This paper reports on the validation and mass measurement of K2-263b, a sub-Neptune orbiting a quiet G9V star. Using K2 data from campaigns C5 and C16, we find this planet to have a period of $50.818947pm 0.000094$ days and a radius of $2.41pm0.12$ R$_{oplus}$. We followed this system with HARPS-N to obtain 67 precise radial velocities. A combined fit of the transit and radial velocity data reveals that K2-263b has a mass of $14.8pm3.1$ M$_{oplus}$. Its bulk density ($5.7_{-1.4}^{+1.6}$ g cm$^{-3}$) implies that this planet has a significant envelope of water or other volatiles around a rocky core. EPIC211682544b likely formed in a similar way as the cores of the four giant planets in our own Solar System, but for some reason, did not accrete much gas. The planetary mass was confirmed by an independent Gaussian process-based fit to both the radial velocities and the spectroscopic activity indicators. K2-263b belongs to only a handful of confirmed K2 exoplanets with periods longer than 40 days. It is among the longest periods for a small planet with a precisely determined mass using radial velocities.
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