high viscosity of Theia is taken to be 1014Pa ∗s here, the composition of the debris disk will be totally made of materials of proto-Earth if Theia’s viscosity is taken to be extremely large value of 1021Pa ∗s. It’s like throwing a stone into water, the stuff that splashes out is all just water.

[Figure: Figure 1. The big circle represents the target planet with mass Mt and the small circle is the impactor planet with mass Mi. vc is the speed at first contact of the impactor with the target’s surface. The target planet rotates clockwise.]

proto-Earth mantle material, thereby explaining the Earthlike isotopic composition of the Moon. During their formation and early evolution, rocky planets may experience several episodes of extensive melting. The resulting magma oceans are generated by the radioactive decay of short-lived isotopes, the release of gravitational energy accompanying core formation, and large impact events. Small planets cool faster than larger ones due to small planets’ larger surface area to volume ratio. Therefore, solidification of magma ocean of small planet would be quicker than that of larger ones, resulting that small planet may already solidify while magma ocean are still on larger planets, and that the viscosity (1021Pa ∗s) of the mantle of the small planets would be far larger than that (0.1Pa ∗s to 10Pa ∗s) of larger ones which may still be covered by magma ocean.
3. DISCUSSIONS We propose a new theory for the origin of the Moon’s Earth-like isotopic composition in this work. Giant impact between a high-viscosity Theia and a low-viscosity proto-Earth could significantly affect the composition of debris disk. The larger the viscosity contrast, the higher portion of materials of proto-Earth in the debris disk. It can be envisioned that the composition of the debris disk produced by giant impact will be completely made of materials of proto-Earth if Theia’s viscosity is extremely large and proto-Earth is covered by deep magma ocean. Furthermore, since Theia would reach solid state, material strength would enhance the result presented in this work. Due to the large viscosity of Theia, the complete simulations with the large viscosity of Theia and material strength will be conducted very soon. Given that smaller bodies such as Vesta and Mars typically have mantles with a higher iron content than Earth’s mantle ( ´Cuk & Stewart 2012; Fischer et al. 2024), it is plausible that Theia possessed a mantle enriched in iron relative to that of the proto-Earth (Yuan et al. 2023), meaning that the density of materials of Theia’s mantle is greater than that of proto-Earth’s mantle and that material originating from Theia’s mantle would sink to the lower layer of Earth after giant impact.
2. VISCOUS GIANT IMPACT The numerical approach for investigating giant impacts is smoothed particle hydrodynamics (SPH). In such simulations, both the target and the impactor are represented by particles whose dynamics are governed primarily by gravitational forces and material pressure. The impact scenario shown in Figure 1 is specified by the impact parameter b = sin(β) and the speed at first contact of the impactor with the target’s surface vc. We set the initial position of the impactor in order to let the contact occur 3 seconds after the simulation’s start. β is set to be 30o and vc to be vesc where vesc = � 2G(Mt + Mi)/(Rt + Ri) is the mutual escape speed of the system. Here, we set Mt = 0.887ME and Mi = 0.133ME where ME is the mass of the Earth. To determine the radii of the non-rotating target and impactor, each body is divided into a rocky mantle and an iron core, accounting for 70% and 30% of the mass, respectively. In reality, the outer portion of the proto-Earth may have existed as a magma ocean due to planetesimal accretion and multiple giant impacts. Here, we adopt the ANEOS equations of state for Fe85Si15 and forsterite (Stewart et al. 2020)

[Figure: Figure 2. Up and bottom panel represent the giant impact with same viscosity and with viscosity contrast, respectively. From left to right, the results are shown with simulation times of 0 hr, 0.56 hr, 1.12 hr and 1.68 hr.]