The three-body problem

Abstract

Abstract. The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis, search for periodic orbits and resonances, and application of the results to some interesting astronomical and space dynamical settings. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.

Effects of inclined star-disk encounter on protoplanetary disk size

“…In addition, we assume that viscous forces can be neglected because the encounter time is short compared to the viscous timescale and disk-size changes mainly affect the outer disk areas where viscosity effects are negligible. In the case of a lowmass, non-viscous disk, it is enough to study only three-body interactions by considering the gravitational forces between the two stars and each disk particle (Hall et al 1996;Kobayashi & Ida 2001;Pfalzner 2003;Pfalzner et al 2005b;Breslau et al 2014;Musielak & Quarles 2014).…”

Desvendando o Endereço Físico do Telescópio James Webb

“…O problema Newtoniano clássico da interação gravitacional entre corpos celestes e seus movimentosé de extrema importância no contexto da Física e da Astronomia e foi objeto de diversas investigações de grandes físicos, astrônomos e matemáticos por mais de 300 anos [20]. Dentre os notáveis nomes que abordaram e contribuiram significativamente para este problema destacam-se Euler, Lagrange, Laplace, Jacobi, Le Verrier, Hamilton, Poincaré e Birkhoff, Hill entre outros [21].…”

High-speed visual target tracking with mixed rotation invariant description and skipping searching

“…Especially, we further found the additional 27 families of periodic orbits (with the periods less than 100) by means of the Newton-Raphson method [22][23][24] for the modifications of initial conditions and using the high-order Taylor series method (in 100-digit precision with truncation errors less than 10 −70 ) for the evolution of motion equations (1), instead of the ODE solver dop853 [21] based on the Runge-Kutta method in double precision. In addition, we use the CNS with even smaller round-off error (in 120-digit precision) and truncation error (less than 10 −90 ) to guarantee the reliability of these 27 families.…”

“…The famous three-body problem [1] can be traced back to Isaac Newton in 1680s. According to Poincaré [2], a three-body system is not integrable in general.…”

“…Besides, orbits of three-body problem are often chaotic [3], say, sensitive to initial conditions [2], although there exist periodic orbits in some special cases. In the 300 years since this "three-body problem" [1] was first recognized, only three families of periodic solutions had been found, until 2013 wheň Suvakov and Dmitrašinović [4] made a breakthrough to find 13 new distinct periodic collisionless orbits belonging to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. Before their elegant work, only three families of periodic three-body orbits were found: (1) the Lagrange-Euler family discovered by Lagrange and Euler in 18th century; (2) the Broucke-Hadjidemetriou-Hénon family [5][6][7][8][9]; (3) the Figure-eight family, first discovered numerically by Moore [10] in 1993 and rediscovered by Chenciner and Montgomery [11] in 2000, and then extended to the rotating case [12][13][14][15].…”