Numerical experiment applicable to planet formation

1984 ◽  
Vol 75 ◽  
pp. 675-676
Author(s):  
Anny Cazenave
Keyword(s):  
Numerical Model ◽  
Numerical Experiment ◽  
Numerical Integration ◽  
Body Problem ◽  
Three Dimensional ◽  
Dynamical Evolution ◽  
The Sun ◽  
Gravitational Perturbations ◽  
N Body Problem ◽  
Fragmentation Processes

A three-dimensional numerical model has been developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (~ moon-size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of Greenberg et al. (1978).

scholarly journals Orbital features of distant trans-Neptunian objects induced by giant gaseous clumps

2020 ◽  
Vol 642 ◽  
pp. L20
Author(s):  
V. V. Emel’yanenko
Keyword(s):  
Simple Model ◽  
Solar Nebula ◽  
Dynamical Evolution ◽  
Outer Solar System ◽  
The Sun ◽  
High Eccentricity ◽  
Small Bodies ◽  
Dynamical Characteristics ◽  
Gravitational Perturbations ◽  
The Hill

Context. The discovery of distant trans-Neptunian objects has led to heated discussions about the structure of the outer Solar System. Aims. We study the dynamical evolution of small bodies from the Hill regions of migrating giant gaseous clumps that form in the outer solar nebula via gravitational fragmentation. We attempt to determine whether the observed features of the orbital distribution of distant trans-Neptunian objects could be caused by this process. Methods. We consider a simple model that includes the Sun, two point-like giant clumps with masses of ∼10 Jupiter masses, and a set of massless objects initially located in the Hill regions of these clumps. We carry out numerical simulations of the motions of small bodies under gravitational perturbations from two giant clumps that move in elliptical orbits and approach each other. The orbital distribution of these small bodies is compared with the observed distribution of distant trans-Neptunian objects. Results. In addition to the known grouping in longitudes of perihelion, we note new features for observed distant trans-Neptunian objects. The observed orbital distribution points to the existence of two groups of distant trans-Neptunian objects with different dynamical characteristics. We show that the main features of the orbital distribution of distant trans-Neptunian objects can be explained by their origin in the Hill regions of migrating giant gaseous clumps. Small bodies are ejected from the Hill regions when the giant clumps move in high-eccentricity orbits and have a close encounter with each other. Conclusions. The resulting orbital distribution of small bodies in our model and the observed distribution of distant trans-Neptunian objects have similar features.

Global Regularization of a Restricted Four-Body Problem

2014 ◽  
Vol 24 (07) ◽  
pp. 1450092 ◽  
Author(s):  
Martha Alvarez-Ramírez ◽  
Joaquín Delgado ◽  
Claudio Vidal
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Binary Collision ◽  
Type Transformation ◽  
Collision Singularity ◽  
Double Collision ◽  
N Body Problem ◽  
Four Body Problem ◽  
Collision Orbits ◽  
Global Regularization

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birkhoff-type transformation. This transformation has the important property to provide a simultaneous regularization of three singularities due to binary collision. We present some ejection–collision orbits after the regularization of the restricted four-body problem (RFBP) with equal masses, which were obtained by numerical integration.

scholarly journals New Periodic Orbits for the n-Body Problem

2006 ◽  
Vol 1 (4) ◽  
pp. 307-311 ◽  
Author(s):  
Cristopher Moore ◽  
Michael Nauenberg
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Fourier Coefficients ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Three Body Problem ◽  
Cubic Symmetry ◽  
Numerical Evidence ◽  
N Body Problem ◽  
Three Body

Since the discovery of the figure-eight orbit for the three-body problem [Moore, C., 1993, Phys. Rev. Lett., 70, pp. 3675–3679] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have appeared in the literature are either planar or are obtained from perturbations of planar orbits. Here we exhibit a number of new three-dimensional periodic n-body orbits with equal masses and cubic symmetry, including some whose moment of inertia tensor is a scalar. We found these orbits numerically, by minimizing the action as a function of the trajectories’ Fourier coefficients. We also give numerical evidence that a planar three-body orbit first found in [Hénon, M., 1976, Celest. Mech., 13, pp. 267–285], rediscovered by [Moore, 1993], and found to exist for different masses by [Nauenberg, M., 2001, Phys. Lett., 292, pp. 93–99], is dynamically stable.

scholarly journals HYPER-SYSTOLIC PROCESSING ON APE100/QUADRICS: n2-LOOP COMPUTATIONS

1996 ◽  
Vol 07 (04) ◽  
pp. 485-501 ◽  
Author(s):  
THOMAS LIPPERT ◽  
GERO RITZENHÖFER ◽  
UWE GLAESSNER ◽  
HENNING HOEBER ◽  
ARMIN SEYFRIED ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Body Problem ◽  
Three Dimensional ◽  
Dynamics Simulation ◽  
Parallel Computer ◽  
Massively Parallel ◽  
Interprocessor Communication ◽  
Communication Costs ◽  
N Body Problem ◽  
Performance Gains

We investigate the performance gains from hyper-systolic implementations of n2-loop problems on the massively parallel computer Quadrics, exploiting its three-dimensional interprocessor connectivity. For illustration we study the communication aspects of an exact molecular dynamics simulation of n particles with Coulomb (or gravitational) interactions. We compare the interprocessor communication costs of the standard-systolic and the hyper-systolic approaches for various granularities. We predict gain factors as large as three on the Q4 and eight on the QH4 and measure actual performances on these machine configurations. We conclude that it appears feasible to investigate the thermodynamics of a full gravitating n-body problem with O(16.000) particles using the new method on a QH4 system.

scholarly journals A Collisional and Self-Gravitational Model to Simulate Numerically the Dynamics of Planetary Disks

1992 ◽  
Vol 152 ◽  
pp. 109-114
Author(s):  
Filomena Pereira Gama ◽  
Jean-Marc Petit ◽  
Hans Scholl
Keyword(s):  
Body Problem ◽  
Dynamical Evolution ◽  
Inelastic Collisions ◽  
Connection Machine ◽  
N Body Problem ◽  
Gravitational Model ◽  
Mesh Method ◽  
Detailed Simulation ◽  
Sharp Edges ◽  
Number Of Particles

The dynamical evolution of the planetary rings is simulated by means of a numerical model in which particles interact through mutual attraction and inelastic collisions. We use a mixed simulation: a deterministic integration of the N - body problem for large distances (“particle-mesh” method with an expansion of density and potential in spherical harmonics) and a Monte Carlo treatment for the close encounters. The implementation is done in the Connection Machine in order to be able to make a detailed simulation using a greater number of particles (of the order of 105). The deterministic calculation of the action of a shepherding satellite on the particles will allow us to study the effect of resonances on the formation and the evolution of the sharp edges of the rings.

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