29th October 2012, Pasadena
GTOC 6 REPORT
Team 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 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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