Cantelli was born in Palermo, Sicily. He attended the local university where he graduated in 1899 in mathematics with a thesis on celestial mechanics. Cantelli’s advisor, Filippo Angelitti, was Director of the Palermo Astronomical Observatory, and he began working as Angelitti’s assistant while still a student. Cantelli remained at the Observatory until 1903. His first publications were about v...

We consider maps defined on an open set of Rnþm having a fixed point whose linear part is the identity. We provide sufficient conditions for the existence of a stable manifold in terms of the nonlinear part of the map. These maps arise naturally in some problems of Celestial Mechanics. We apply the results to prove the existence of parabolic orbits of the spatial elliptic three-body problem. r ...

The effect of a cosmological constant on the precession of the line of apsides is O(Λcr/GM) which is 3(H◦P ) /8π ≈ 10 for a vacuum-dominated Universe with Hubble constant H◦ = 65 km/sec/Mpc and for the orbital period P = 88 days of Mercury. This is unmeasurably small, so planetary perturbations cannot be used to limit the cosmological constant, contrary to the suggestion by Cardona & Tejeiro (1...

The method of variation of constants is an important tool used to solve systems of ordinary differential equations, and was invented by Euler and Lagrange to solve a problem in orbital mechanics. This methodology assumes that certain "constants" associated with a homogeneous problem will vary in time in response to an external force. It also introduces one or more constraint equations. We show ...

Abstract The aim of this paper is to present a new, analytical, method for computing the exact number relative equilibria in planar, circular, restricted 4-body problem celestial mechanics. new approach allows very efficient computer-aided proof, and opens potential pathway proving harder instances n -body problem.

In this article, we give two refinements of Franks' theorem: For orientation and area preserving homeomorphisms the closed or open annulus, existence k-periodic orbits ((k,n0)=1) forces infinitely many periodic with periods prime to n0. Moreover, if f is reversible, above could be symmetric. Our improvements theorem can applied Reeb dynamics celestial mechanics, for example, some precise inform...

The accurate computation of families of periodic orbits is very important in the analysis of various celestial mechanics systems. The main difficulty for the computation of a family of periodic orbits of a given period is the determination within a given region of an individual member of this family which corresponds to a periodic orbit. To compute with certainty accurate individual members of ...

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets ...

The problem of stability of the action variables in nearly{integrable (real{ analytic) Hamiltonian systems is considered. Several results (fully described in CG2]) are discussed; in particular: (i) a generalization of Arnold's method (A]) allowing to prove instability (i.e. drift of action variables by an amount of order 1, often called \Arnold's diiusion") for general perturbations of \a{prior...

We restrict our attention in this paper to the case where the potential (or force) at a point is a sum of pairwise An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles interactions. More specifically, we consider potentials of whose interactions are Coulombic or gravitational in nature. For a the form system of N pa...