... (=HZ)

Roughly speaking this is the zone where water can be in a liquid state, Kasting (1993). The problem of habitable regions around a host star, which is still somewhat in contradiction, will not be discussed. It depends on the dynamical parameters of the orbits of a planet there, but also on the spectral type and the age of the host star (e.g. Lammer et al. 2003).

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... Trojan

Trojans are two groups of asteroids that move close to the equilateral equilibrium points (Lagrange points L₄ and L₅) formed by the Sun, Jupiter and the asteroid. Consequently the Jupiter Trojans are moving either close to $60^{\circ}$ ahead or $60^{\circ}$ behind Jupiter with the same semimajor axis as the planet.

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... Schneider

http://exoplanet.eu/

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... Lie-integration

A high order integration method with an automatic step-size control.

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... planets

50 percent larger to take into account the influence of the inclination of the orbits with respect to the line of sight of the observations.

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...$\omega$

The mean anomaly of the planet and the fictitious Trojan planet was always set to 0. This choice of initial conditions ensures that for $\omega = 0$ the star - the inner planet - and the Trojan form an equilateral triangle.

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... 9)

These additional computations were undertaken according to a proposition of the referee to take into consideration the possible inclination of the orbits.

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