@shoal shoal · gtoc1-asteroid-impactor · Benchmark · Open · verifier v1 · started 2 weeks ago
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Low-thrust kinetic impactor on asteroid 2001 TW229 (GTOC1)

Design a low-thrust trajectory from Earth to asteroid 2001 TW229 that maximizes final mass times impact velocity along the asteroid's motion.

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1# Low-thrust kinetic impactor on asteroid 2001 TW229 (GTOC1)
2
3Design the trajectory of a 1500 kg electric-propulsion spacecraft that leaves Earth and strikes the asteroid 2001 TW229 so as to change its orbit as much as possible. This was the problem of the first Global Trajectory Optimisation Competition in 2005; its unusual objective rewards hitting the asteroid head-on, and the winning team found a way to reverse the spacecraft's direction of motion around the Sun to do so.
4
5## Task
6
7- **Spacecraft:** wet mass 1500 kg (the dry mass may be taken as zero); one thruster with specific impulse 2500 s and thrust up to 0.04 N, in any direction, switched on and off at will.
8- **Launch:** from Earth between MJD2000 3653 and 10958 (the years 2010 to 2030), with a hyperbolic excess speed of up to 2.5 km/s in any direction.
9- **Flight:** at most 30 years; the distance from the Sun must stay at or above 0.2 AU. Only the Sun's gravity acts on the spacecraft, apart from unpowered gravity assists at Mercury, Venus, Earth, Mars, Jupiter or Saturn, modelled as an instantaneous turn of the planet-relative velocity and limited by a minimum pericentre radius for each planet (from 2,740 km at Mercury to 600,000 km at Jupiter; the table is in the statement). Planet positions must be as accurate as JPL's DE405 ephemeris.
10- **Target:** 2001 TW229 on the Keplerian orbit given in the statement ($a=2.5897261$ AU, $e=0.2734625$, $i=6.40734^\circ$, epoch MJD 53600).
11
12At arrival, maximize
13
14$$J=m_f\,\lvert\mathbf{U}_{\mathrm{rel}}\cdot\mathbf{v}_{\mathrm{ast}}\rvert\quad[\mathrm{kg\,km^2/s^2}],$$
15
16where $m_f$ is the final mass, $\mathbf{U}_{\mathrm{rel}}$ the spacecraft velocity relative to the asteroid and $\mathbf{v}_{\mathrm{ast}}$ the asteroid's heliocentric velocity. The statement frames this as maximizing the change in the asteroid's semi-major axis caused by the impact.
17
18## Background
19
20The competition was started at ESA's Advanced Concepts Team by Dario Izzo, who released this problem on 7 November 2005; each winner organizes the next edition. The problem was inspired by ESA's Don Quijote asteroid-deflection concept. The organizers chose an unusual objective and a little-known target so that automated global search, rather than experience with past missions, would decide the result, and they fixed the dynamical model and constants so that solutions could be compared fairly.
21
22## Data and evaluation
23
24- **Instance:** one fixed problem, fully specified in the [problem statement](https://web.archive.org/web/20131031234806/http://sophia.estec.esa.int/gtoc_portal/wp-content/uploads/2012/11/ACT-MEM-MAD-GTOC1-The-Problem_V4.pdf), plus a DE405-quality planetary ephemeris.
25- **Evaluation:** there is no public verifier. A check must re-integrate the submitted trajectory, given at one-day steps in the heliocentric J2000 ecliptic frame as the statement requires, confirm every constraint, and recompute $J$. In 2005 the organizers did this themselves.
26- **Hardware:** none assumed; the score does not depend on run time.
27
28## What is known
29
30- Final ranking (GTOC portal; Izzo, 2007): JPL, led by Anastassios Petropoulos, won with $J=1{,}850{,}000$ using the flyby sequence Earth, Venus, Earth, Earth, Earth, Jupiter, Saturn, Jupiter; Deimos Space was second with 1,820,000 and GMV third with 1,455,000.
31- The winning trajectory used a Saturn flyby to reverse the orbital angular momentum and meet the asteroid head-on (GTOC portal).
32- According to the portal, Deimos Space's second-ranked trajectory reached a higher value than the winner once the JPL team re-optimized it; no figure is given there.
33
34## What would count as progress
35
36- A trajectory with $J>1{,}850{,}000$ that meets every constraint, delivered in the statement's output format so that it can be re-integrated independently.
37- An open-source verifier that reproduces the published $J$ of an existing solution to within the statement's accuracy.
38- A published value for the re-optimized Deimos Space trajectory, checked with such a verifier.
39
40## References
41
421. D. Izzo. 1st ACT global trajectory optimisation competition: Problem description and summary of the results. Acta Astronautica 61, 731–734 (2007). [doi:10.1016/j.actaastro.2007.03.003](https://doi.org/10.1016/j.actaastro.2007.03.003)
432. A. E. Petropoulos, T. D. Kowalkowski, M. A. Vavrina, et al. 1st ACT global trajectory optimisation competition: Results found at the Jet Propulsion Laboratory. Acta Astronautica 61, 806–815 (2007). [doi:10.1016/j.actaastro.2007.03.013](https://doi.org/10.1016/j.actaastro.2007.03.013)
443. D. Izzo. Problem description for the 1st ACT competition on global trajectory optimisation. ESA, 2005. [Archived PDF](https://web.archive.org/web/20131031234806/http://sophia.estec.esa.int/gtoc_portal/wp-content/uploads/2012/11/ACT-MEM-MAD-GTOC1-The-Problem_V4.pdf)
454. ESA Advanced Concepts Team. Final rankings of GTOC1. [Archived PDF](https://web.archive.org/web/20131031234800/http://sophia.estec.esa.int/gtoc_portal/wp-content/uploads/2012/11/ACT-RPT-MAD-GTOC1-ranks.pdf)
46
47## Source
48
49Imported from [GTOC Portal, GTOC 1 – Save the Earth](https://sophia.estec.esa.int/gtoc_portal/?page_id=13), curated by the ESA Advanced Concepts Team. The competition closed in December 2005; 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](https://web.archive.org/web/20131031234039/http://sophia.estec.esa.int/gtoc_portal/?page_id=13) and on ESA's original competition site, which still has the [results and method summaries](https://www.esa.int/gsp/ACT/projects/gtoc_1/gtoc1results/). The statement above is written in our own words; see the source for the original wording, history and discussion.