GTOC 6 Report

29th October 2012, Pasadena

GTOC 6 REPORTTeam 5

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

… and its Mascot

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)

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

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

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

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

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

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

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

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

Transfer legs (II)

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

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

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

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

Winning Trajectory (IV)

# of flybys

# of hit faces

Satellite Revs

Resonances used Notes

Callisto 20 20 25 1:1 2:3 2 useful faces hit during capture

Ganymede 26 23 37 1:1 3:2 6 useful faces hit during capture

Europa 28 28 52 1:1 4:5 5:4 4:3 No repetitions

Io 33 32 71 1:1 5:4 4:3 One face repeated

Europa (II) 4 4 9 1:1 4:5 4:3 Complete the coverage

Ganymede (II) 2 2 1 1:1 One face missed

Summary of the resonant flyby sequences

Winning Trajectory (V) J = 311

TOF =1453.3 days

# offlybys

# of hit faces

# of repetitions

Callisto 22 22 0Ganymede 36 31 5Europa 32 32 0Io 33 32 1

TOTAL 123 117 6

Final mass = 1016.8 kg

207 revs around Jupiter

Initial Epoch: 59527.4 MJD 09-Nov-21 09:42:55 UT

Envisaged improvement Less redundant Ga coverage (2 Ga periods saved)

Fast hyperbolic legArrival 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