1. 29 th October 2012, Pasadena

2. Team 5 Lorenzo Casalino, professor † Guido Colasurdo, professor ‡ Stefano Federici, master student ‡ Francesca Letizia, PhD student † Alessandro Longo, PhD student ‡ Dario Pastrone, professor † Francesco Simeoni, PhD Student † Alessandro Zavoli, PhD Student ‡ † Politecnico di Torino - Dip. di Ingegneria Meccanica e Aerospaziale ‡ Università di Roma ‘Sapienza’ - Dip. di Ingegneria Meccanica e Aerospaziale

3. … and its Mascot

4. Introduction  Very complex problem with an embedded rationale  Basic lines of mission are soon available  Computations will suggest improved strategies  Propulsion use is deemed marginal due to low thrust acceleration  Mass is used to pay perijoves penalties  Time is the scarcest resource  Complete coverage is mandatory for Eu (score bonus) and Io (short period)

5. Introduction (II)  High-score faces of Ca and Ga are seeked, skipping some low-score faces  Low-penalty and low-duration sequences of resonant flybys are deemed necessary  Fast capture is needed to start resonant flybys soon  Initial time is kept free till the most convenient phasing between satellites is found  Moon resonances (typically 2:1) make the transfers between satellites difficult  7:3 Ca-Ga resonance complicates the capture and fixes a series of 322 mission time windows

6. Capture  Spacecraft is moved from inbound hyperbole to low-period Ca-resonant orbit  Initial braking is left to Ca and Ga, as Io would help but makes spacecraft orbit too eccentric  Ca and Ga alone are able to put spacecraft into a medium-period orbit  Maneuver can be repeated (rotated by 90°) after an integer number of Ca-Ga synodic periods  Every 4 synodic period the maneuver is repeated with satellites in the same positions

7. Capture (II)  High-V ∞ resonant flybys are necessary to further reduce energy  Low V ∞ is instead necessary to start Ca-resonant flyby sequence  Heavier and faster Ga is preferred for braking  Exterior Ca circularizes orbit and reduces V ∞  Initial Ca-Ga gravity assists put arriving spacecraft into 10:1 or 8:1 Ga-resonant orbit  After a series of Ga-flybys a Ga-Ca-Ga-Ca transfer moves the spacecraft into 1:1 Ca-resonant orbit

8. Capture (III)  Prescribed repeated encounters require adequate Ca-Ga phasing and rule the overall time-length of the capture maneuver  Thrust is used during capture to adjust V ∞ and to correct imperfect phasing  The second Ga-resonant orbit (4:1 with outbound departure and inbound arrival) displaces flyby position on Ga orbit to improve phasing  Moon eccentricity and inclination make a capture every 4 Ca-Ga synodic periods interesting  Indirect optimization is used to improve capture

9. Resonant flybys  V ∞ magnitude and moon position are constant during the whole flyby sequence  Strategies for low-penalty minimum-time complete coverage are assessed by assuming design V ∞  Resonant flybys are recomputed after the transfer legs are defined and actual initial V ∞ is available  Low V ∞ increases flyby rotation but also rotation needed to change resonance  Nevertheless low relative velocities (V ∞ < 2.5 km/s) are preferred for all moons

11. Resonant flybys (II)  Sequences are defined manually, resorting on graphical aids  A reference frame tied to moon velocity is useful  Parallels are loci of the V ∞ corresponding to an assigned m:n resonance  Frame rotation relative to body-fixed frame depends on satellite flight path angle  Maintaining resonance keeps pericentre above equator  Changing resonance moves pericentre at higher latitudes

13. Resonant flybys (III)  For each moon the best resonances are selected  Low m (# of satellite orbits) contains time-length  Low n (# of spacecraft orbits) contains penalties  Resonance 1:1 is normally used  Moving to m:n resonance is immediately followed by return to 1:1, hitting the moon opposite face  On arrival, base 1:1 resonance may be attained directly; sometimes intermediate orbit is needed  Similar problem on leaving base 1:1 resonance to enter the leaving transfer trajectory

14. Transfer legs  From resonance with current moon to resonance with the next one  Initial V ∞ is assigned  Final V ∞ must be suitable for the next sequence  Initial time (i.e., moon position) is assigned  It can be moved forward at step of 4 Ca-Ga synodic periods keeping a good capture maneuver  Transfers are essentially ballistic  Precise phasing between moons is needed

15. Transfer legs (II)

16. Search for mission opportunities  Moon orbits are assumed circular and coplanar  For each moon a range of admissible V ∞ is assigned  For any pair of arrival and departure V ∞ an ellipse is found and four branches are considered  Transfer is feasible if angular and time lengths match the movement of the target moon  Multiple revolutions of the spacecraft are permitted  An additional orbit of departure moon is permitted  Several opportunities are discharged due to eccentricity and inclination effects

17. Winning Trajectory  Initial DesignJ = 308 Features of capture maneuver  First ellipse is 10:1 Ga-resonant orbit  Ga flybys all over northern hemisphere 4 sequences of resonant flybys descending from Callisto to Ganymede, Europa and finally Io 4 Ga faces in southern hemisphere are skipped Europa complete coverage repeats 4 flybys over northern hemisphere

18. Winning Trajectory (II)  First ImprovementJ = 309 Revised capture maneuver  First ellipse is 8:1 Ga-resonant orbit  More time is available during descent  After achieving 2:1 Ga resonance, spacecraft is moved back to 3:1 resonance  A face in Ga northern hemisphere can be hit

19. Winning Trajectory (III)  Second ImprovementJ = 311 Eu resonant flybys  4 useful flybys and 4 repeated flybys are removed  4 flybys are inserted after Io has been fully covered Saved time is used to reach 2 Ga faces in southern hemisphere Transfer between satellites becomes more complex and difficult

20. Winning Trajectory (IV) # of flybys # of hit faces Satellite Revs Resonances usedNotes Callisto20 251:1 2:32 useful faces hit during capture Ganymede2623371:1 3:26 useful faces hit during capture Europa28 521:1 4:5 5:4 4:3No repetitions Io3332711:1 5:4 4:3One face repeated Europa (II) 4 4 91:1 4:5 4:3Complete the coverage Ganymede (II) 2 2 11:1One face missed Summary of the resonant flyby sequences

21. Winning Trajectory (V)  J = 311  TOF =1453.3 days # of flybys # of hit faces # of repetitions Callisto22 0 Ganymede36315 Europa32 0 Io33321 TOTAL1231176  Final mass = 1016.8 kg  207 revs around Jupiter  Initial Epoch: 59527.4 MJD 09-Nov-21 09:42:55 UT

22. Envisaged improvement  Less redundant Ga coverage (2 Ga periods saved)  Fast hyperbolic leg Arrival trajectory as in the initial design No southern Ga face is hit during capture Thrust-Coast-Brake control could save additional time  Saved time is used to hit four southern faces at the end of mission completing Ga coverage  Possible cherry on the cake: a final hit to Callisto