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Astron. Astrophys. 354, 1091-1100 (2000)

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3. Numerical setup

The equations of motion for (1868) Thersites, as well as for a distribution of fictitious asteroids, were integrated for 50 Myrs using the Lie integration method (Lichtenegger, 1984; Hanslmeier & Dvorak, 1984). The dynamical model used in this integration was the Outer Solar System (OSS), consisting of the Sun and the four giant planets (Jupiter-Saturn-Uranus-Neptune) gravitationally interacting. The mass of the Sun was increased by the sum of the masses of the inner planets 2. Relativistic corrections were not taken into account. Our initial distribution can be separated into a group of Thersites' `clones' (C-group) and a group of `neighbors' (N-group).

The N-group is composed of 16 fictitious asteroids whose initial conditions were taken by adding small deviations [FORMULA] (shown in Table 1) to the initial values of the elements used for Thersites. The initial conditions for Thersites, taken from the catalogue of Bowell et al. (1994), are [FORMULA] AU, [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA]. Following the standard notation of celestial mechanics, a denotes the semi-major axis of a body, e the eccentricity, i the inclination of the plane of motion to the invariant plane, [FORMULA] the argument of perihelion, [FORMULA] the longitude of the ascending node and M the mean anomaly.


Table 1. Classification of the orbits. A `name' is given to each orbit in the first column. The initial deviation from the elements of (1868) Thersites is given in the second column. The third column labels the orbit, according to the classification made in Sect. 3. The escape time, [FORMULA], is also given for the ESC-orbits (fourth column).

Since Thersites lies on a chaotic orbit, it is only natural to expect that the results of two numerical integrations conducted in two different machines will not be the same; this is certainly true for integration times much longer than the Lyapunov time, [FORMULA], which, in this case, is about [FORMULA] years (Milani et al., 1997). In fact, numerical noise produced in different machines can alter the final outcome when integrating chaotic orbits. For this reason 5 `clones' of Thersites (the [FORMULA]group) were integrated using the same model, numerical scheme, accuracy and initial conditions, but on different machines.

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© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000