Chaos and resonances in the Edgeworth-Kuiper-belt
Final Report Abstract
The work that was executed in the frame of this DFG project focused on two aspects. A major part of the work was dedicated lo a detailed investigalion of the various resonance regions in the Edgeworth-Kuiper belt with respect to regular and chaotic structures. For our investigations we focused on the 3:5, 4:7 and 1:2 mean motion resonance with Neptune. While the 3:5 mean motion resonance was investigated in detail for the first lime, reasons for some previously unexplained dynamics inside the 4:7 mean motion resonance have been found during the this work. The investigalion of Nesvomy & Roig (2001) have been verified for the 1:2 mean motion resonance and the dynamical behavior of all known asteroids in this region was determined. To calculate the stability of asteroid orbits the new MEGNO chaos indicator (Cincotta, Giordano & Simö (2003)) was implemented and used. As a sub-task the problem of computability of chaos indicators was studied in great detail. A new index for the computability of a chaos indicator (Lyapunov time or MEGNO) was introduced; it reflects the way how the immediate neighborhood of a certain initial point in phase space is structured. In addition lo those numerical investigations new analytical tools for the description of asteroid motion based on the method of Lie-series were developed and applied for the special case of an asteroid moving in the gravitational field of a migrating planet. First ideas for the construction of a new averaging scheme in celestial mechanics have been developed.
Publications
- Tupikova, I. (2007b): Analytical theory for the motion of an asteroid in the gravitational field of migrating planet, Les Journees 2007. Systems de reference spatio-temporels, Paris, 2007
- Sidlichovsky, M., Geriach, E. (2008) Secular evolution of exoplanetary systems and close encounters, Proc. of lAU Symposium 249: EXOPLANETS - Detection, Formation and Dynamics 479-484.
- Geriach, E. (2008) On the numerical computability of Lyapunov times, International Conference on the Dynamics of Celestial Bodies, Litohoro, Greece, 23.-26.06.2008.
- Geriach, E., (2008) Stabilitätsuntersuchungen an Asteroidenbahnen in ausgewählten Bahnresonanzen des Edgeworth.Kuiper-Gürtels, Dissertation, TU Dresden
- Geriach, E., Klioner, S., (2006) "On the numerical Computability of Chaos Indicators", 26th General Assembly, lAU, 14.-25. Aug., Prag V
- Sidlichovsky, M., Geriach, E. (2008) Secular evolution of exoplanetary systems and close encounters, lAU Symposium 249: EXOPLANETS - Detection, Formation and Dynamics, Suzhou, China, 22.-26.10.2007.
- Tupikova, I. (2007) Perturbation theory for asteroid motion in the gravitational field of a migrating planet, Conf. "Analytical Methods of Celestial Mechanics ", St.-Petersburg, 2007
- Tupikova, I., (2008) Towards an analytical theory for asteroid motion with fully interacting perturbing planets, 7th Alexander v.Humboldt Coll. for Celest. Mechanics, Bad Hofgastein, 2008
