Related papers: Relativistic three-body effects in hierarchical tr…
Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the…
We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal…
Continuing work initiated in an earlier publication [Ichita, Yamada and Asada, Phys. Rev. D 83, 084026 (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three…
A model of three-body motion is developed which includes the effects of gravitational radiation reaction. The radiation reaction due to the emission of gravitational waves is the only post-Newtonian effect that is included here. For…
We study the long-term evolution of selected hierarchical triple systems in Newtonian gravity. We employ analytic equations derived in Paper II for the evolution of orbit-averaged orbital elements for both inner and outer orbits, which…
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical…
Most galaxies have supermassive black holes (SMBH) at their centres, surrounded by stars with binary systems also present in this environment. We use two schemes - post-Newtonian (PN) and a scalar perturbation to a background metric to…
The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…
A hierarchical three-body model can be widely applied to diverse astrophysical settings, from satellite-planet-star systems to binaries around supermassive black holes. The octupole-order perturbation on the inner binary from the tertiary…
We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
A new kind of the relativistic three-body equations for the three fermion systems are suggested. These equations are derived in the framework of the standard field-theoretical $S$-matrix approach in the time-ordered three dimensional form.…
We describe a new kind of resonance occuring in relativistic three-body hierarchical systems: the precession resonance, occuring when the relativistic precession timescale of a binary equals the period of a distant perturber. We find that,…
The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets, stars to black holes. In such a system two objects are on a tight orbit, and the…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be…
We analyze how corrections linear in the effective range, r_0, affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using…