High precision symplectic integrators for the Solar System

Farrés, Ariadna; Laskar, Jacques; Blanes, Sergio; Casas, Fernando; Makazaga, Joseba; Murua, Ander

doi:10.1007/s10569-013-9479-6

Cited by 61 publications

(79 citation statements)

References 40 publications

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“…The orbits of the planets were integrated with the symplectic integrator SABA1064 of Farrés et al (2013), using a step size of 5×10 −3 yr and general relativity corrections. The fundamental frequencies of the systems are the mean motions n b and n c , and the two secular frequencies of the pericenters g 1 and g 2 (Table 6).…”

Section: Secular Couplingmentioning

confidence: 99%

An extreme planetary system around HD 219828

Santos

Santerne

Faria

et al. 2016

A&A

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Context. With about 2000 extrasolar planets confirmed, the results show that planetary systems have a whole range of unexpected properties. This wide diversity provides fundamental clues to the processes of planet formation and evolution. Aims. We present a full investigation of the HD 219828 system, a bright metal-rich star for which a hot Neptune has previously been detected. Methods. We used a set of HARPS, SOPHIE, and ELODIE radial velocities to search for the existence of orbiting companions to HD 219828. The spectra were used to characterise the star and its chemical abundances, as well as to check for spurious, activity induced signals. A dynamical analysis is also performed to study the stability of the system and to constrain the orbital parameters and planet masses. Results. We announce the discovery of a long period (P = 13.1 yr) massive (m sin i = 15.1 M Jup ) companion (HD 219828 c) in a very eccentric orbit (e = 0.81). The same data confirms the existence of a hot Neptune, HD 219828 b, with a minimum mass of 21 M ⊕ and a period of 3.83 days. The dynamical analysis shows that the system is stable, and that the equilibrium eccentricity of planet b is close to zero. Conclusions. The HD 219828 system is extreme and unique in several aspects. First, ammong all known exoplanet systems it presents an unusually high mass ratio. We also show that systems like HD 219828, with a hot Neptune and a long-period massive companion are more frequent than similar systems with a hot Jupiter instead. This suggests that the formation of hot Neptunes follows a different path than the formation of their hot jovian counterparts. The high mass, long period, and eccentricity of HD 219828 c also make it a good target for Gaia astrometry as well as a potential target for atmospheric characterisation, using direct imaging or high-resolution spectroscopy. Astrometric observations will allow us to derive its real mass and orbital configuration. If a transit of HD 219828 b is detected, we will be able to fully characterise the system, including the relative orbital inclinations. With a clearly known mass, HD 219828 c may become a benchmark object for the range in between giant planets and brown dwarfs.

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Section: Secular Couplingmentioning

confidence: 99%

An extreme planetary system around HD 219828

Santos

Santerne

Faria

et al. 2016

A&A

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“…The coefficients of these methods can be optimized according to many criteria, for example to reduce the coefficients associated to certain types of elementary differentials appearing in the leading error term [260], or to have maximal performance for particular families of applications, such as celestial mechanics [37,127]. For many applications, for example celestial mechanics, such high order methods, and improved variants, are extremely useful, but in the setting of molecular dynamics, it is often found that second-order methods provide a 'good enough' option for numerical integration, the computational price-tag of higher order methods outweighing potential numerical gains.…”

Section: Higher Order Symplectic Methods: the Suzuki-yoshida Methodsmentioning

confidence: 99%

Molecular Dynamics

Leimkuhler¹,

Matthews²

2015

Interdisciplinary Applied Mathematics

161

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Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics.The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and, secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself.The series will consist of monographs and high-level texts from researchersworking on the interplay between mathematics and other fields of science and technology.More information about this series at

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“…Long-term simulations of the stability of the solar system [40,29] (18-digit and 31-digit arithmetic).…”

Section: Computations That Require Extra Precisionmentioning

confidence: 99%