Colombo, C.

Frey, S.

Gkolias, I.

Frey S.

Gkolias I.

Colombo C.

Archivio istituzionale della ricerca - Politecnico di Milano

Design of end-of-life of disposal manoeuvres and re-entry modelling with PlanODynStefan Frey, Ioannis Gkolias, Camilla Colombo7th European workshop on satellites end of life - 25 Jan. 2018INTRODUCTION25/01/2018 7th Satellites End of Life Workshop, CNES 2Introduction25/01/2018 7th Satellites End of Life Workshop, CNES 3Trajectory design, orbit prediction and maintenance are a challenging task when the effects of orbit perturbations are relevant Design of planet centred orbits Space situation awareness• Design of end-of-life disposal trajectories• Graveyard orbit stability• Prediction of spacecraft re-entry• Modelling the evolution of space debrisNatural dynamics can be studied and leveraged to reduce the propellant requirements, thus creating new opportunitiesPLANODYN25/01/2018 7th Satellites End of Life Workshop, CNES 4Planetary Orbital DynamicsPlanetary Orbital Dynamics5Why averaged dynamics25/01/2018 7th Satellites End of Life Workshop, CNES--- Semi analytic single average--- High fidelity dynamicsAverage variation of orbital elements over one orbit revolution Filter high frequency oscillations Reduce stiffness of the problem Decrease computational time for long term integrationPlanetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 6Applications: Preliminary design where many initial conditions and spacecraft parameters have to be determined/studied Optimisations of EOL disposal Sensitivity analysis Propagation of many objects (clouds of debris fragments, space debris population)Why averaged dynamicsPlanetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 7PlanODyn suiteSpace Debris Evolution, Collision risk, and MitigationFP7/EU Marie Curie grant 302270End-Of-Life Disposal Concepts for Lagrange-Point, Highly Elliptical Orbit missions, ESA GSPEnd-Of-Life Disposal Concepts Medium Earth Orbit missions, ESA GSPEOL disposal in “Revolutionary Design of Spacecraft through Holistic Integration of Future Technologies” ReDSHIFT, H2020COMPASS, ERC “Control for orbit manoeuvring through perturbations for supplication to space systems”Planetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 8For conservative orbit perturbation effectsOrbit propagation based on averaged dynamicsDisturbing potential function Planetary equations in Lagrange form,d Rfdt∂ =  ∂ αααSRP zonal 3 Sun 3 MoonR R R R R− −= + + + [ ]ω= Ω Ta e i Mα,d Rfdt ∂=  ∂ αααSRP zonal 3 Sun 3 MoonR R R R R− −= + + + Single average,d Rfdt ∂=   ∂ αααSRP zonal 3 Sun 3 MoonR R R R R− −= + + + Double averageAverage over one orbit revolution of the spacecraft around the primary planetAverage over the revolution of the perturbing body around the primary planetPlanetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 9PlanODyn: Planetary Orbital DynamicsEPHEMERIDESof perturbing bodies:- Analytical- NASA SPICE/MICESOLAR RADIATION PRESSURE- Averaged potential- Double averaged potential- Averaged JacobianEARTH ZONAL HARMONICS- Averaged potential- Averaged JacobianTHIRD BODY - Sun- Averaged potential- Double averaged potential- Averaged JacobianTHIRD BODY - Moon- Averaged potential- Double averaged potential- Averaged JacobianAERODYNAMIC DRAG- Averaged variation of elementsLagrange Eqs.Gauss Eqs.INPUT- Propagation time- Spacecraft parameters- Atmosphere file- Central planet- Initial stateOUTPUT- Time- Mean orbit element- Mean Jacobian►Colombo C.,  “Planetary Orbital Dynamics Suite for Long Term Propagation in Perturbed Environment,” ICATT, ESA/ESOC, 2016. Planetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 10Perturbation in planet centred dynamicsZonal+tesseralSRPDragMoonSun Atmospheric drag• Non-spherical smooth exponential model• J2 short period coupling Earth gravity potential• Zonal up to order 6 with  J2 contribution• Tesseral resonant terms Solar radiation pressure with cannonball model Third body perturbation of the third body (Moon and Sun) up to order 5 in the parallax factorEphemerides options Analytical approximation based on polynomial expansion in time Numerical ephemerides through the NASA SPICE toolkitOrbital elements in planet centred frame2Planetary Orbital Dynamics25/01/2018 7th Satellites End of Life Workshop, CNES 11In this presentation two applications will be shownApplicationsDisposal design in Geosynchronous orbitsDrag induced re-entry modellingDISPOSAL DESIGN IN GEOSYNRONOUS ORBIT25/01/2018 7th Satellites End of Life Workshop, CNES 12Conservative perturbationsDynamical model25/01/20187th Satellites End of Life Workshop, CNES 13Third body potential Written in terms of the ratio between orbit semi-major axis and distance of the third body Composition of rotation in orbital elements Series expansion in Average over one orbit revolution Include averaged potentialin Lagrange equationsThird body potential'arδ =δ( ) ( )32', ' , , ,'kB kkR r r F A B e Erµ δ∞== ∑( ) ( )32', ' , ,'kB kkR r r F A B erµ δ∞== ∑►Kaufman and Dasenbrock, NASA report, 197925/1/2018Validation25/01/2018 7th Satellites End of Life Workshop, CNES 14Propagation time: 1999/12/15 to 2013/01/01Initial Keplerian elements from ESA on 1999/12/15 at 15:00:a = 67045 km, e = 0.7951, i = 0.67988 rad, Ω = 4.1192 rad, ω = 0.99259 radSystem: Earth centred, equatorial J2000XMM-Newton trajectory25/01/2018 7th Satellites End of Life Workshop, CNES 15ValidationGeostationary orbita = RGEO, e = 0.01, i = 4°, Ω = 0°, ω = 0°4x4 Geopotential, 5th order lunisolar, cannonball SRP, Earth’s precessionDisposal design25/01/2018 7th Satellites End of Life Workshop, CNES 16 Long-term orbit propagation from many initial conditions on a grid of orbital elements Different stating epochs (i.e., different orientation of s/c-Moon-Sun) and spacecraft parameters (i.e., A/m considered) The variation of the orbital elements can be used as a measure of the orbit stability Optimal manoeuvre can be designed to target graveyard or re-entry solutionsStrategy25/01/2018 7th Satellites End of Life Workshop, CNES 17Disposal designΕffect of the Earth’s triaxiality - Eye plotsDynamics caused by Earth’striaxiality can be appreciated bypropagating an initial GEO orbitfor different starting values ofthe resonant angle λ25/01/2018 7th Satellites End of Life Workshop, CNES 18Disposal designLuni-solar effects - Ω-ω plotsCoupling between J2 , luni-solar, and SRP effect.25/01/2018 7th Satellites End of Life Workshop, CNES 19Disposal strategyDisposal designInputs:- End of mission operational orbit- available Δv on boardReachable orbital element domainExclude orbits crossing the GEOprotected regionOptimal transfer with 2-burn manoeuvre with a grid-based optimisationPareto front solutions:- Required Δv for disposal- Re-entry time/orbit stability Gkolias, I., Colombo, C., End-of-life disposal of geosynchronous satellites, Proceedings of the 68th IAC, 201725/01/2018 7th Satellites End of Life Workshop, CNES 20Disposal designEnd-of-life of GEO orbitsInitial post-mission orbit: a = RGEO , e = 0.001, Ω = 0°, ω = 0° , maximum available Δv = 200 m/sPareto front graveyard for regular GEO (i = 0°) Pareto front re-entry for highly inclined GEO (i = 75°)DRAG INDUCED RE-ENTRY MODELLING25/01/2018 7th Satellites End of Life Workshop, CNES 21Non-conservative perturbationsDynamical model25/01/2018 7th Satellites End of Life Workshop, CNES 22 Average out fast moving variable (𝑓𝑓, 𝐸𝐸 or 𝑀𝑀), assuming the other mean elements to be fixed The change 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑is a function the Keplerian elements, 𝒌𝒌, the density, 𝜌𝜌, at altitude, ℎ, and the effective area-to-mass ratio, 𝛿𝛿 = 𝑐𝑐𝐷𝐷 𝐴𝐴𝑚𝑚Averaging̅?̇?𝑥 = ∆𝑥𝑥𝑃𝑃= 1𝑃𝑃�02𝜋𝜋 𝑑𝑑𝑥𝑥𝑑𝑑𝐸𝐸𝑑𝑑𝐸𝐸𝒌𝒌T = (a, e, i,Ω,𝜔𝜔,𝐸𝐸)𝑑𝑑𝑥𝑥𝑑𝑑𝐸𝐸= 𝑓𝑓𝑥𝑥(𝒌𝒌,𝜌𝜌 ℎ 𝒌𝒌 , 𝛿𝛿)𝑥𝑥 ∈ [𝑎𝑎, 𝑒𝑒]ℎ = ℎ𝑚𝑚+ ∆ℎ𝜀𝜀+ ∆ℎ𝐽𝐽2Short periodic variationAltitude above ellipsoid variationMean altitudeDynamical model25/01/2018 7th Satellites End of Life Workshop, CNES 23 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 exponentially decaying atmosphere model (next slide)− Series expansion in eccentricity (solved for low and high eccentricities by KH)+ Only one density evaluation+ Analytical estimation of the Jacobian available Both are implemented in PlanODyn, with the (Superimposed) King-Hele method as defaultAveraging method 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, 1964Dynamical model25/01/2018 7th Satellites End of Life Workshop, CNES 24 KH requires atmosphere to decay exponentially Fit superimposed partial exponential atmospheres to any desired model Can include temporal or spatial changes E.g. fit to Jacchia-77 with solar activityAtmospheric model𝜌𝜌 ℎ = �𝑝𝑝𝜌𝜌0,𝑝𝑝 exp− ℎ𝐻𝐻𝑝𝑝 Jacchia, L. G., Thermospheric temperature, density, and composition: new models. SAO Special Report, 1977.Validation25/01/2018 7th Satellites End of Life Workshop, CNES 25 ℎ𝑝𝑝/ ℎ𝑎𝑎=500/2000 km, 𝑖𝑖 = 90°, Ω/𝜔𝜔/𝑓𝑓 = 0°, A/m = 1 m2/kg, 𝑐𝑐𝐷𝐷 = 2.1 Perturbations: drag, Earth flattening and 𝐽𝐽2 Full  numerical: Jacchia-77 (fixed, 𝑇𝑇∞ = 1000 K) Semi-analytical: Smooth exponential atmosphere (fitted to aforementioned model) and superimposed King-HeleDrag representative exampleLifetime CPU time1.7685 years 118.89 s1.7668 years 0.29 sUsing a variable-step/variable-order Adams-Bashforth-Moulton integrator(rel. tol. 𝛾𝛾𝑟𝑟𝑟𝑟𝑟𝑟 = 10-9)Applications25/01/2018 7th Satellites End of Life Workshop, CNES 26Drag induced re-entry: two examples Maps of effective area-to-mass ratio required for re-entry in 𝑥𝑥years (optimisation) Evolution of clouds of fragments (collision or explosion) or entire space debris population Frey, S., Colombo, C., Lemmens, S., Krag H., Evolution of Fragmentation Cloud in Highly Eccentric Orbit using Representative, Proceedings of the 68th IAC, 2017 Semi-analytical methods can be used to characterise the stability of graveyard orbits and identify re-entry options• Get an insight on the orbit evolution• Leverage the dynamics for end-of-life disposal Semi-analytical methods shows accuracy against numerical propagation• Especially for conservative forces• Also for drag induced forces up until shortly before re-entry Possible applications• Disposal trajectory design• Re-entry modelling and orbit determination• Sensitivity analysis to spacecraft parameters and model uncertainties25/01/2018 7th Satellites End of Life Workshop, CNES 27ConclusionsDesign of end-of-life of disposal manoeuvres and re-entry modelling with PlanODynstefan.frey@polimi.it, ioannis.gkolias@polimi.it, camilla.colombo@polimi.itThe research leading to these results has received funding from the Horizon 2020 Program of the European Union’s Framework Programme for Research and Innovation (H2020-PROTEC-2015) under REA grant agreement number 687500 – ReDSHIFTThis 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)

Design of end-of-life of disposal manoeuvres and re-entry modelling with PlanODyn

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Design of end-of-life of disposal manoeuvres and re-entry modelling with PlanODyn

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