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### Models of the Formation of Saturn's Rings

Saturn's prominent ring system consists primarily of water ice ($H_2O$) with trace amounts of rocky material and organic compounds. Geochemists and astrophysicists have proposed different models to explain the origin of these rings.

Model 1 (Tidal Disruption Model)
According to this model, about $100$ million years ago, a mid-sized, icy satellite (moon) with a rocky core migrated inward toward Saturn due to orbital resonances. As the satellite crossed Saturn's Roche limit (approximately $140,000\text{ km}$ from the center of Saturn), Saturn's gravitational tidal forces overcame the satellite's self-gravity. The outer icy mantle of the satellite was stripped away and spread into a disk, while the denser rocky core spiraled into Saturn. This model predicts that the rings are relatively young (less than $100$ million years old) and consist of highly pure ice because the rocky core was segregated and lost.

Model 2 (Collisional Shattering Model)
According to this model, Saturn's rings are ancient structures formed over $4$ billion years ago during the Late Heavy Bombardment. A population of large, organic-rich comets from the outer solar system was gravitationally pulled toward Saturn. Several of these comets collided at high velocities with pre-existing inner moons of Saturn. The energy of these impacts shattered both the comets and the moons, distributing the fragments into orbit. Because comets and ancient moons contain significant amounts of rocky silicates and complex organic compounds, the primordial ring material originally had a higher concentration of non-ice components, which have since been slowly eroded by micrometeorite bombardment.

Based on the models presented, match each physical description or formation scenario of Saturn's rings to the correct model or models.