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In this chapter, we summarize the underlying numerical methods needed for efficient $N$-body integration of planetary systems. We discuss how symplectic integrators have been developed to tackle the complementary problems of long-term…

Earth and Planetary Astrophysics · Physics 2026-04-13 Simon L. Grimm , Joachim G. Stadel

We investigate the formation of multiple-planet systems in the presence of a hot Jupiter using extended N-body simulations that are performed simultaneously with semi-analytic calculations. Our primary aims are to describe the planet…

Earth and Planetary Astrophysics · Physics 2015-06-19 Masahiro Ogihara , Hiroshi Kobayashi , Shu-ichiro Inutsuka

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 architecture and masses of planetary systems in the habitable zone could be strongly influenced by outer giant planets, if present. We investigate here the impact of outer giants on terrestrial planet formation, under the assumption…

Earth and Planetary Astrophysics · Physics 2024-07-03 Zhihui Kong , Anders Johansen , Michiel Lambrechts , Jonathan H. Jiang , Zong-Hong Zhu

Terrestrial planet formation (TPF) is a difficult problem that has vexed researchers for decades. Numerical models are only partially successful at reproducing the orbital architecture of the inner planets, but have generally not considered…

Earth and Planetary Astrophysics · Physics 2025-06-12 R. Brasser

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

The process leading to the formation of the terrestrial planet remains elusive. In a previous publication, we have shown that, if the first generation of planetesimals forms in a ring at about 1 AU and the gas disk's density peaks at the…

Earth and Planetary Astrophysics · Physics 2024-04-29 J. M. Y. Woo , D. Nesvorny , J. Scora , A. Morbidelli

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array…

Earth and Planetary Astrophysics · Physics 2017-09-05 Volker Hoffmann , Simon L. Grimm , Ben Moore , Joachim Stadel

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include 1) the orbits, in particular the small eccentricities, and 2) the masses of the terrestrial planets --…

Earth and Planetary Astrophysics · Physics 2015-05-13 Sean N. Raymond , David P. O'Brien , Alessandro Morbidelli , Nathan A. Kaib

During the late stage of planet formation when Mars-size cores appear, interactions among planetary cores can excite their orbital eccentricities, speed their merges and thus sculpture the final architecture of planet systems. This series…

Earth and Planetary Astrophysics · Physics 2015-03-13 Huigen Liu , Ji-lin Zhou , S. Wang

The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets. We investigated the effects of the…

Earth and Planetary Astrophysics · Physics 2013-08-05 Patryk Sofia Lykawka , Takashi Ito

Recent high precision meteoritic data improve constraints on the formation timescale and bulk composition of the terrestrial planets. High resolution N-body simulations allow direct comparison of embryo growth timescale and accretion zones…

Earth and Planetary Astrophysics · Physics 2021-02-11 Jason Man Yin Woo , Simon L. Grimm , Ramon Brasser , Joachim Stadel

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

We report on the stability of hypothetical Super-Earths in the habitable zone of known multi-planetary systems. Most of them have not yet been studied in detail concerning the existence of additional low-mass planets. The new N-body code…

Earth and Planetary Astrophysics · Physics 2015-06-16 S. Elser , S. L. Grimm , J. G. Stadel

Recent observational findings have suggested a positive correlation between the occurrence rates of inner super-Earths and outer giant planets. These results raise the question of whether this trend can be reproduced and explained by planet…

Earth and Planetary Astrophysics · Physics 2021-12-08 M. Schlecker , C. Mordasini , A. Emsenhuber , H. Klahr , Th. Henning , R. Burn , Y. Alibert , W. Benz

The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of…

Earth and Planetary Astrophysics · Physics 2021-06-23 Matthew S. Clement , Nathan A. Kaib , Sean N. Raymond , John E. Chambers

The giant planets of the solar system likely played a large role in shaping the architecture of the terrestrial planets. Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship…

Earth and Planetary Astrophysics · Physics 2019-02-13 Anna C. Childs , Elisa Quintana , Thomas Barclay , Jason H. Steffen

Many features of the outer solar system are replicated in numerical simulations if the giant planets undergo an orbital instability that ejects one or more ice giants. During this instability, Jupiter and Saturn's orbits diverge, crossing…

Earth and Planetary Astrophysics · Physics 2015-12-09 Nathan A. Kaib , John E. Chambers

New equations of state (EOS) for hydrogen, helium, and compounds containing heavier elements are used to construct models for the structures of the planets Jupiter and Saturn. Good agreement with the gravitational moments J2 and J4 is…

Earth and Planetary Astrophysics · Physics 2013-07-12 Gerald I. Kerley

We examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13 - 1.7 AU due to gas disk dispersal.…

Earth and Planetary Astrophysics · Physics 2015-05-13 M. J. Fogg , R. P. Nelson
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