FOLLOW-UP STUDIES OF THE SMALL PLANETS DETECTED BY KEPLER HAVE REVEALED A REMARKABLE DIVERSITY OF PLANET DENSITIES INDICATING THAT PREDICTING PLANETARY PROPERTIES FROM A RADIUS MEASUREMENT ALONE COULD LEAD TO SIGNIFICANT ERRORS IN OUR ESTIMATE OF THE FREQUENCY OF ROCKY (AND POSSIBLY HABITABLE) WORLDS. WE PROPOSE TO STUDY THE RELATIONSHIP BETWEEN THE MASSES RADII INSOLATION AND METALLICITIES OF SMALL PLANETS BY TARGETING MODERATELY BRIGHT STARS WITH K2 CONDUCTING RECONNAISSANCE SPECTROSCOPY AND ULTIMATELY GATHERING HIGHLY PRECISE RADIAL VELOCITY (RV) MEASUREMENTS WITH HARPS-N. OUR GOAL IS TO OBTAIN A MASS PRECISION OF 15% THE MINIMUM VALUE REQUIRED TO DISTINGUISH BETWEEN COMPOSITIONAL MODELS. THIS PROJECT REQUIRES NEW K2 DATA FOR TWO REASONS. FIRST MOST TRANSITING SMALL PLANETS DETECTED BY KEPLER ORBIT STARS TOO FAINT FOR RV OBSERVATIONS AND SOME OF THE BRIGHT KEPLER HOST STARS ARE NOT AMENABLE TO RV OBSERVATIONS BECAUSE OF THE VARIABILITY OF THE HOST STAR OR THE PRESENCE OF NEARBY STARS. SECOND THE ANTICIPATED NUMBER OF SMALL PLANETS ORBITING QUIET BRIGHT STARS DETECTED IN K2 CAMPAIGNS TO DATE IS SMALL AND THE PROPERTIES OF THE SYSTEMS TO DATE DO NOT ADEQUATELY SAMPLE THE DESIRED RANGE OF PLANETARY AND STELLAR PROPERTIES. WE PROPOSE A RANKED LIST OF 10 433 FGKM DWARF STARS THAT ARE BRIGHT ENOUGH FOR RV FOLLOW-UP AND SCHEDULED TO BE OBSERVED IN CAMPAIGNS 17 18 AND 19. WE USED THE AVAILABLE PHOTOMETRY TO REMOVE LIKELY GIANTS AND CONSTRAIN THE PROPERTIES OF THE REMAINING DWARFS. WE WILL ALSO ANALYZE SHORT CADENCE OBSERVATIONS OF FOUR TARGETS THAT WERE FOUND TO HAVE PLANETS IN PREVIOUS K2 CAMPAIGNS AND ARE CURRENT TARGETS FOR MASS MEASUREMENT WITH HARPS-N. WE WILL IDENTIFY PLANET CANDIDATES USING THE PLANET DETECTION PIPELINE DEVELOPED BY OUR TEAM MEMBERS. WE WILL VET CANDIDATES BY MEASURING THE CENTROID SHIFTS ACQUIRING HIGH-RESOLUTION ADAPTIVE OPTICS IMAGES AND GATHERING HIGH-RESOLUTION SPECTRA. WE WILL THEN CONDUCT HARPS-N OBSERVATIONS OF THE BEST CANDIDATES WITH SMALL RADII AND SPANNING THE RANGE OF INSOLATION AND STELLAR METALLICITIES. THE HARPS-N INSTRUMENT LOCATED AT THE TELESCOPIO NAZIONALE GALILEO IN LA PALMA SPAIN IS AN EXTREMELY STABLE FIBER-FED ECHELLE SPECTROGRAPH DESIGNED TO MEASURE RADIAL VELOCITIES WITH EXQUISITE PRECISION. ALL OF THE MEMBERS OF OUR PROPOSAL TEAM ARE MEMBERS OF THE HARPS-N CONSORTIUM WHICH HAS 80 NIGHTS PER YEAR OF GUARANTEED TIME PER YEAR. THE FOLLOW-UP OF SMALL PLANETS FROM KEPLER AND K2 IS THE TOP SCIENTIFIC PRIORITY OF HARPS-N. WE WILL DELIVER THE FOLLOWING VALUE-ADDED COMMUNITY RESOURCE PRODUCTS TO THE NASA ARCHIVES: LIGHT CURVES AND ESTIMATED STELLAR PARAMETERS FOR ALL TARGETS; PHASE-FOLDED LIGHT CURVES AND RECONNAISSANCE SPECTRA FOR PLANET-CANDIDATE HOST STARS; AND TABLES OF PRECISE RADIAL VELOCITIES FOR THE SUBSET OF PLANET CANDIDATE HOST STARS PURSUED BY HARPS-N. OUR TEAM HAS ALREADY DELIVERED SUCH PRODUCTS FOR PREVIOUS K2 CAMPAIGNS; IN PARTICULAR OUR WE HAVE UPLOADED OVER 1000 OF THE 1485 K2 RECONNAISSANCE SPECTRA LISTED ON THE EXOFOPK2 WEBSITE AS OF 11 APRIL 2018. OUR CAMPAIGN TO MEASURE THE MASSES OF SMALL K2 PLANETS WITH PRECISION BETTER THAN 15% WILL HAVE A SIGNIFICANT IMPACT ON OUR UNDERSTANDING OF SMALL PLANETS. BY INCREASING THE NUMBER OF SMALL PLANETS WITH PRECISE MASS AND RADIUS ESTIMATES WE WILL ENABLE INVESTIGATIONS OF THE FRACTION OF ROCKY PLANETS AS A FUNCTION OF PLANETARY AND STELLAR PARAMETERS SUCH AS ORBITAL PERIOD THE PRESENCE OF ADDITIONAL PLANETS AND STELLAR METALLICITY. IMPROVING OUR UNDERSTANDING OF THE RELATIONSHIP BETWEEN THE MASSES AND RADII OF SMALL PLANETS WILL PROVIDE USEFUL INFORMATION WHEN SELECTING TARGETS FOR ATMOSPHERIC CHARACTERIZATION WITH THE JAMES WEBB SPACE TELESCOPE AND PRIORITIZING THE FOLLOW-UP OBSERVATIONS OF PLANETS DETECTED BY THE TRANSITING EXOPLANET SURVEY SATELLITE.