* Astronomy

Asteroid 2010 TK7 is the first Earth trojan asteroid to be discovered; it precedes Earth in its orbit around the Sun.
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On July 27, 2011, astronomers reported a trojan asteroid companion, 2010 TK7, librating around the leading Lagrange triangular point, L4, of Earth in Earth's orbit around the Sun.
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Title: The orbit of 2010 TK7. Possible regions of stability for other Earth Trojan asteroids
Authors: 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.

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The 200 - 450 metre wide asteroid 2010 TK7 will make a close pass (77.5 lunar distances, 0.1991 AU), travelling at 14.62 km/second, to the Earth-Moon system on the 5th December, 2011 @ 20:14 UT ±00:01.

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The Lunar Distance (LD), the distance between Earth and the Moon, equals 384,401 km, (or 0.00256 AU).

According to news reports I have just read and partially understood, Alberta space scientist Martin Connors and his colleagues recently spotted Earth's first "Trojan asteroid," a teeny-tiny space rock that has apparently been happily cruising along with us as we orbit the sun since our planet was formed.
Our itsy-bitsy space companion, known affectionately at the moment as Asteroid 2010 TK7, is about 300 metres across, located anywhere from 20 million to 50 million kilometres away, and reportedly makes a nifty dancing motion as it leads our planet in its dizzying journey around the sun.
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