Chaotic Diffusion Analyses in Regions near the Jupiter 3:2, 2:1, 4:3 Mean-Motion Resonances


Asteroid is one of small body type in the solar system. The complexity of asteroid orbits is an interesting topic in the domain of celestial mechanics. Some of asteroids which are located in region near the Mean Motion Resonance (MMR) of a planet have complex orbits. Hilda�s region (3:2 MMR with Jupiter) is one of these examples.
Indication of orbital complexity is an existence of chaotic diffusion process. Chaotic diffusion process shifts asteroid�s proper orbital elements. In general, for a celestial body, this alteration is hard to detect by observation because of an orbital secular motion. Moreover, this process is also hard to detect with simulation because it needs long time integration with small integration step. Fortunately, in the case of asteroids, this alteration is possible to detect using simulation with massive computational work.

The alteration of proper elements is also caused by thermal effects. The effects only work dominantly in small bodies of solar system. Therefore, chaotic diffusion and thermal effects are two mechanisms which cause the alteration of asteroid�s proper elements.

Chaos is a dynamical state when small perturbation occurring in a system can imply large variation in dynamical behavior of the system. In celestial body dynamics, concept of chaos was proposed after Henri Poincar� concluded that general motion of three-body problem is non-integrable. Besides, the existence of heteroclinic orbit, which later enhanced by Kolmogorov and Arnold, provides many chaotic motions in dynamical system (Laskar 1996).

Chaotic diffusion is a process of transformation of dynamical state from stable to chaotic that occurs in a very long time. The process is found in motions of many celestial bodies in Solar System. Ito & Tanikawa (2002) and Laskar (2008) analyzed chaotic diffusion in motions of all planets. Beyond planets, chaotic diffusion is also found in motion of minor planets (Morbidelli 1997, Robutel et al. 2005, Tsiganis et al. 2005, Tiscareno & Malhorta 2009, Broz & Vokrouhlicky 2008, and Delisle & Laskar 2012).
The process of chaotic diffusion is found more frequent in regions near MMR. Narrow chaotic area in the regions produces small variations in proper orbital elements of minor planets that accumulate slowly. Later this becomes the cause of chaotic diffusion process. Morbidelli (1997) analyzed chaotic diffusion for region near 2:3 MMR in Kuiper belt, whereas Ferraz-Mello et al. (1996) studied it for some regions near MMR in Main belt.

Orbital movement mechanism from stable state to chaotic is not only yielded by chaotic diffusion. The movement can also be resulted from collisions of minor planets and thermal effects acting on them. The movement obtained by collisional and thermal effects depends on sizes of minor planet (small size body is more efficient to move). This is on the contrary with chaotic diffusion which do not depend on sizes of minor planets.

Thus, it will be intriguing to perform numerical simulations to study chaotic diffusion in regions near the Jupiter 3:2, 2:1, 4:3 MMR.

Broz, M. dan Vokrouhlicky, D., 2008, MNRAS, 390, 715.
Delisle, J. �B. dan Laskar, J., 2012, A&A, 540, 118.
Ferraz-Mello, S. et al., 1996, CeMDA, 64, 93.
Ito, T. dan Tanikawa, K., 2002, MNRAS, 336, 483.
Laskar, J., 1995, XIth ICMP Colloquium, Paris.
Laskar, J., 1996, CeMDA, 64, 115.
Laskar, J., 2008, Icarus, 196, 1.
Morbidelli, A., 1997, Icarus, 127, 1.
Robutel, P., Gabern, F., dan Jorba, A., 2005, CeMDA, 92, 53.
Tiscareno, M. S. dan Malhorta, R., 2009, AJ, 138, 827.
Tsiganis, K., Varvoglis, H., dan Dvorak, R., 2005, CeMDA, 92, 71.

Celestial mechanics, method: numeric, chaotic diffusion, orbital resonance

- To comprehend the chaotic diffusion process of asteroids in regions near the MMR 3:2, 2:1, and 4:3 with Jupiter.
- To analyse role of the thermal effects on the orbital dynamics of asteroids in these regions.


Recent references are very helpful for supporting recent development of this study. Numerical experiments are performed by using integrator package (open source) Swift4 which is available in This package can be implemented for thermal effects inclusions in orbital integration.


Advisor: Dr. Budi Dermawan
Student: Ibnu Nurul Huda

6.Computation plan (required processor core hours, data storage, software, etc)

at least 10 (ten)

7.Source of funding
International Journal (one article)
9.Date of usage
01/04/2016 - 31/05/2016
10.Gpu usage
11.Supporting files
12.Created at
13.Approval status