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In the framework of restricted five bodies problem, the existence and stability of the libration points are explored and analysed numerically, under the effect of non--isotropic mass variation of the fifth body (test particle or…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
The orbits of asteroids from the MPC catalogue of May 31, 2020 with absolute magnitudes H < 16m, in the 3:1, 5:2 and 2:1 mean motion resonances (MMRs) with Jupiter were selected. The number of the orbits in the 2:1 MMR is dozens times…
The description of unstable motions in the Restricted Planar Circular 3-Body Problem, modeling the dynamics of a Sun-Planet-Asteriod system, is one of the fundamental problems in Celestial Mechanics. The goal of this paper is to analyze…
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states.…
In a variant of the Randall-Sundrum braneworld model which has a charged black hole in an anti-de Sitter bulk, the 4D speed of gravity depends upon one's location in the bulk, and in general differs from the speed of light on a given…
We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of $(3n-2)$--dimensional quasi--periodic motions in the spacial, planetary $(1+n)$--body problem away from…
We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating…
The planetary exospheres are poorly known in their outer parts, since the neutral densities are low compared with the instruments detection capabilities. The exospheric models are thus often the main source of information at such high…
Dynamical studies of asteroid populations in retrograde orbits, that is with orbital inclinations greater than 90 degrees, are interesting because the origin of such orbits is still unexplained. Generally, the population of retrograde…
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…
In soft and condensed matter physics, effective interactions often emerge as a result of the spatial confinement of a fluctuating field. For instance, microscopic particles in a binary liquid mixture are subject to critical Casimir forces…
Recently, it was conjectured that the Lyapunov exponent of chaotic motion of a particle in a black hole is universally bounded from above by the surface gravity of the black hole. On the other hand, the minimal length appears in various…
We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on…
We investigate the three-dimensional, general relativistic Poynting-Robertson effect in the case of rigidly rotating spherical source which emits radiation radially in the local comoving frame. Such radiation field is meant to approximate…
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [Astroph. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies,…
We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
Asteroids smaller than about 100 meters are observed to rotate very fast, with periods often much shorter than the critical limit of 2.2 h. Some of these super-fast rotators can also achieve a very large semi-major axis drift induced by the…
A hypothetical gravitating body in the outer Solar System, the so-called Planet Nine, was proposed to explain the unexpected clustering of the Kuiper Belt Objects. As it has not been observed via telescopes, it was conjectured to be a…