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In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special…

Earth and Planetary Astrophysics · Physics 2025-10-23 Arcelia Hermosillo Ruiz , Ruth Murray-Clay , Kathryn Volk , Rosemary Pike

In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational $N$-body…

Earth and Planetary Astrophysics · Physics 2021-06-17 Yota Ishigaki , Junko Kominami , Junichiro Makino , Masaki Fujimoto , Masaki Iwasawa

We present results from a suite of N-body simulations that follow the accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5--4.0 AU…

Earth and Planetary Astrophysics · Physics 2015-05-19 Ryuji Morishima , Joachim Stadel , Ben Moore

The dynamics of planetesimals plays an important role in planet formation, because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in protoplanetary discs, their orbits are nearly circular and…

Earth and Planetary Astrophysics · Physics 2020-11-25 Sebastian Lorek , Anders Johansen

The large number of exoplanets found to orbit their host stars in very close orbits have significantly advanced our understanding of the planetary formation process. It is now widely accepted that such short-period planets cannot have…

Earth and Planetary Astrophysics · Physics 2011-12-07 Jianghui Ji , Sheng Jin , C. G. Tinney

In the standard model of terrestrial planet formation, planets are formed through giant impacts of planetary embryos after the dispersal of the protoplanetary gas disc. Traditionally, $N$-body simulations have been used to investigate this…

Earth and Planetary Astrophysics · Physics 2025-05-28 Tadahiro Kimura , Haruka Hoshino , Eiichiro Kokubo , Yuji Matsumoto , Masahiro Ikoma

The solar system's terrestrial planets are thought to have accreted over millions of years out of a sea of smaller embryos and planetesimals. Because it is impossible to know the surface density profile for solids and size frequency…

Earth and Planetary Astrophysics · Physics 2020-05-11 Matthew S. Clement , Nathan A. Kaib , John E. Chambers

The final stage of terrestrial planet formation is known as the giant impact stage where protoplanets collide with one another to form planets. So far this stage has been mainly investigated by N-body simulations with an assumption of…

Earth and Planetary Astrophysics · Physics 2015-05-18 Eiichiro Kokubo , Hidenori Genda

$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be…

Earth and Planetary Astrophysics · Physics 2020-02-26 David M. Hernandez , Sam Hadden , Junichiro Makino

Our understanding of the process of terrestrial planet formation has grown markedly over the past 20 years, yet key questions remain. This review begins by first addressing the critical, earliest stage of dust coagulation and concentration.…

Earth and Planetary Astrophysics · Physics 2024-11-07 Matthew S. Clement , Andre Izidoro , Sean N. Raymond , Rogerio Deienno

We present the results of planet formation N-body simulations based on a comprehensive physical model that includes planetary mass growth through mutual embryo collisions and planetesimal/boulder accretion, viscous disc evolution, planetary…

Earth and Planetary Astrophysics · Physics 2016-02-17 Gavin A. L. Coleman , Richard P. Nelson

Over the course of the recent decades, $N$-body simulations have become a standard tool for quantifying the gravitational perturbations that ensue in planet-forming disks. Within the context of such simulations, massive non-central bodies…

Earth and Planetary Astrophysics · Physics 2020-08-12 Shirui Peng , Konstantin Batygin

We present a fragmentation module and a composition tracking code for the $n$-body code REBOUND. Our fragmentation code utilises previous semi-analytic models and follows an implementation method similar to fragmentation for the $n$-body…

Earth and Planetary Astrophysics · Physics 2022-02-09 Anna C. Childs , Jason H. Steffen

A planetary instability occurring at time $<100$ My after formation of the giant planets in our solar system can be responsible for some characteristics of the inner solar system. However, the actual influence of the instability on the…

Earth and Planetary Astrophysics · Physics 2021-10-13 Fernando Roig , David Nesvorný , Rogerio Deienno , Matias J. Garcia

Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there…

Earth and Planetary Astrophysics · Physics 2017-11-29 Soko Matsumura , Ramon Brasser , Shigeru Ida

The intermediate phases of planet formation are not directly observable due to lack of emission from planetesimals. Planet formation is, however, a dynamically active process resulting in collisions between the evolving planetesimals and…

Earth and Planetary Astrophysics · Physics 2015-06-18 Zoë M. Leinhardt , Jack Dobinson , Philip J. Carter , Stefan Lines

This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical…

Earth and Planetary Astrophysics · Physics 2012-08-24 Alessandro Morbidelli , Jonathan I. Lunine , David P. O`brien , Sean N. Raymond , Kevin J. Walsh

The past decade has seen major progress in our understanding of terrestrial planet formation. Yet key questions remain. In this review we first address the growth of 100 km-scale planetesimals as a consequence of dust coagulation and…

Earth and Planetary Astrophysics · Physics 2018-12-05 Andre Izidoro , Sean N. Raymond

Building the terrestrial planets has been a challenge for planet formation models. In particular, classical theories have been unable to reproduce the small mass of Mars and instead predict that a planet near 1.5 AU should roughly be the…

Earth and Planetary Astrophysics · Physics 2016-01-20 Harold F. Levison , Katherine A. Kretke , Kevin Walsh , William Bottke

Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and…

Earth and Planetary Astrophysics · Physics 2018-06-06 Sotiris Sotiriadis , Anne-Sophie Libert , Sean N. Raymond