Rudolf Dvorak, Christoph Lhotka, Liyong Zhou
Recently the first Earth Trojan has been observed (Connors et al., Nature
475) and found to be on an interesting orbit close to the Lagrange point L4. In
the present study we therefore perform a detailed investigation on the
stability of its orbit and moreover extend the study to give an idea of the
probability to find additional Earth-Trojans. Our results are derived using
different approaches: a) we derive an analytical mapping in the spatial
elliptic restricted three-body problem to find the phase space structure of the
dynamical problem. We explore the stability of the asteroid in the context of
the phase space geometry, including the indirect influence of the additional
planets of our Solar system. b) We use precise numerical methods to integrate
the orbit forward and backward in time in different dynamical models. Based on
a set of 400 clone orbits we derive the probability of capture and escape of
the Earth Trojan asteroids 2010 TK7. c) To this end we perform an extensive
numerical investigation of the stability region of the Earth's Lagrangian
points. We present a detailed parameter study in the regime of possible stable
tadpole and horseshoe orbits of additional Earth-Trojans, i.e. with respect to
the semi-major axes and inclinations of thousands of fictitious Trojans. All
three approaches underline that the Earth Trojan asteroid 2010 TK7 finds
himself in an unstable region on the edge of a stable zone; additional
Earth-Trojan asteroids may be found in this regime of stability.
View original:
http://arxiv.org/abs/1202.1086
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