Multiple asteroid systems where an asteroid has one or more satellites are interesting subjects to investigate since they provide collisional history of our Solar System and are natural laboratories to study surface alteration processes and evolution for asteroids with different sizes, shapes, densities and environments. 243 Ida in the main asteroid belt (MAB) is the first asteroid to be identified as a binary asteroid in 1994 and the first triple asteroid, 87 Silvia in the MAB, is announced in 2004. Then, in 2021, after the third moon was discovered, and 130 Elektra in the MAB became the first quadruple asteroid to be recognized. Currently, 386 binary asteroids, 13 triple asteroids and 1 quadruple asteroid are identified (trans-Neptunian objects are not included here). NASA’s Double Asteroid Redirection Test (DART) visited the binary asteroid system 65803 Didymos and tested a kinetic impacter technology, and ESA’s Hera mission will visit this binary system for the in-depth exploration. The Brazilian Space Agency (AEB) proposed the ASTER mission [1] to send a spacecraft to a near-Earth triple asteroid system 2001 SN263 which will be the first mission to explore a triple asteroid system.

The dynamics around triple asteroid systems is highly complex and time non-autonomous since the secondary and tertiary asteroids create the chaotic dynamical environment. Several works explore the dynamical environment and orbits around the triple asteroid system 45 Eugenia [2], 87 Sylvia [3] and 2001 SN263 related to ASTER mission [1]. Notably, it is shown that terminator orbits can be quite stable in a chaotic triple asteroid environment for at least a month without any orbital maneuvers [1]. We developed the perturbed Hill restricted five-body problem (PHR5BP) and used to investigate bounded motions around triple asteroid systems in our previous work [4]. Our study demonstrates that various bounded motions can exist, including the quasi-frozen orbits (QFOs), over the period of 100 days depending on the inclinations of the two moonlets. This study also confirms that terminator orbits can be stable for more than 60 days.

Aforementioned existing works consider that the properties of the asteroid systems, such as mass of the asteroids and the orbital elements of the two moonlets, are perfectly determined. However, in reality, these properties are determined with some degree of uncertainties due to the limited observation capability from the Earth. Even if a spacecraft reaches near the asteroid system, it is still challenging to completely eliminate these uncertainties. Since a spacecraft typically stays on one orbit for a couple of weeks to months to conduct scientific observations, these uncertainties would significantly perturb the trajectory, leading to the escape from the system or collision with the asteroids. Thus, it is essential to identify orbits which are robust against these uncertainties in order to ensure the spacecraft safety and mission success. In this study, we investigate the robustness of the previously identified bounded motions including the QFOs and the terminator orbits around a triple asteroid system under the uncertainties of the system properties. A simple station keeping algorithm is also implemented to evaluate the fuel consumption on the robust orbits in comparison to the non-robust orbits. Our objective is to propose stable and robust orbits and station keeping strategy near a triple asteroid system. This work will contribute to the mission and trajectory design for future triple asteroid exploration missions.

References
[1] K. Wickhusen et al. Terminator orbits around the triple asteroid 2001-sn263 in application to the deep space mission aster. Acta Astronautica, 198:631–641, 2022.
[2] RAN Araujo, RV Moraes, AFBA Prado, and OC Winter. Mapping stable direct and retrograde orbits around the triple system of asteroids (45) eugenia. Monthly Notices of the Royal Astronomical Society, 472(4):3999–4006, 2017.
[3] Yu Jiang. Dynamical environment in the triple asteroid system 87 sylvia. Astrophysics and Space Science, 364(4):60, 2019.
[4] Tomohiro Ishizuka, Daniel J. Scheeres, and Stéphanie Lizy-Destrez. Perturbed hill restricted five-body problem applied to a triple asteroid system. Journal of Guidance, Control, and Dynamics, pages 1–15, September 2025.