arXiv subjects

Ugo Locatelli

Publications and source records attributed to Ugo Locatelli.

22 records · Page 2Linked to original sources

arXiv2013

Kolmogorov and Nekhoroshev theory for the problem of three bodies

We investigate the long time stability in Nekhoroshev's sense for the Sun-Jupiter-Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.

math-ph↗

arXiv2013

A Semi-Analytic Algorithm for Constructing Lower Dimensional Elliptic Tori in Planetary Systems

We adapt the Kolmogorov's normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus. As a byproduct, our procedure can also provide some analytic expansions of the motions on elliptic tori. By extensively using algebraic manipulations on a computer, we explicitly apply our method to a planar four-body model not too different with respect to the real Sun--Jupiter--Saturn--Uranus system. The frequency analysis method allows us to check that our location of the initial conditions on an invariant elliptic torus is really accurate.

math.DS↗

arXiv2013

On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system

We investigate the long time stability of the Sun-Jupiter-Saturn-Uranus system by considering the planar, secular model. Our method may be considered as an extension of Lagrange's theory for the secular motions. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a torus which is invariant up to order two in the masses; therefore, we investigate the stability of the elliptic equilibrium point of the secular system for small values of the eccentricities. For the initial data corresponding to a real set of astronomical observations, we find an estimated stability time of $10^7$ years, which is not extremely smaller than the lifetime of the Solar System ($\sim 5$ Gyr).

math-ph↗

arXiv2008

A HST study of the environment of the Herbig Ae/Be star LkHa 233 and its bipolar jet

We present the results of HST/STIS and WFPC2 observations of LkHa 233 and its environment. LkHa233 is a Herbig Ae/Be star with a collimated bipolar jet. We investigate optical forbidden lines along the LkHa 233 jet to determine physical parameters of this jet (electron density n_e, hydrogen ionisation fraction x_e, electron temperature T_e, and mass density n_H). The knowledge of these parameters allows us a direct comparison of a jet from a Herbig star with those from T Tauri stars. The WFPC2 images in broad-band filters clearly show a dark lane caused either by a circumstellar disk or a dust torus. In the blueshifted lobe, n_e is close to or above the critical density for [SII] lines (2.5x10^4 cm^-3) in the first arcsecond and decreases with distance from the source. The ionisation x_e~0.2-0.6 gently rises for the first 500 AU of the flow and shows two re-ionisation events further away from the origin. The T_e varies along the flow between 10^4 K and 3x10^4 K. The (radial) outflow velocities are ~ 80-160 km s^(-1), and they appear to increase with distance from the source. In the redshifted lobe, T_e, n_e, x_e, and n_H are all lower than in the blueshifted lobe, but have the same order of magnitude. All these derived parameters are just beyond or at the upper limits of those observed for classical T Tauri star jets. This may indicate that the flows from the higher mass Herbig stars are indeed scaled-up examples of the same phenomenon as in T Tauri stars.

astro-ph↗