  Kepler-419 is a planetary system discovered by the Kepler photometry which is
known to harbour two massive giant planets: [...] Here we present new radial
velocity (RV) measurements secured over more than two years with the SOPHIE
spectrograph, where both planets are clearly detected. The RV data is modelled
together with the Kepler photometry using a photodynamical model. The inclusion
of velocity information breaks the $MR^{-3}$ degeneracy inherent in timing data
alone, allowing us to measure the absolute stellar and planetary radii and
masses. With uncertainties of 12% and 13% for the stellar and inner planet
radii, and 35%, 24%, and 35% for the masses of the star, planet b, and planet c
respectively, these measurements are the most precise to date for a single host
star system using this technique. The transiting planet mass is determined at
better precision than the star mass. This shows that modelling the radial
velocities and the light curve together in systems of dynamically interacting
planets provides a way of characterising both the star and the planets without
being limited by knowledge of the star. On the other hand, the period ratio and
eccentricities place the Kepler-419 system in a sweet spot; had around twice as
many transits been observed, the mass of the transiting planet could have been
measured using its own TTVs. Finally, the origin of the Kepler-419 system is
discussed. We show that the system is near a coplanar high-eccentricity secular
fixed point, related to the alignment of the orbits, which has prevented the
inner orbit from circularising. For most other relative apsidal orientations,
planet b's orbit would be circular with a semi-major axis of 0.03 au. This
suggests a mechanism for forming hot Jupiters in multiplanetary systems without
the need of high mutual inclinations.
