  WASP-47 hosts a remarkable planetary system containing a hot Jupiter (WASP-47
b; P = 4.159 days) with an inner super-Earth (WASP-47 e; P = 0.7896 days), a
close-orbiting outer Neptune (WASP-47 d; P = 9.031 days), and a long period
giant planet (WASP-47 c; P = 588.4 days). We use the new TESS photometry to
refine the orbital ephemerides of the transiting planets in the system,
particularly the hot Jupiter WASP-47 b, for which we find an update equating to
a 17.4 min shift in the transit time. We report new radial velocity
measurements from the ESPRESSO spectrograph for WASP-47, which we use to refine
the masses of WASP-47 d and WASP-47 e, with a high cadence observing strategy
aimed to focus on the super-Earth WASP-47 e. We detect a periodic modulation in
the K2 photometry that corresponds to a 32.5$\pm$3.9 day stellar rotation, and
find further stellar activity signals in our ESPRESSO data consistent with this
rotation period. For WASP-47 e we measure a mass of 6.77$\pm$0.57 M$_{\oplus}$
and a bulk density of 6.29$\pm$0.60 gcm$^{-3}$, giving WASP-47 e the second
most precisely measured density to date of any super-Earth. The mass and radius
of WASP-47 e, combined with the exotic configuration of the planetary system,
suggest the WASP-47 system formed through a mechanism different to systems with
multiple small planets or more typical isolated hot Jupiters.
