Families of periodic orbits in the general three-body problem for the Sun-Jupiter-Saturn mass-ratio and their stability

1976 ◽  
Vol 45 (1) ◽  
pp. 207-233 ◽  
Author(s):  
P. Delibaltas
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
The Sun ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Families Of Periodic Orbits ◽  
Three Body

scholarly journals Progression of bifurcated family f type periodic orbits in the circular restricted three-body problem

2017 ◽  
Vol 5 (2) ◽  
pp. 69
Author(s):  
Nishanth Pushparaj ◽  
Ram Krishan Sharma
Keyword(s):  
Solar Radiation ◽  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Three Body

Progression of f-type family of periodic orbits, their nature, stability and location nearer the smaller primary for different mass ratios in the framework of circular restricted three-body problem is studied using Poincaré surfaces of section. The orbits around the smaller primary are found to decrease in size with increase in Jacobian Constant C, and move very close towards the smaller primary. The orbit bifurcates into two orbits with the increase in C to 4.2. The two orbits that appear for this value of C belong to two adjacent separate families: one as direct orbit belonging to family g of periodic orbits and other one as retrograde orbit belonging to family f of periodic orbits. This bifurcation is interesting. These orbits increase in size with increase in mass ratio. The elliptic orbits found within the mass ratio 0 < µ ≤ 0.1 have eccentricity less than 0.2 and the orbits found above the mass ratio µ > 0.1 are elliptical orbits with eccentricity above 0.2. Deviations in the parameters: eccentricity, semi-major axis and time period of these orbits with solar radiation pressure q are computed in the frame work of photogravitational restricted Three-body problem in addition to the restricted three-body problem. These parameters are found to decrease with increase in the solar radiation pressure.

Families of periodic orbits in the photogravitational three-body problem

1996 ◽  
Vol 245 (1) ◽  
pp. 1-13 ◽  
Author(s):  
K. E. Papadakis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Three Body Problem ◽  
Families Of Periodic Orbits ◽  
Three Body

Families of periodic orbits in the planar three-body problem

1975 ◽  
Vol 12 (2) ◽  
pp. 175-187 ◽  
Author(s):  
John D. Hadjidemetriou ◽  
Th. Christides
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Three Body Problem ◽  
Families Of Periodic Orbits ◽  
Three Body

scholarly journals Integrals of Motion

1975 ◽  
Vol 69 ◽  
pp. 209-225 ◽  
Author(s):  
G. Contopoulos
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Threshold Energy ◽  
Three Body Problem ◽  
Integrals Of Motion ◽  
Surface Of Section ◽  
Families Of Periodic Orbits ◽  
Stable Periodic ◽  
Three Body

The properties of conservative dynamical systems of two or more degrees of freedom are reviewed. The transition from integrable to ergodic systems is described. Nonintegrability is due to the interaction of two, or more, resonances. Then one sees, on a surface of section, infinite types of islands of various orders, while the asymptotic curves from unstable invariant points intersect each other along homoclinic and heteroclinic points producing an apparent ‘dissolution’ of the invariant curves. A threshold energy is defined separating near integrable systems from near ergodic ones. The possibility of real ergodicity for large enough energies is discussed. In the case of many degrees of freedom we also distinguish between integrable, ergodic, and intermediate cases. Among the latter are systems of particles interacting with Lennard-Jones interparticle potential. A threshold energy was derived, which is proportional to the number of particles. Finally some recent results about the general three-body problem are described. One can extend the families of periodic orbits of the restricted problem to the general three-body problem. Many of these orbits are stable. An empirical study of orbits near the stable periodic orbits indicates the existence of 2 integrals of motion besides the energy.

scholarly journals Three-body problem - from Newton to supercomputer plus machine learning

2021 ◽  
Author(s):  
Shijun LIAO ◽  
Xiaoming Li ◽  
Yu Yang
Keyword(s):  
Machine Learning ◽  
Periodic Orbits ◽  
High Performance ◽  
Body Problem ◽  
Ann Model ◽  
Three Body Problem ◽  
Starting Point ◽  
Families Of Periodic Orbits ◽  
Artificial Neural Network Ann ◽  
Three Body

Abstract The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effective approach and a roadmap to numerically gain planar periodic orbits of three-body systems with arbitrary masses by means of machine learning based on an artificial neural network (ANN) model. Given any a known periodic orbit as a starting point, this approach can provide more and more periodic orbits (of the same family name) with variable masses, while the mass domain having periodic orbits becomes larger and larger, and the ANN model becomes wiser and wiser. Finally, we have an ANN model trained by means of all obtained periodic orbits of the same family, which provides a convenient way to give accurate enough predictions of periodic orbits with arbitrary masses for physicists and astronomers. It suggests that the high-performance computer and artificial intelligence (including machine learning) should be the key to gain periodic orbits of the famous three-body problem.

Sign in / Sign up

Export Citation Format

Share Document