Global mapping of Jupiter's Galilean moons by flybys (GTOC6)

Steer a low-thrust spacecraft around Jupiter so that its close flybys of Io, Europa, Ganymede and Callisto pass over as much of each moon's surface as possible within four years. The sixth Global Trajectory Optimisation Competition (2012) scored this with a soccer-ball grid on each moon; the theoretical maximum is 324, the winners reached 311, a search after the competition reached 316, and whether 324 can be reached at all is still debated.

Task

• Start: at a range of 1000 Jupiter radii ($R_J=71{,}492$ km) and a speed of 3.4 km/s relative to Jupiter, in any direction, at a time between MJD 58849 and 62867 (the years 2020 to 2030).
• Spacecraft: initial mass 2000 kg; thrust up to 0.1 N with specific impulse 2000 s, in any direction, while the mass stays above 1000 kg.
• Dynamics: Jupiter is a point mass and the Sun is ignored; the four moons move on the Keplerian orbits given in the statement and act only through patched-conic flybys, which must match the moon's position (to 1 km) and keep an altitude of at least 50 km. The range to Jupiter must stay at or above $2R_J$, and the final flyby must come within 4 years of the start.
• Radiation penalty: after each flyby the mass drops by $5\sum_i\big[1-\big(\tfrac{r_{p,i}/R_J-2}{15}\big)^2\big]\big(1+\tfrac{1}{1+r_{a,i}/R_J-r_{p,i}/R_J}\big)$ kg, summed over the bound close approaches to Jupiter since the previous flyby with perijove $r_{p,i}<17R_J$ ($r_{a,i}$ is the osculating apojove).

Score. Each moon's surface is divided into the 32 pentagons and hexagons of a truncated icosahedron (a soccer ball), fixed in the moon's body frame. A flyby with altitude between 50 and 2000 km scores the face that its closest-approach vector passes through, if that face has not been scored before:

$$J=\sum_{\text{flybys}}W_S\,F_V,$$

with $W_S=2$ for Europa and 1 for the other moons, and face values $F_V$ of 1, 2 or 3 (faces 1–8, 9–14 and 27–32, and 15–26 have values 1, 2, 3 on Io and Europa and 3, 2, 1 on Ganymede and Callisto). Higher is better; covering every face gives $J=324$.

Background

GTOC6 was set by Anastassios Petropoulos of JPL's Outer Planets Mission Analysis Group and released on 10 September 2012; 33 teams registered and had a month to answer. The GTOC portal called it the most difficult GTOC problem released up to then, and noted its relevance to the Jupiter Europa Orbiter concept as a demonstration that flybys, rather than orbiters, can map the moons globally. It replaces the asteroid-selection puzzles of earlier editions with a choice of flyby geometries among just four bodies.

Data and evaluation

• Instance: one fixed problem; the problem statement gives the moon orbits, the face vertices and every constant.
• Evaluation: there is no public verifier. A check must re-integrate the submitted trajectory (at the time steps the statement prescribes), confirm each flyby, the perijove and mass limits and the radiation penalty, and recompute $J$ from the flyby geometry.
• Hardware: none assumed; the score does not depend on run time.

What is known

• Final ranking (GTOC portal): Politecnico di Torino with Sapienza University of Rome won with $J=311$ from 123 flybys, mapping part of Callisto, then all of Ganymede, Europa and Io in turn. ESA's Advanced Concepts Team with the Hong Kong University of Science and Technology was second with 308, switching moons much more often; the University of Texas at Austin was third with 267.
• After the competition, Izzo et al. (2013) found a trajectory scoring 316 with self-adaptive differential evolution and an asynchronous island model; Petropoulos validated it.
• The portal notes that it is debated whether 324 can be reached.

What would count as progress

• A trajectory scoring above 316 that meets every constraint, with its flyby list and full trajectory for re-integration.
• A proof that 324 cannot be reached under these rules, or a trajectory that reaches it.
• An open-source verifier for GTOC6, validated on a published solution such as the winning trajectory of Colasurdo et al. (2014).

References

1. A. E. Petropoulos. Problem description for the 6th Global Trajectory Optimisation Competition. Jet Propulsion Laboratory, 2012. Archived PDF
2. G. Colasurdo, A. Zavoli, A. Longo, et al. Tour of Jupiter Galilean moons: Winning solution of GTOC6. Acta Astronautica 102, 190–199 (2014). doi:10.1016/j.actaastro.2014.06.003
3. D. Izzo, L. F. Simões, M. Märtens, et al. Search for a grand tour of the Jupiter Galilean moons. Proceedings of GECCO 2013, 1301–1308. doi:10.1145/2463372.2463524
4. GTOC6 rankings. Archived PDF

Source

Imported from GTOC Portal, GTOC 6 – Global mapping of Galilean moons, curated by the ESA Advanced Concepts Team. The competition closed in October 2012; the problem stays public and is used as a benchmark. The portal could not be reached on 2026-10-20, so this write-up relies on an archived copy of the page. The statement above is written in our own words; see the source for the original wording, history and discussion.