1. The Three Trojan Problem 5th Austrio-Hungarian Workshop April, 9th – April, 10th Vienna Observatory

2. The five Lagrange points SUN + JUPITER

3. Equilibrium point L_4

4. What happens when we have not only 2 equilibrium points but several– a whole ring of celestial bodies around a central body?

8. Full cercles –stable orbits 2 3 4 5 6

9. 7 8 9

11. 1 m_E 100 m_E Libration around ‚L_4‘

12. 1000 M_E 1600 M_E Libration around ‚L_4‘

13. 6 M_E 60 M_E Libration Libration Initial distance from central Trojan

15. pp a=a+0.01 a=a+0.02

16. a=a-0.01 a=a-0.02

17. a=a+0.01 a=a-0.01 a=a+0.02 a=a-0.02

19. JJJ Three equal masses Extension to very large masses 1500 = 5 M_Jup

20. EJE Two equal masses Extension to very large masses 1500 = 5 M_Jup

21. Conclusions Stable region around equilibrium points a=a+/-0.02 m<1500 m_E Libration for L_4 for l<~100deg Ongoing study: Mass ratios different a=a+/-0.0? Inclinations?