Numerical analysis of the compliance of interplanetary CubeSats with planetary protection requirements Francesca Letizia, Camilla Colombo University of Southampton 5th Interplanetary CubeSat Workshop Session A.4 Oxford, 24 th May 2016
Planetary protection requirements Compliance for interplanetary missions Spacecraft and launchers used for interplanetary missions and missions to the Lagrangian points may come back to the Earth or impact with other planets (example: Apollo launchers) Breakup of the object WT110F during re-entry (November 2015) Planetary protection requirements: avoid the risk of contamination The compliance with requirements should be verified for the nominal trajectory considering inaccuracy & failures 2
Planetary protection requirements Peculiarities of interplanetary CubeSats > Martin-Mur, Gustafon, Young, 2015 Artistic impression of InSight & MarCO probes InSight (main mission) built in a clean environment to loosen the requirement on the impact probability over 50 years (10-2 ) Image Credit: NASA/JPL-Caltech MarCO (cubesats) processes, components & reliability significantly different from those of traditional spacecraft (requirement = 10-4 ) 3
SNAPPshot: Suite for Numerical Analysis of Planetary Protection Max impact prob. Confidence level number of Monte Carlo runs trajectories number of impacts Covariance matrix Other distributions e.g. area-to-mass ratio Monte Carlo initialisation initial conditions Trajectory propagation B-plane analysis Increase number of runs No Are the requirements satisfied? Yes Contract 4000115299/15/D/MB Planetary Protection Compliance Verification Software Produce output 4
MonteCarlo initialisation Number of runs & generation of the initial conditions > Jehn 2015 > Wallace 2015 Number of runs (n) to verify the maximum level of impact probability (p), with a level of confidence (α), from the expression of the one-sided Wilson s confidence interval Example: p = 10-4, α = 0.99 n~50000 p p + z2 2n + z2 p 1 p n 1 + z2 n + z2 4n 2 z = α-quantile of a standard normal distribution number of impacts p = n Generation of the initial conditions launcher uncertainty (e.g. covariance matrix) failure of the propulsion system (random failure time) Additional distributions area-to-mass ratio user provides known values and select a distribution (e.g. uniform, triangular) 5
y [km] Trajectory propagation Force model, ephemerides & propagator Coordinates Cartesian coordinates in the J2000 reference frame centred in the Solar System Barycentre Force model gravitational forces + solar radiation pressure (cannonball model) Ephemerides ESA routine for planetary ephemerides or SPICE toolkit Propagator Runge-Kutta methods with step size control technique (adaptive methods or regularised steps) Additional features event functions and dense output 2 1 0-1 -2 Integration of the trajectory of Apophis & validation against Horizons ephemeris x 10 8-2 -1 0 1 2 x [km] x 10 8 Horizons RK5(4) + ESA RK5(4) + SPICE 6
B-plane tool B-plane definition Plane orthogonal to the object planetocentric velocity (U) when the object enters the planet s sphere of influence (SOI) η-axis: parallel to the planetocentric velocity ζ-axis: parallel to the projection on the b-plane of the planet velocity, but in the opposite direction ξ-axis: to complete a positively oriented reference system B, intersection of the incoming asymptote and the b-plane Distance of B from the centre of the planet (b), impact parameter 7
B-plane tool State characterisation: impact 6 x 10 4 Impact region 4 2 R IR = R p 1 + 2μ p R p U 2 [km] 0-2 -4 Impact region R p -6-5 0 5 [km] x 10 4 Figure readapted from Davis et al. 2006 8
[km] B-plane tool Additional information on the b-plane 6 4 2 0-2 -4-6 x 10 4 Impact region b-plane of the Earth for the encounter with Apophis Resonance circles b B intersection of the incoming asymptote with b-plane planet radius -5 0 5 [km] x 10 4 Impact condition if B within the area of the projection of planet on the b-plane + Decoupling distance & time ξ coordinate related to the minimum geometrical distance between the planet s and the object s orbits ζ coordinate related to the phasing between the planet and the object + Resonances, applying the analytical theory by Valsecchi et al. (2003) 9
B-plane tool State characterisation: multiple fly-bys When multiple fly-bys are recorded, only one state should be selected to characterise the trajectory. Two options: first encounter worst encounter To select the worst encounter, the states need to be sorted: Distance-driven the worst case is the one with the minimum distance from the planet State-driven e.g. resonance > simple close approach e.g. Mars > Mercury [km] x 10 5 6 4 2 0-2 -4-6 Evolution of one GAIA Fregat trajectory on the Earth s b-plane for 100 years of propagation 3 Consecutive fly-bys -5 0 5 [km] x 10 5 1 2 10
RESULTS 11
Mission scenario Simulation settings Representation of the trajectory of InSight Reference trajectory: Phoenix (Horizons) Release at: launch epoch + 4 days Uncertainty: initial velocity (1 m/s) Propagator: RK8(7) Propagation time: 100 years When multiple encounters: worst Encounter ranking: state Number of runs = 10000 Number of impacts = 1 (Earth), 1 (Mars) Image Credit: B. Banerdt, InSight Mission Status, JPL 12
Planetary protection analysis Radial dispersion Uncertainty on velocity Along-track dispersion 13
Planetary protection analysis Radial dispersion Uncertainty on velocity: state of the trajectory 89% of the simulated cases enter in the sphere of influence of Mars Along-track dispersion 14
Planetary protection analysis Radial dispersion Uncertainty on velocity: state of the trajectory 1 impact with Mars out of 10000 runs is enough to invalidate the requirement on the impact probability 2 resonances with Mars that need to be studied to check for possible subsequent returns Along-track dispersion 15
Planetary protection analysis Uncertainty on velocity: b-plane visualisation Nominal trajectory 16
Planetary protection analysis Uncertainty on velocity: b-plane visualisation Additional plots available for the frequency of events in time B-plane visualisation at specific times miss distance from the bodies For example, most of the iterations (and the two impacts) occurs after 50 years, so the studied case could still be compliant to the planetary protection regulations (50 years). Impact 17
Mission scenario Simulation settings Representation of the trajectory of Phoenix Reference trajectory: Phoenix (Horizons) Uncertainty: release date + Δv (1 m/s) Propagator: RK8(7) Propagation time: 100 years When multiple encounters: worst Encounter ranking: state Number of runs = 1000 Release window 18
Number of cases Mission analysis Release date & arrival to Mars 90 80 70 60 50 40 30 20 10 0 No close approach Earth: Resonance Earth: Close approach Mars: Close approach Release time after launch [hours] 19
Mission analysis Release date & arrival to Mars The same approach can be used to study a failure of the propulsion system during a random time of operation The single trajectories generated by the Monte Carlo analysis can be easily reproduced to perform a more in depth analysis (e.g. distance from Mars for the trajectories with different release dates) Sphere of Influence of Mars Code still in development to further increase its flexibility 20
Conclusions Launchers and spacecraft used for interplanetary missions and missions to the Lagrangian points may be inserted in trajectory that will impact a celestial body. Need to estimate their compliance with planetary protection requirements. A new tool, SNAPPshot, was developed for this purpose. A Monte Carlo analysis is performed considering the dispersion of the initial condition and of other parameters. Each run is characterised by studying the close approaches through the b-plane representation to detect conditions of impacts and resonances. The method can be applied to study the compliance with planetary protection requirements for interplanetary CubeSats considering the uncertainty on the initial condition. Flexible tool: applicability can be extended to the robust design of missions or to the study of swarms of CubeSats. 21
The present study was funded by the European Space Agency through the contract 4000115299/15/D/MB, Planetary Protection Compliance Verification Software. Technical Responsible University of Southampton: Camilla Colombo, c.colombo@soton.ac.uk Numerical analysis of the compliance of interplanetary CubeSats with planetary protection requirements Questions? Francesca Letizia Astronautics Research Group Faculty of Engineering and the Environment University of Southampton f.letizia@soton.ac.uk