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Astron. Astrophys. 361, 379-387 (2000)

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5. The triple system around Upsilon Andromedae

After the submission of the present paper, the evidence that Ups And has two additional planets was reported (Butler et al. 1999). This report provides us with a new occasion to test for the [FORMULA] law in a relative way using a three planet system, as already done for the three planets around the pulsar PSR B1257+12 (Nottale 1996b , 1998b). As can be seen in Fig. 3, the result obtained is very precise. Indeed, we find that the observed periods of the three planets Ups And b, c, d follow the above relation:

[FIGURE] Fig. 3. The system of three planets around Ups And. The observed values of the semi-major axes of the three planet orbits are compared with the possible values predicted for the peaks of probability density, [FORMULA] with [FORMULA] km/s. An excellent agreement is found for [FORMULA]. Note that the large eccentricities of the orbits of planets c and d may explain the emptiness of the other "orbitals".

[EQUATION]

This is a strong indication that [FORMULA], which can be checked directly from the "absolute" analysis (see Table 1) according to which the three planets rank respectively [FORMULA]1, 4, 7 with a precision better than 10%.

Let us compute the probability to get such an agreement of the observed orbital periods with the theoretical prediction for this system. The differences between the observed values of [FORMULA] and the nearest integers for the three planets are respectively 0.09(b), 0.08(c) and 0.09(d). The probability to get such a result by chance is only [FORMULA]. This is confirmed by a Kolmogorov-Smirnov test: we obtain [FORMULA] for 3 points, which corresponds to a 1% probability.

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© European Southern Observatory (ESO) 2000

Online publication: September 5, 2000
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