Origin of the Earth and Moon

According to the giant impact hypothesis, the Moon formed from a disk created by an impact between the proto-Earth and an impactor. Three major models for this hypothesis are (a) standard model: a Mars-sized impactor hit the Earth; (b) fast-spinning Earth model: a small impactor hit a rapidly spinning Earth; and (c) sub-Earths model: two half-Earth sized planets collided. These models have been supported because they can explain several observed features of the Earth-Moon system, such as the Moon's mass, angular momentum, and potentially geochemical measurements that suggest that the Earth and Moon have nearly identical isotopic ratios. However, it is uncertain if these models are consistent with other geochemical constraints. For example, isotopic measurements of Earth's rocks indicate that the early Earth's mantle was chemically heterogeneous and this signature was preserved for billions of years. However, it is not clear if the giant impact hypothesis is consistent with this geochemical constraint because the giant impact could have been so energetic that the Earth's mantle could have completely mixed and homogenized. Furthermore, the fraction of the Earth's mantle that became molten by the impact is not well known, even though it is known to have significantly affected the subsequent evolutions of the Earth's interior and atmosphere. Additionally, the water and volatile content of the Moon may have an important implication for the lunar origin. Since the Moon-forming disk formed through a giant impact process, it must have been hot and partially vaporized. From this disk, a significant amount of water and volatiles may have escaped to space. However, this idea may contradict recent geochemical studies that indicate that Moon may not be as dry as previously thought. Furthermore, moons of other planets may provide comprehensive pictures of the origin and evolution of the moons. For example, the Pluto-Charon system could have formed via a giant impact. Recent studies also suggest that Mars' satellites Phobos and Deimos could have formed in the same way. In contrast, satellites around the gas giants could have formed in situ from their proto-satellite disks and by gravitational capture. One of the Saturnian satellites, Enceladus has very unique geological and dynamical features. Cassini spacecraft observed that water plumes are emanating from cracks on the surface (so-called ``tiger stripes''). These plumes may originate from a few kilometer deep subsurface liquid ocean. Along the cracks, strong thermal emissions have been observed and these are thought to be related to the plume activities, but the connection has been still unclear. In my Ph.D. thesis, I aim to understand the origin and evolution of the Earth, Moon, and the Saturnian moon Enceladus. In order to understand the initial state of the Earth's mantle and the Moon-forming disk, I perform giant impact simulations with a method called smoothed particle hydrodynamics (SPH). I show that the Earth's mantle becomes mostly molten by the impact and that the mantle remains unmixed in (a), but it may be at least partly mixed in (b) and (c). Therefore, (a) is most consistent with the preservation of the mantle heterogeneity. As for the Moon-forming disk, my calculations show that the disk of the standard model has a relatively low temperature (up to 4500 K) and low vapor mass fraction (~20-30%) while the disk formed by other models could be much hotter (6000-7000 K) and has a higher vapor mass fraction (80-90 %). Furthermore, I investigate the structure of the Moon-forming disk and estimated the extent of water escape. I show that escape is in the diffusion-limited regime and water escape from the disk to space is minor. This result could explain recent measurements on lunar water abundance. Furthermore, I develop a dynamical model that includes flow dynamics and flow-ice wall interaction that explains the Enceladus plume mass flux, heat flux, and several observed signatures. These studies will deepen comprehensive understanding of the origin of the moons in the solar system.