ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O B-Instrument O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: are compatible with the literature data and achieve an accuracy similar or better with respect to the published measurements, which is a good test for this new instrument. The orbital fit is a minimum fitting, as described in Esposito et al. (2013) , where all the four orbits are simultaneously taken into consideration, using the assumption that the planet periods are commensurate. The IFS measurement is used for the closest planet e, as it provides smaller error bars. We assumed circular and non-coplanar orbits and tested three different configurations for the orbital period ratios between the planets. The fitted orbits are shown in Fig. 5 . The parameters of the orbital solutions are summarized in Table 7 . The uncertainties on the parameters were estimated using a quadratic combination of statistical and systematic errors. The statistical errors stem from the sensitivity of the fit to the errors bars on the astrometric measurements and are derived from 1000 random trials of the astrometric measurements assuming normal distributions ( Maire et al. 2015 ). The systematic errors are related to the uncertainties on the stellar mass and distance (Table 7 ), which propagate into the derivation of the semimajor axis. To assess them, we performed two sets of orbital fits. The first set assumes the nominal values for the stellar mass and distance, and the second set assumes a combination of values at the edge of the derived ranges, which provides the largest offset in orbital periods. Two orbital solutions are favored with similar reduced , with the orbital period ratios 2d:1e and 3d:1e. The IFS data point for planet e is out of the orbital solution with the orbital period ratio 5d:2e at 2.5 significance level. Further astrometric monitoring is required to distinguish between the orbital period ratios 2d:1e and 3d:1e. Fig. 5 Relative astrometry for the planets around HR 8799. The points available from the literature are represented with black filled circles, while new SPHERE measurements are represented with purple filled squares. The solid blue lines represent the orbital solution labeled A in Table 7 . Red lines connect the predicted and observed positions for all the data points. The dotted and dashed lines in the panel for HR 8799 e indicate the orbital solutions labeled B and C in Table 5, respectively. Table 7 Orbital elements fitted on the astrometric data in Fig. 5 . Notes. Case A: orbital solution setting circular orbits and 8b:4c:2d:1e mean motion resonance. Case B: orbital solution setting circular orbits and 4b:2c:1d and 5d:2e mean motion resonances. Case C: orbital solution setting circular orbits and 4b:2c:1d and 3d:2e mean motion resonances. For each planet, the notations refer to the orbital period, inclination, longitude of the ascending node, eccentricity, argument of periapsis, time of periapsis passage, and semimajor axis. The error bars on the orbital parameters are at 1 (see text). We also indicate the reduced for the nominal