Deimos Space, 4 European Space Agency6th European Space Debris modelling and Remediation workshop, Milano, 18-20 May 2022C. Colombo et al. - EUSDM workshop - 2022Apollo mission 2019. Simulation COMPASS Virtual Reality game. Actual space debris orbits, artistic representation of objects218/05/2022IntroductionSpace debris like other environmental issues18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 3 Maury T., Loubet P., Trisolini M., Gallice A., Sonnemann G., Colombo C., ”Assessing the impact of space debris on orbital resource in Life Cycle Assessment: a proposed method and case study”, Science of the Total Environment, 2019. Earth system trend original image by Steffen, W., Broadgate, W., Deutsch, L., Gaffney, O., & Ludwig, C. (2015). The trajectory of the anthropocene: The great acceleration. Anthropocene Review, 2(1), 81–98. https://doi.org/10.1177/2053019614564785Goals: To assess the impact of a space mission on the space environment To assess the overall Space capacity and the contribution of each mission to itScientific development: A statistical density-based approach used for propagating explosion and collision fragments Definition and extension of space debris index to all orbital regions, including LEO, GEO, MEO, GTO, HEO Analysis of possible capacity proxy and capacity threshold Software development: Integration with existing ESA tools such as DISCOS, MASTER, DRAMA, OSCAR Single score output of the environmental analysis in the ESA database DISCOS for reporting analyses and for integration into a life cycle assessment procedure Develop a web-based interface for the submission and evaluation of the space by several usersIntroductionGoals and noveltiesC. Colombo et al. - EUSDM workshop - 2022 418/05/2022THEMIS SOFTWARE TOOLC. Colombo et al. - EUSDM workshop - 2022 518/05/2022Space debris mode to allow different users to assess the impact of a space mission on the space debris environment based on mission information such as orbit, mass, cross-section, and risk of fragmentation due to accidental collisions or break-up  to determine the share of the capacity of space used by that mission under analysisSpace capacity mode to allow the computation of the overall space capacity used by orbiting spacecraft to analyse possible definitions and proxy of the capacity thresholdTHEMIS software toolTracking the Health of the Environment and Missions In Space18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 6Interface for external users: to analyse missions and their impact to have an overview of the overall status of the space environment for registered users to submit user-defined mission for evaluation of its environmental impact both in terms of index and capacity consumption  for operators to declare new missions profilesTHEMIS software toolSoftware designTHEMIS frontend Computation of the environmental index:• Create and propagate a mission profile• Compute the collision probability• Compute the explosion probability• Determine the collision effect• Determine the explosion effects• Interface with ESA tools Computation of the space capacity:• Long-term propagation using ESA DELTA• Compute the available capacity of the space environmentTHEMIS backend18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 7THEMIS software designOverall software design and flow18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 8THEMIS software designOverall software design and flow18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 9THEMIS software designOverall software design and flow18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 10THEMIS software toolBasic functional analysis of the system subdivided by sections18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 11SPACE DEBRIS INDEX18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 12Space debris index ECOB formulation index to assess the risk = probability x severitySpace debris indexIndex formulationC. Colombo et al. - EUSDM workshop - 2022 Letizia, F., Colombo, C., Lewis, H. G., & Krag, H. (2016). Assessment of breakup severity on operational satellites. Advances in Space Research, 58(7), 1255-1274.1318/05/2022p = probabilitye = effects (severity)Collision probabilityFragmentation effect𝐼𝐼(𝑡𝑡) = 𝑝𝑝𝑐𝑐 ⋅ 𝑒𝑒𝑐𝑐 + 𝑝𝑝𝑒𝑒 ⋅ 𝑒𝑒𝑒𝑒Fragmentation effectExplosion probability18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Space debris indexCollision probabilityFragmentation effect𝐼𝐼(𝑡𝑡) = 𝑝𝑝𝑐𝑐 ⋅ 𝑒𝑒𝑐𝑐 + 𝑝𝑝𝑒𝑒 ⋅ 𝑒𝑒𝑒𝑒Fragmentation effectExplosion probability DISCOS• Objects properties• Active / Inactive• Explosion probability• PMD manoeuvres14Space debris indexExplosion probabilitySpace debris index18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 15LEO region representative targets in a semi-major axis and inclination gridGEO region representative targets in a longitude and inclination gridRepresentative targetsMEO region representative targets in a right ascension of ascending node and inclination gridSpace debris indexExplosion probability18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 16Survival rate evaluated using the Kaplan-Meyer estimator𝑆𝑆(𝑡𝑡) = �𝑡𝑡𝑖𝑖<𝑡𝑡1 −𝑑𝑑𝑖𝑖𝑛𝑛𝑖𝑖𝐻𝐻(𝑡𝑡) = �𝑡𝑡𝑖𝑖<𝑡𝑡𝑑𝑑𝑖𝑖𝑛𝑛𝑖𝑖 Kaplan, E. L., Meier, P . (1958), Nonparametric Estimation from Incomplete Observations. Acta Astronautica, 53(282), 457-481. O. Aalen, (1978), Nonparametric Inference for a Family of Counting Processes. The annals of statistics, 6(4), 701-726.Explosion probability evaluated using the Nelson-Aalen estimator18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Space debris indexCollision probabilityFragmentation effect𝐼𝐼(𝑡𝑡) = 𝑝𝑝𝑐𝑐 ⋅ 𝑒𝑒𝑐𝑐 + 𝑝𝑝𝑒𝑒 ⋅ 𝑒𝑒𝑒𝑒Fragmentation effectExplosion probabilityARES• CAM reliabilityDRAMAMASTER• Debris fluxes• Impact velocity• Density value vs object size (integration with DELTA)17THEMIS software designSubcomponent: index evaluation – collision probabilityCollision probability without CAM capability Collision probability considering CAM capability18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Collision probability evaluation as function of the semi-major axis and inclination considering: Cross-section = 10 𝑚𝑚2 Time discretisation = 1 year  18STARLING18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Space debris indexCollision probability𝐼𝐼(𝑡𝑡) = 𝑝𝑝𝑐𝑐 ⋅ 𝑒𝑒𝑐𝑐 + 𝑝𝑝𝑒𝑒 ⋅ 𝑒𝑒𝑒𝑒Fragmentation effectExplosion probabilityPlanODyn• Density propagation• Dynamics propagationDISCOS• Objects properties• Active / Inactive• Explosion probability• PMD manoeuvres19THEMIS software designCloud characterisation and propagation18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Input: Fragmentation grid: coordinates of the subset of characteristic Keplerian elements of the orbital region under analysisOutput: Density distributions: density values stored in ECRS* format, for each fragmentation at each time snapshot*Compressed row storage applied to extended Karnaugh map representation of the density array20Inputs: Fragmentation settings specifying:• Parent orbit• Fragmentation type • Parameters (mass, fragments’ size, scaling factor) Interpolation settings specifying:• Interpolation variables• Step-sizes for binning• Method (Monte Carlo or Weighted Monte Carlo)• Re-entry altitudeTHEMIS software designSubcomponent: initial density estimation and sampling18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Output: Initial characteristics: coordinates (𝑎𝑎, 𝑒𝑒, 𝑖𝑖, Ω, 𝜔𝜔, 𝑀𝑀, ⁄𝐴𝐴 𝑀𝑀𝑑𝑑, ⁄𝐴𝐴 𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠) and density value of each characteristic to be propagatedProcess: Probabilistic definition of the phase space domain Estimation of the density distribution through a binning approach Characteristics’ sampling according to bins’ size and (possibly) expected dynamical behaviour of the cloudPhase space, 𝒙𝒙Density, 𝒏𝒏21Inputs: Initial characteristics: coordinates (𝑎𝑎, 𝑒𝑒, 𝑖𝑖, Ω, 𝜔𝜔, 𝑀𝑀, ⁄𝐴𝐴 𝑀𝑀𝑑𝑑, ⁄𝐴𝐴 𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠) and density value of each characteristic to be propagated Propagation settings specifying:• Snapshots’ times (start, end, step-size)• Integration settings (tolerances, solver) • Dynamical model (parameters and flags, Jacobian, density model, ephemerides)THEMIS software designSubcomponent: characteristics’ propagation18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Output: Propagated characteristics: coordinates and density values at each snapshot timeProcess: Propagation of characteristics using PlanODyn (semi-analytical tool) with set perturbations Storing in at some specified epochsPhase space, 𝒙𝒙Density, 𝒏𝒏22Inputs: Interpolation settings specifying:• Interpolation variables• Step-sizes for binning• Method (Monte Carlo or Weighted Monte Carlo)• Re-entry altitude Propagated characteristics: coordinates and density values at each snapshot timeTHEMIS software designSubcomponent: density interpolation18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Output: Density distributions at each specified snapshot timestored in ECRS formatProcess: Density distributions are recovered from the propagated characteristics through binning in an (up to) 6D phase space Nearest-neighbour – like interpolation among neighbouring bins is implemented to avoid missing data in the distributionPhase space, 𝒙𝒙Density, 𝒏𝒏23THEMIS software designMain block: fragmentation effect18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Input: Density distributions at each specified snapshot time stored in ECRS formatOutput: Effects: coordinates of one fragmentation defined in the fragmentation grid and the relative effect on the representative targets24Inputs: DISCOS active objects Grid parameters:• Keplerian elements ranges and steps• Orbit type Target settings specifying the fixed Keplerian elementsTHEMIS software designSubcomponent: representative targets18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Output: Representative targets: Keplerian elements, area, and total area of each representative targetProcess: Reading DISCOS file with active objects Generation of the grid in Keplerian elements (according to the orbital region) and computation of the total and average areas in each cell of the grid Identification of the representative targets considering the cells containing the 90% of the cumulative cross-sectional area25THEMIS software designSubcomponent: representative targets18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Representative targets in LEO region - 14/02/2022Grid parameters: Semi-major axis range: [6778 − 8378] km Semi-major axis step: 10 km Inclination range: [0 − 180] deg Inclination step: 10 deg26THEMIS software designMain block: fragmentation effect18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 27Impact rates:?̇?𝜂 for different target positions (according to an equally-spaced grid in mean anomaly) at each specified snapshot time?̇?𝜂 = 𝐴𝐴𝑐𝑐 �ℝ3�𝑘𝑘=14𝑛𝑛𝜶𝜶 𝜶𝜶13,𝜶𝜶46𝑘𝑘| det 𝐽𝐽𝑘𝑘| 𝒗𝒗 𝛼𝛼13,𝛼𝛼46𝑘𝑘 − 𝒗𝒗∗ d𝜶𝜶13Process: The density distribution is sampled in the subset of Keplerian elements (𝑎𝑎, 𝑒𝑒, 𝑖𝑖) By imposing intersection with target position, the full set of samples’ coordinates is retrieved The density values in correspondence of the samples’ coordinates is computed The impact rate is evaluated by integrating the flux of fragments over the target areaTHEMIS software designMain block: fragmentation effect18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 28Cumulative collision probability:𝑝𝑝𝑐𝑐 𝑡𝑡 at each specified snapshot time𝑝𝑝𝑐𝑐 𝑡𝑡 = 1 − exp 𝜂𝜂 𝑡𝑡 = 1 − exp �𝑡𝑡0𝑡𝑡?̇?𝜂 𝒓𝒓∗,𝒗𝒗∗ d𝑠𝑠Process: The number of impacts with the target is estimated through midpoint integration The probability of collision is computed from the cumulative number of impacts at final time, through an analogy with kinetic gas theoryTHEMIS software designMain block: fragmentation effect18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 29Fragmentation effect:𝑒𝑒: weighted (according to shared area) cumulative collision probability of one fragmentation with the representative targets𝑒𝑒 = �𝑘𝑘=1𝑁𝑁𝑡𝑡 𝐴𝐴𝑐𝑐𝑘𝑘𝐴𝐴𝑐𝑐tot𝑝𝑝𝑐𝑐𝑘𝑘( 𝑡𝑡𝑓𝑓), 𝐴𝐴𝑐𝑐tot = �𝑘𝑘=1𝑁𝑁𝑡𝑡𝐴𝐴𝑐𝑐𝑘𝑘Process:The effect of a fragmentation is computed as the weighted sum of the collision probabilities according to the share of overall cross-sectional area of each targetFragmentation examplePayload explosion in low-Earth orbit18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 Fragmentation orbit: 𝑎𝑎 = 7236 km, 𝑒𝑒 = 0.001, 𝑖𝑖 = 85 deg Target orbit: 𝑎𝑎 = 7226 km, 𝑒𝑒 = 0.001, 𝑖𝑖 = 75 deg Perturbation model:  𝐽𝐽2 and drag Collision probability: randomisation in 𝜔𝜔,Ω,𝑀𝑀 assumedFragments’ number (𝑁𝑁) distribution over time – heatmaps in 𝑎𝑎, 𝑒𝑒 and 𝑖𝑖Fragments number (𝑁𝑁), impact rate (?̇?𝜂) and number of impacts (𝜂𝜂) over time30Effects mapPayload explosions in low-Earth orbit18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Cumulative collision probability at 15 years from fragmentation on 48 representative targets 31 The index assessed over time to get its evolution and cumulative value for the mission lifetime𝐼𝐼 = �𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡 Each mission profile is divided in mission phases: e.g. launch, injection, orbit raising, operational orbit, deorbiting etc. The basic formulation expanded to include the reliability of post-mission disposal (PMD) manoeuvres with a coefficient (α)𝐼𝐼 = �𝑡𝑡0𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡 +𝛼𝛼 ⋅ �𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝑓𝑓𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡 + 1 − 𝛼𝛼 ⋅ �𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝑓𝑓𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡Space debrisECOB formulation overviewC. Colombo et al. - EUSDM workshop - 2022 Letizia, F., Colombo, C., Lewis, H. G., & Krag, H. (2016). Assessment of breakup severity on operational satellites. Advances in Space Research, 58(7), 1255-1274.3218/05/2022disposal no disposal18/05/2022 C. Colombo et al. - EUSDM workshop - 2022Space debris indexCollision probabilityFragmentation effect𝐼𝐼(𝑡𝑡) = 𝑝𝑝𝑐𝑐 ⋅ 𝑒𝑒𝑐𝑐 + 𝑝𝑝𝑒𝑒 ⋅ 𝑒𝑒𝑒𝑒 Letizia, F., Colombo, C., Lewis, H. G., & Krag, H. (2016). Assessment of breakup severity on operational satellites. Advances in Space Research, 58(7), 1255-1274.Fragmentation effectExplosion probability• Disposal scenarios• Mission phases• Spacecraft parametersOSCAR• Disposal scenarios• Identify orbit for natural decay• Orbit propagationDRAMAIntegrate along the trajectory• Collision probability• Explosion probability• Fragmentation effects𝐼𝐼 = �𝑡𝑡0𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡 +𝛼𝛼 ⋅ �𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝑓𝑓𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡 + 1 − 𝛼𝛼 ⋅ �𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝑓𝑓𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑑𝑑𝑡𝑡PMD reliability33THEMIS software designIndex evolution – dummy mission18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 Phase 1: Keplerian elements from an .oemfile Phase 2: constant Keplerian elements PMD/NO-PMD: OSCAR propagation, considering a Re-orbit at 500 km using  chemical propulsionIndex evolution over time – each color represents a single phase of the mission, and the index is computed at each time epoch 34THEMIS software designFrontend – Evaluation Output View18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 35CONCLUSIONSC. Colombo et al. - EUSDM workshop - 2022 3618/05/2022Steps completed Staling 2.0 tool applied to computation of the space debris index Space matrix approach for efficient binning Development of space debris ingredients for any orbital region Interfaces with ESA tools: DISCOS, MASTER, DRAMANext steps Space debris implementation and validation Capacity formulation and definition of capacity threshold Engaging with the space community…stay tunedConclusions18/05/2022 C. Colombo et al. - EUSDM workshop - 2022 37Credit: iStock.com/slavemotionTHEMIS: Tracking the health of the environment and missions in spaceCamilla Colombo 1, Andrea Muciaccia1, Mirko Trisolini 1, Lorenzo Giudici 1, Juan Luis Gonzalo 1, Stefan Frey 2, Borja del Campo 3, Francesca Letizia 4, Stijn Lemmens 41 Politecnico di Milano, 2 Vyoma, 3 Deimos Space, 4 European Space Agency6th European Space Debris modelling and Remediation workshop, Milano, 18-20 May 2022@COMPASS_ERCwww.compass.polimi.itThis project has received funding from the European Space Agency contract 4000133981/21/D/KSMICO Milano Convention Centre11-18October 2024MI LANCANDIDATE CITY TO HOST T H EINTERNATIONALASTRONAUTICALCONGRESSR E S P O N S I B L E S P A CE F O R S U S T A I N A B I L I T Y

THEMIS: Tracking the Health of the Environment and Missions In Space

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THEMIS: Tracking the Health of the Environment and Missions In Space

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