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Unformatted text preview: Restricted four and five body problems in the Solar System Frederic Gabern and ` Angel Jorba CDS Seminar. October 8, 2003. Frederic Gabern Applied Mathematics and Analysis Control and Dynamical Systems University of Barcelona California Institute of Technology 1 Contents Introduction. The Trojan asteroids. Review of the existing results. Motivation for the present work. Periodic models. The Bicircular Coherent Problem. The Elliptic Restricted Three Body Problem. Quasiperiodic models. The Bianular Problem. The Tricircular Coherent Problem. Conclusions. 2 The Trojan asteroids (I) Sun Jupiter 60 60 L5: Trojan asteroids L4: Greek asteroids L 4 : L 5 : Achilles Patroclus Hector Aeneas Nestor Memnon Agamemnon Paris 3 The Trojan asteroids (II) 4 The Trojan asteroids (III) 5 Previous Work The Restricted Three Body Problem Analytic Tools. Semianalytic tools. Theoretical Results m The Outer Solar System Frequency analysis. Lyapunov exponents. Numerical Results 6 The Restricted Three Body Problem The dynamics around the triangular points of the SunJupiter system has been studied using analytical and semianalytical tools (transformation of the Hamiltonian to a normal form , computation of some approximate first integrals ) by several authors: Giorgilli, Delshams, Fontich, Galgani & Simo , 1989; Simo , 1989; Celletti & Giorgilli , 1991; Jorba & Simo , 1994 (in the elliptic case); Giorgilli & Skokos , 1997; Skokos & Dokoumetzidis , 2000. 7 Realistic Model: OSS The dynamics of some jovian Trojan asteroids has been studied in several papers using the Outer Solar System : Bien & Schubart , 1987; Milani , 1993; Levison, Shoemaker & Shoemaker , 1997; PilatLohinger, Dvorak & Burger , 1999; Tsiganis, Dvorak & PilatLohinger , 2000. 8 Some New Models We want to build and study models more sophisticated than the RTBP. These models will try to simulate in a better way the relative SunJupiter motion and they will be written as a RTBP perturbation in order the semianalytical tools can be applied. In this work, we focus on the following models: The Bicircular Coherent Problem ( BCCP ). The Elliptic Restricted Three Body Problem ( ERTBP ). The Bianular Problem ( BAP ). The Tricircular Coherent Problem ( TCCP ). 9 The BCCP Model (I) We look for a periodic solution of the planar SunJupiterSaturn Three Body Problem . The period is chosen to be the relative period of Saturn in the SunJupiter RTBP system: T sat . The osculating eccentricity of Jupiter is small (about 50 times smaller than the real one) but the semimajor axis and the period are quite well adjusted to the actual ones....
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This note was uploaded on 01/04/2012 for the course CDS 280 taught by Professor Marsden,j during the Fall '08 term at Caltech.
 Fall '08
 Marsden,J

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