  We present precise radial velocity observations of WASP-47, a star known to
host a hot Jupiter, a distant Jovian companion, and, uniquely, two additional
transiting planets in short-period orbits: a super-Earth in a ~19 hour orbit,
and a Neptune in a ~9 day orbit. We analyze our observations from the HARPS-N
spectrograph along with previously published data to measure the most precise
planet masses yet for this system. When combined with new stellar parameters
and reanalyzed transit photometry, our mass measurements place strong
constraints on the compositions of the two small planets. We find unlike most
other ultra-short-period planets, the inner planet, WASP-47 e, has a mass (6.83
+/- 0.66 Me) and radius (1.810 +/- 0.027 Re) inconsistent with an Earth-like
composition. Instead, WASP-47 e likely has a volatile-rich envelope surrounding
an Earth-like core and mantle. We also perform a dynamical analysis to
constrain the orbital inclination of WASP-47 c, the outer Jovian planet. This
planet likely orbits close to the plane of the inner three planets, suggesting
a quiet dynamical history for the system. Our dynamical constraints also imply
that WASP-47 c is much more likely to transit than a geometric calculation
would suggest. We calculate a transit probability for WASP-47 c of about 10%,
more than an order of magnitude larger than the geometric transit probability
of 0.6%.
