HR 8799 is currently the only multiple-planet system that has been detected with direct imaging , with four giant planets of masses 7 - 10 M _ { Jup } orbiting at large separations ( 15-68 AU ) from this young late A star .
Orbital motion provides insight into the stability , and possible formation mechanisms of this planetary system .
Dynamical studies can also provide constraints on the planets ’ masses , which help calibrate evolutionary models .
Yet , measuring the orbital motion is a very difficult task because the long-period orbits ( 50-500 yr ) require long time baselines and high-precision astrometry .
This paper studies the three planets HR 8799b , c and d in the archival data set of HR 8799 obtained with the Hubble Space Telescope ( HST ) NICMOS coronagraph in 1998 .
The detection of all three planets is made possible by a careful optimization of the LOCI algorithm , and we used a statistical analysis of a large number of reduced images .
This work confirms previous astrometry for planet b , and presents new detections and astrometry for c and d. These HST images provide a ten-year baseline with the discovery images from 2008 , and therefore offer a unique opportunity to constrain their orbital motion now .
Recent dynamical studies of this system show the existence of a few possible stable solutions involving mean motion resonances , where the interaction between c and d plays a major role .
We study the compatibility of a few of these stable scenarios ( 1d:1c , 1d:2c , or 1d:2c:4d ) with the new astrometric data from HST .
In the hypothesis of a 1d:2c:4b mean motion resonance our best orbit fit is close to the stable solution previously identified for a three-planet system , and involves low eccentricity for planet d ( e _ { d } = 0.10 ) and moderate inclination of the system ( i = 28.0 deg ) , assuming a coplanar system , circular orbits for b and c , and exact resonance with integer period ratios .
Under these assumptions , we can place strong constraints on the inclination of the system ( 27.3 - 31.4 deg ) and on the eccentricity for d e _ { d } < 0.46 .
Our results are robust to small departures from exact integer period ratios , and consistent with previously published results based on dynamical studies for a three-planet system prior to the discovery of the fourth planet .