1. The Shock Hugoniot of Solid Ice: We present a complete description of the solid ice Hugoniot based on new shock wave experiments conducted at an initial temperature of 100 K and previously published data obtained at 263 K. We identify five regions on the solid ice Hugoniot: (1) elastic shock waves, (2) ice Ih deformation shocks, transformation shocks to (3) ice VI, (4) ice VII, and (5) liquid water. In each region, data obtained at different initial temperatures are described by a single Us - Δup shock equation of state. The dynamic strength of ice Ih is strongly dependent on temperature. The Hugoniot Elastic Limit varies from 0.05 to 0.62 GPa, as a function of temperature and peak shock stress. We estimate the entropy and temperature along the 100 and 263 K Hugoniots and derive the critical pressures for shock-induced incipient (IM) and complete (CM) melting upon release. On the 100 K Hugoniot, the critical pressures are about 4.5 and between 5-6 GPa for IM and CM, respectively. On the 263 K Hugoniot, the critical pressures are 0.6 and 3.7 GPa for IM and CM, lower than previously suggested. Shock-induced melting of ice will be widespread in impact events. 2. Rampart Crater Formation on Mars: We present a model for the fluidization of Martian rampart crater ejecta blankets with liquid water based on the shock physics of cratering onto an ice-rich regolith. We conducted simulations of crater formation on Mars, explicitly accounting for the equations of state and shock-induced melting criteria for both the silicate and ice components and using strength models constrained by the observed transition diameter DTr from simple to complex craters on Mars, where DTr = 8 km corresponds to an effective yield strength of 107 Pa. For the observed size range of rampart craters (diameters D ≾ 30 km) and typical asteroidal impact conditions (silicate impactors, D ≾ 1 km, at 10 km s-1), we find that the hemispherical volume where subsurface ice is partially melted by the impact shock has a radius of about 15 projectile radii (rp), much larger than previous predictions of about 6 rp. The radius of the final crater is comparable to the radius of partial melting and more than half the ice within the excavated material is melted. Thus, the amount of shock-melted water incorporated into the continuous ejecta blanket is within a factor of two of the near-surface ground ice content. We find that fluidized ejecta blankets may form in the current climate with mean surface temperatures of 200 K. Decreasing the effective yield strength of the modeled materials, e.g., by increasing the ice content or porosity, modifies the impact-induced flow in the excavated cavity, resulting in deeper projectile penetration, steeper ejection angles, higher crater rim uplift, and reduced final crater diameter. The volume fraction of shock-melted water in the ejecta blanket increases with distance from the crater rim. The horizontal flow velocities during emplacement of fluidized ejecta (~ 10 - 1000 m s-1) is nearly constant in the continuous ejecta blanket and within the range of large terrestrial landslides. Therefore, ground-hugging debris flow conditions are achieved. The ejecta blanket properties from impacts into a Martian regolith containing 20-40%vol near-surface ice are consistent with the fraction of liquid water inferred from models of ejecta flow rheologies which produce rampart morphologies, about 10-30% liquid water by volume [Ivanov, B. A., Solar System Research, 30, 43-58, 1996]. We present a model for the formation of different rampart ejecta morphologies which may be used in conjunction with an ejecta blanket debris flow model to map the distribution of ground ice. In addition, we find that formation of single or multiple-rampart ejecta blankets does not require pre-existing liquid water in the Martian crust. We estimate the minimum water content in observed rampart ejecta blankets to be equivalent to a global layer of water 0.6 m thick. Based on the crater sampling efficiency, the implied global Martian ice content, within the upper 2 km of the crust, is equivalent to a global layer of water 100 m deep. This result is comparable to other estimates of HM2O content in the Martian crust.