  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.
