Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The orbit of 2010 TK7. Possible regions of stability for other Earth
  Trojan asteroids   Recently the first Earth Trojan has been observed (Mainzer et al., ApJ 731)
and found to be on an interesting orbit close to the Lagrange point L4 (Connors
et al., Nature 475). 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.

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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics