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- Celletti, Alessandra [x] 16 (%)
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## Preface

### Celestial Mechanics and Dynamical Astronomy (2006-05-01) 95: 1-2 , May 01, 2006

## Sylvio Ferraz-Mello: Canonical Perturbation Theories. Degenerate Systems and Resonance

### Celestial Mechanics and Dynamical Astronomy (2008-04-01) 100: 331-333 , April 01, 2008

## Dependence on the observational time intervals and domain of convergence of orbital determination methods

### Celestial Mechanics and Dynamical Astronomy (2006-05-01) 95: 327-344 , May 01, 2006

In the framework of the orbital determination methods, we study some properties related to the algorithms developed by Gauss, Laplace and Mossotti. In particular, we investigate the dependence of such methods upon the size of the intervals between successive observations, encompassing also the case of two nearby observations performed within the same night. Moreover we study the convergence of Gauss algorithm by computing the maximal eigenvalue of the jacobian matrix associated to the Gauss map. Applications to asteroids and Kuiper belt objects are considered.

## Normal Form Invariants Around Spin-orbit Periodic Orbits

### Celestial Mechanics and Dynamical Astronomy (2000-09-01) 78: 227-241 , September 01, 2000

We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends upon the parameters provided by the equatorial oblateness of the satellite and its orbital eccentricity. Normal form transformations around the main spin-orbit resonances are carried out explicitly. As an outcome, one can compute some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariants provides also the stability of the spin-orbit resonances, since it guarantees the existence of invariant curves surrounding the periodic orbit.

## Preface

### Celestial Mechanics and Dynamical Astronomy (2008-09-01) 102: 1-2 , September 01, 2008

## Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison

### Celestial Mechanics and Dynamical Astronomy (2005-09-01) 93: 1-52 , September 01, 2005

The discovery of the asteroid Ceres by Piazzi in 1801 motivated the development of a mathematical technique proposed by Gauss, (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, 1963) which allows to recover the orbit of a celestial body starting from a minimum of three observations. Here we compare the method proposed by Gauss (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, New York, 1963) with the techniques (based on three observations) developed by Laplace (Collected Works 10, 93–146, 1780) and by Mossotti (Memoria Postuma, 1866). We also consider another method developed by Mossotti (Nuova analisi del problema di determinare le orbite dei corpi celesti, 1816–1818), based on four observations. We provide a theoretical and numerical comparison among the different procedures. As an application, we consider the computation of the orbit of the asteroid Juno.

## Non-integrability of the problem of motion around an oblate planet

### Celestial Mechanics and Dynamical Astronomy (1995-09-01) 61: 253-260 , September 01, 1995

We provide a result of non-analytic integrability of the so-called *J*_{2}-problem. Precisely by using the Lerman theorem we are able to prove the existence of a region of the phase space, where the dynamical system exhibits chaotic motions.

## Stability of the synchronous spin-orbit resonance by construction of librational trapping tori

### Celestial Mechanics and Dynamical Astronomy (1993-10-01) 57: 325-328 , October 01, 1993

## Estimate of the Transition Value of Librational Invariant Curves

### Celestial Mechanics and Dynamical Astronomy (2002-05-01) 83: 257-274 , May 01, 2002

We investigate the break-down threshold of librational invariant curves. As a model problem, we consider a variant of a mapping introduced by M. Hénon, which well describes the dynamics of librational motions surrounding a stable invariant point. We verify in concrete examples the applicability of Greene's method, by computing the instability transition values of a sequence of periodic orbits approaching an invariant curve with fixed noble frequency. However, this method requires the knowledge of the location of the periodic orbits within a very good approximation. This task appears to be difficult to realize for a libration regime, due to the different topology of the phase space. To compute the break-down threshold, we tried an alternative method very easy to implement, based on the computation of the fast Lyapunov indicators and frequency analysis. Such technique does not require the knowledge of the periodic orbits, but again, it appears very difficult to have a precision better than Greene's method for the computation of the critical parameter.

## Frequency analysis of the stability of asteroids in the framework of the restricted three-body problem

### Celestial Mechanics and Dynamical Astronomy (2004-11-01) 90: 245-266 , November 01, 2004

The stability of some asteroids, in the framework of the restricted three-body problem, has been recently proved in (Celletti and Chierchia, 2003), by developing an isoenergetic KAM theorem. More precisely, having fixed a level of energy related to the motion of the asteroid, the stability can be obtained by showing the existence of nearby trapping invariant tori existing at the same energy level. The analytical results are compatible with the astronomical observations, since the theorem is valid for the realistic mass-ratio of the primaries.

The model adopted in (Celletti and Chierchia, 2003), is the planar, circular, restricted three-body model, in which only the most significant contributions of the Fourier development of the perturbation are retained. In this paper we investigate numerically the stability of the same asteroids considered in (Celletti and Chierchia, 2003), (namely, Iris, Victoria and Renzia). In particular, we implement the nowadays standard method of frequency-map analysis and we compare our investigation with the analytical results on the planar, circular model with the truncated perturbing function. By means of frequency analysis, we study the behaviour of the bounding tori and henceforth we infer stability properties on the dynamics of the asteroids. In order to test the validity of the truncated Hamiltonian, we consider also the complete expression of the perturbing function on which we perform again frequency analysis. We investigate also more realistic models, taking into account the eccentricity of the trajectory of Jupiter (planar-elliptic problem) or the relative inclination of the orbits (circular-inclined model). We did not find a relevant discrepancy among the different models.