Orbital Motion of HR 8799 b,c, d using Hubble Space Telescope data from   1998: Constraints on Inclination, Eccentricity and Stability
  HR 8799 is currently the only multiple-planet system that has been detected with direct imaging, with four giant planets orbiting at large separations 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 HST NICMOS coronagraph in 1998. The detection of all three planets is made possible by a careful optimization of the LOCI algorithm. 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 (ed = 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 ed < 0.46. 
Remi Soummer, J. Brendan Hagan, Laurent Pueyo, Adrien Thormann,   Abhijith Rajan, Christian Marois
astro-ph.EP