Related papers: Perihelion librations in the secular three--body p…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral…
We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic…
The hierarchical three-body problem has many applications in relativistic astrophysics, and can play an important role in the formation of the binary black hole mergers detected by LIGO/Virgo. However, many studies have only included…
The dynamics of the pseudo-Newtonian restricted four-body problem has been studied in the present paper, where the primaries have equal masses. The parametric variation of the existence as well as the position of the libration points are…
I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variation of the Newtonian constant of gravitation. I perturbatively…
One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for…
In this note, we show there exist infinitely many trajectories which are bi-normal (i.e. normal at initial and final times) to the xz-plane, in the Spatial Circular Restricted Three-Body Problem, for energies below or slightly above the…
The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is investigated analytically and solved for both rotating and librating Kozai-Lidov cycles (KLCs) with…
We present the secular theory of coplanar $N$-planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the…
The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…
We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k…
It is not known if, in addition to the Newton's inverse square law component, the gravitational force has some non-Newtonian, long-range components that have escaped detection until now. For example, the non-Newtonian component of the…
We consider the partial average i.e., the Lagrange average with respect to {\it just one} of the two mean anomalies, of the Newtonian part of the perturbing function in the three--body problem Hamiltonian. We prove that such a partial…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
The elliptical instability is a generic instability which takes place in any rotating flow whose streamlines are elliptically deformed. Up to now, it has been widely studied in the case of a constant, non-zero differential rotation between…