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The chemical compositions of Earth's core and mantle provide insight into the processes that led to their formation. N-body simulations, on the other hand, generally do not contain chemical information, and seek to only reproduce the masses and orbits of the terrestrial planets. These simulations can be grouped into four potentially viable scenarios of Solar System formation (Classical, Annulus, Grand Tack, and Early Instability) for which we compile a total of 433 N-body simulations. We relate the outputs of these simulations to the chemistry of Earth's core and mantle using a melt-scaling law combined with a multi-stage model of core formation. We find the compositions of Earth analogs to be largely governed by the fraction of equilibrating embryo cores and the initial embryo masses in N-body simulations. Simulation type may be important when considering magma ocean lifetimes, where Grand Tack simulations have the largest amounts of material accreted after the last giant impact. However, we cannot rule out any accretion scenarios or initial embryo masses due to the sensitivity of Earth's mantle composition to different parameters and the stochastic nature of N-body simulations. Comparing the last embryo impacts experienced by Earth analogs to specific Moon-forming scenarios, we find the characteristics of the Moon-forming impact are dependent on the initial conditions in N-body simulations where larger initial embryo masses promote larger and slower Moon-forming impactors. Mars-sized initial embryos are most consistent with the canonical hit-and-run scenario onto a solid mantle. Our results suggest that constraining the fraction of equilibrating impactor core and the initial embryo masses in N-body simulations could be significant for understanding both Earth's accretion history and characteristics of the Moon-forming impact.

At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to $\sim$95\% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction ($\gtrsim95\%$) of unstable systems with a sprinkling ($\lesssim5\%$) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (${\rm N\geq2}$) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet--planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths (abridged)., Accepted in A&A, version including language editing

Small bodies are time-capsules of different eras of solar system history from the most primitive materials within the solar system to evolved pieces of larger bodies. A small body sample return program is an essential component of small body exploration, and such a program should include opportunities for both missions and laboratory analysis., Comment: A White Paper submitted to the Planetary Science and Astrobiology Decadal Survey 2023-2032

The current disparity in computational knowledge is a critical hindrance to the diversity and success of the field. Recommendations are outlined for policies and funding models to enable the growth and retention of a new generation of computational researchers that reflect the demographics of the undergraduate population in Astronomy and Physics., Astro2020 APC White Paper: State of the Profession Consideration

International audience; Exoplanet surveys have discovered that a large fraction of planetary systems (perhaps, a third around Sun-like stars) possess super-Earth planets on orbits tighter than Earth's. These super-Earths with masses between that of Earth and Neptune are not found in the Solar System, however it has been proposed that they formed in a similar way to our terrestrial planets. Instead, we find that these two inner planetary system architectures correspond to two clearly defined planet formation pathways regulated by the pebble mass-flux. Radio observations of protoplanetary disks reveal large reservoirs of "pebbles" (approximately cm-sized objects), which spiral inwards towards the central star through the disk due to drag with the nebular gas. Protoplanets embedded in the disk accrete a portion of these pebbles as they drift by. Pebble accretion can be the most efficient growth process of solid material. We modeled the growth of a system of rocky protoplanets embedded in disks of varying pebble mass-fluxes, and we find that a change of less than a factor of two in the pebble mass-flux significantly alters the architecture of the final planetary system. When the pebble mass-flux is low, protoplanets grow slowly and remain small. Their low-mass strongly limits their migration and so they are located near where they originally grew in the disk. When the gas disappears, they naturally become dynamically unstable, collide with one another, and a smaller number of larger planets remain, i.e. the terrestrial planet formation process. We find the largest final planets are at most a few Earth masses, which grow from embryos that are at most a third of an Earth mass when the gas disappears and pebble accretion ceases. If the pebble mass-flux is higher, protoplanets grow faster and become more massive while the protoplanetary disk still possesses nebular gas. These massive protoplanets interact with the gas disk and migrate inward leading to stronger planet-planet interactions, mutual merging, and even faster growth. As the nebular gas dissipates, it leaves behind a system of close-in super-Earths, which eventually undergo dynamical instabilities responsible for further growth and the removal of orbital resonances.

International audience; Previous simulations of planet formation utilizing single bodies including pebble accretion and planet migration imply that giant planets found in orbits exterior to 1 AU originate from the outer regions of protoplanetary discs (30-40 AU). Here we generalize such models to include the mutual gravity between a high number of growing planetary bodies. We investigate how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that giant planets originate from 30-40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100-200 Earth masses per Myr, enough to grow Jupiter within the lifetime of the solar nebula. However, planetary embryos growing interior to 30-40 AU also grow and migrate inwards to the inner system (r

Satellites of asteroids have been discovered in nearly every known small body population, and a remarkable aspect of the known satellites is the diversity of their properties. They tell a story of vast differences in formation and evolution mechanisms that act as a function of size, distance from the Sun, and the properties of their nebular environment at the beginning of Solar System history and their dynamical environment over the next 4.5 Gyr. The mere existence of these systems provides a laboratory to study numerous types of physical processes acting on asteroids and their dynamics provide a valuable probe of their physical properties otherwise possible only with spacecraft. Advances in understanding the formation and evolution of binary systems have been assisted by: 1) the growing catalog of known systems, increasing from 33 to nearly 250 between the Merline et al. (2002) Asteroids III chapter and now, 2) the detailed study and long-term monitoring of individual systems such as 1999 KW4 and 1996 FG3, 3) the discovery of new binary system morphologies and triple systems, 4) and the discovery of unbound systems that appear to be end-states of binary dynamical evolutionary paths. Specifically for small bodies (diameter smaller than 10 km), these observations and discoveries have motivated theoretical work finding that thermal forces can efficiently drive the rotational disruption of small asteroids. Long-term monitoring has allowed studies to constrain the system's dynamical evolution by the combination of tides, thermal forces and rigid body physics. The outliers and split pairs have pushed the theoretical work to explore a wide range of evolutionary end-states., 42 pages, 4 figures, contribution to the Asteroids 4 book

The formation of the Earth's core is a consequence of planetary accretion and processes in the Earth's interior. The mechanical process of planetary differentiation is likely to occur in large, if not global, magma oceans created by the collisions of planetary embryos. Metal-silicate segregation in magma oceans occurs rapidly and efficiently unlike grain scale percolation according to laboratory experiments and calculations. Geochemical models of the core formation process as planetary accretion proceeds are becoming increasingly realistic. Single stage and continuous core formation models have evolved into multi-stage models that are couple to the output of dynamical models of the giant impact phase of planet formation. The models that are most successful in matching the chemical composition of the Earth's mantle, based on experimentally-derived element partition coefficients, show that the temperature and pressure of metal-silicate equilibration must increase as a function of time and mass accreted and so must the oxygen fugacity of the equilibrating material. The latter can occur if silicon partitions into the core and through the late delivery of oxidized material. Coupled dynamical accretion and multi-stage core formation models predict the evolving mantle and core compositions of all the terrestrial planets simultaneously and also place strong constraints on the bulk compositions and oxidation states of primitive bodies in the protoplanetary disk., Accepted in Fischer, R., Terasaki, H. (eds), Deep Earth: Physics and Chemistry of the Lower Mantle and Core, AGU Monograph

The growth and composition of Earth is a direct consequence of planet formation throughout the Solar System. We discuss the known history of the Solar System, the proposed stages of growth and how the early stages of planet formation may be dominated by pebble growth processes. Pebbles are small bodies whose strong interactions with the nebula gas lead to remarkable new accretion mechanisms for the formation of planetesimals and the growth of planetary embryos. Many of the popular models for the later stages of planet formation are presented. The classical models with the giant planets on fixed orbits are not consistent with the known history of the Solar System, fail to create a high Earth/Mars mass ratio, and, in many cases, are also internally inconsistent. The successful Grand Tack model creates a small Mars, a wet Earth, a realistic asteroid belt and the mass-orbit structure of the terrestrial planets. In the Grand Tack scenario, growth curves for Earth most closely match a Weibull model. The feeding zones, which determine the compositions of Earth and Venus follow a particular pattern determined by Jupiter, while the feeding zones of Mars and Theia, the last giant impactor on Earth, appear to randomly sample the terrestrial disk. The late accreted mass samples the disk nearly evenly., Comment: Accepted for publication in Early Earth an AGU Monograph edited by James Badro and Michael J. Walter