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GTOC 6 Report

Team 5. GTOC 6 Report. 29 th October 2012, Pasadena. Team 5. Lorenzo Casalino , professor † Guido Colasurdo , professor ‡ Stefano Federici , master student ‡ Francesca Letizia , PhD student †

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GTOC 6 Report

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  1. Team 5 GTOC 6 Report 29th 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 ‡ †Politecnicodi Torino - Dip. diIngegneriaMeccanica e Aerospaziale ‡Universitàdi Roma ‘Sapienza’ - Dip. diIngegneriaMeccanica 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-Gasynodic 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-Gasynodic 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

  10. 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

  11. 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

  12. 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-Gasynodic periods keeping a good capture maneuver • Transfers are essentially ballistic • Precise phasing between moons is needed

  13. Transfer legs (II)

  14. 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

  15. Winning Trajectory • Initial Design J = 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

  16. Winning Trajectory (II) • First Improvement J = 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

  17. Winning Trajectory (III) • Second Improvement J = 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

  18. Winning Trajectory (IV) Summary of the resonant flyby sequences

  19. Winning Trajectory (V) • Final mass = 1016.8 kg • 207 revs around Jupiter • J = 311 • TOF =1453.3 days • Initial Epoch: 59527.4 MJD 09-Nov-21 09:42:55 UT

  20. 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

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