On the Stability of High Inclined L4 and L5Trojans |
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| Authors: | Richard Schwarz Markus Gyergyovits Rudolf Dvorak |
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| Institution: | (1) Institute for Astronomy, University of Vienna, Türkenschanzstr. 17, Vienna, A-1180, Austria |
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| Abstract: | The orbits of real asteroids around the Lagrangian points L4 and L 5of Jupiter with large inclinations (i > 20°) were integrated for 50 Myrs. We investigated the stability with the aid of the
Lyapunov characteristic exponents (LCE) but tested also two other methods: on one hand we integrated four neighbouring orbits
for each asteroid and computed the maximum distance in every group, on the other hand we checked the variation of the Delaunay
element H of the asteroid. In a second simulation – for a grid of initial eccentricity versus initial inclination – we examined the
stability of the orbits around both Lagrangian points for 20° < i < 55° and 0.0 < e < 0.20. For the initial semimajor axes
we have chosen the one ofJupiter(a = 5.202 AU). We determined the stability with the aid of the LCEs and also the maximum
eccentricity of the orbits during the whole integration time. The region around L4 turned out to be unstable for large inclinations and eccentricities (i > 55° and e > 0.12). The stable region shrinks for
orbits around L5: we found that they become unstable already for i > 45° and e > 0.10. We interpret it as a first hint why we observe more
Trojans around the leading Lagrangian point. The results confirm the stability behaviour of the real Trojans which we computed
in the first part of the paper. |
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| Keywords: | high inclinations stability limits Trojans |
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