GIVEN THE FAR-REACHING SUCCESS OF THE CASSINI MISSION IT IS CURIOUS AND DISTURBING THAT WE STILL DO NOT UNDERSTAND THE BOMBARDMENT HISTORY OF SATURN S SATELLITES. THIS IS DESPITE THE FACT WE NOW HAVE EXCEPTIONAL IMAGERY OF SATURN S MOONS AND THAT MANY GROUPS HAVE REPORTED ON THEIR CRATER HISTORIES (E.G. KIRCHOFF ET AL. 2009). AS WE SHOW IN THIS PROPOSAL THESE CRATER DATA WHEN CONSIDERED AS A SYSTEM RATHER THAN MOON BY MOON REVEAL SEVERAL INTRIGUING PROBLEMS: 1. THE WAVY CRATER SIZE FREQUENCY DISTRIBUTIONS (SFDS) FOUND ON MIMAS-SIZED BODIES FROM CALLISTO TO MIMAS-IAPETUS ARE REMARKABLY SIMILAR IN SHAPE TO ONE ANOTHER. SHOCKINGLY THIS SHAPE ALSO MATCHES THE SFD OF MAIN BELT ASTEROIDS. DYNAMICALLY ASTEROIDS ARE UNLIKELY TO BE A MAJOR SOURCE OF IMPACTORS FOR SATURN S MOONS SO WHAT DOES THIS MEAN? 2. MIMAS LOCATED DEEP INSIDE SATURN S GRAVITY WELL AT ~3 RSATURN HAS NEARLY THE SAME CRATER SIZE FREQUENCY DISTRIBUTION PER KM+2 AS DISTANT IAPETUS AT ~60 RSATURN. THIS IS SURPRISING; NEITHER SHOWS SIGNS OF RESURFACING AND GRAVITATIONAL FOCUSING OF COMETS THROUGH SATURN S SYSTEM SHOULD CREATE 17 MORE IMPACTS PER KM+2 ON MIMAS THAN IAPETUS! ACCORDINGLY CRATER DATA ON SATURN S MOONS CHALLENGES OUR SATELLITE FORMATION-EVOLUTION MODELS. UNTIL INTERPRETED WE CANNOT EASILY ATTACK KEY DECADAL SURVEY GOALS (E.G. WHEN/HOW DID SATURN S MOONS FORM WERE THEY AFFECTED BY GAS GIANT MIGRATION WHEN WERE GEOLOGIC PROCESSES ACTIVE ON SATURN S MOONS AND DID IMPACTS HEAT UP OR DELIVER ORGANICS TO SATURN S MOONS?). HERE WE PROPOSE TO ATTACK THESE PROBLEMS BY MODELING IMPACTORS STRIKING THESE SATELLITES COMPARING OUR RESULTS TO PUBLISHED CRATER AND SATELLITE GRAVITY DATA AND THEN USING THE RESULTS TO CONSTRAIN UNEXPLORED ASPECTS OF THE NICE MODEL . IN THE NICE MODEL GIANT PLANET MIGRATION SCATTERED A DISK OF PLANETESIMALS ONCE LOCATED BEYOND NEPTUNE. THIS DISK WAS COLLISIONALLY-EVOLVED LIKE THE MAIN BELT WHICH GAVE IT A WAVY MAIN BELT-LIKE SFD. THIS PROCESS NOT ONLY SENT COMET-LIKE BODIES THROUGH SATURN S SYSTEM WHERE MANY HIT SATELLITES BUT IT ALSO CAPTURED COMETS INTO ORBIT AROUND SATURN VIA SATURN-GIANT PLANET ENCOUNTERS. WHILE SOME BECAME STABLE IRREGULAR SATELLITES (NESVORNY ET AL. 2007) MANY MORE SHOULD HAVE STRUCK THE OUTERMOST REGULAR SATELLITES. WE ARGUE THESE IRREGULAR SATELLITES REPRESENT A MISSING BOMBARDMENT POPULATION THAT CAN EXPLAIN WHY MIMAS TO IAPETUS HAVE SIMILAR CRATER SFDS (I.E. ALL PROJECTILES CAME FROM SAME SOURCE) AND WHY HIGH CRATER SPATIAL DENSITIES ARE FOUND ON HYPERION/IAPETUS (I.E. IRREGULARS PREFER HITTING DISTANT MOONS). BY MODELING THIS SCENARIO WE CAN INTERPRET THE HISTORIES OF SATURN S SATELLITES AS TOLD BY THEIR CRATERS AND ALSO DATE THEIR GEOLOGIC FEATURES. OUR TASKS ARE: TASK 1. USING PUBLISHED RESULTS FROM COI NESVORNY'S LATEST VERSION OF THE NICE MODEL WE WILL USE NUMERICAL SIMULATIONS TO TRACK THE ORBITAL HISTORIES IMPACT RATES AND COLLISION VELOCITIES FOR BOTH HELIOCENTRIC PROJECTILES AND CAPTURED IRREGULAR SATELLITES STRIKING SATURN S SATELLITES. TASK 2. APPLYING AN IMPROVED ESTIMATE OF THE PRIMORDIAL DISK SFD ONCE LOCATED BEYOND NEPTUNE TO OUR TASK 1 RESULTS WE WILL INTERPRET CASSINI-DERIVED CRATER RECORDS FROM MIMAS TO PHOEBE DURING THE LATE HEAVY BOMBARDMENT AND GENERATE A NEW CHRONOLOGY FOR GEOLOGIC PROCESSES ON THESE WORLDS. WE WILL ALSO EXPLORE (I) THE LEADING/TRAILING CRATER POPULATIONS FOUND ON RHEA/IAPETUS (II) WHETHER SPECIFIC CRATER SFDS ARE SATURATED (E.G. MIMAS HYPERION) AND (III) HOW COLLISIONAL EVOLUTION AMONG CAPTURED IRREGULARS AFFECTED CRATER PRODUCTION ON PHOEBE. TASK 3. LARGE PROJECTILES CAN DELIVER SUBSTANTIAL IMPACT ENERGY AND HEAT TO SATELLITES. THIS COULD AFFECT THEIR INTERNAL STRUCTURE PRODUCING AN IRREGULAR GRAVITY FIELD OR INDUCE/PRESERVE SUBSURFACE OCEANS. USING OUR IMPACT FLUX MODELS WITH GRAVITY DATA FROM CASSINI FLYBYS WE WILL PROBE THIS ISSUE FOR TETHYS/RHEA USING AN IMPACT-TRIGGERED SATELLITE DIFFERENTIATION MODEL.