Searcharxiv⌕ Search

arXiv subjects

Giuseppe Pucacco

Publications and source records attributed to Giuseppe Pucacco.

At least 19 recordsLinked to original sources

Testing Local Lorentz Invariance with Laser Tracking of the LAGEOS and LAGEOS II Satellites

Violations of Lorentz Invariance, a cornerstone of modern physics, are predicted by theories of quantum gravity and by extensions of General Relativity involving new vector or tensor fields. In the weak-field limit, such a violation would primarily manifest as a non-zero value for the post-Newtonian parameter $α_1$, which is identically zero in General Relativity. We present a new test of Local Lorentz Invariance by searching for this signature in the orbits of the LAGEOS and LAGEOS II satellites. By applying a Phase Sensitive Detection technique to the mean argument of latitude, derived from about 30 years of Satellite Laser Ranging data, we isolate the periodic signal potentially induced by a preferred reference frame aligned with the Cosmic Microwave Background. {Our analysis yields a new constraint $|α_1| \sim 2 \times 10^{-5}$. This result improves upon the previous best limit from Lunar Laser Ranging and provides the most stringent constraint to date on preferred-frame effects in Earth's gravity.}

gr-qc↗

A Local Lorentz Invariance test with LAGEOS satellites

Strong theoretical arguments suggest that a breakdown of Lorentz Invariance could arise under some very particular conditions. From an experimental point of view, it is important to test the Local Lorentz Invariance with ever greater precision and in all contexts, regardless of the theoretical motivation for the possible violation. In this paper we discuss some aspects of the gravitational sector. Tests of Lorentz Invariance in the context of gravity are difficult and rare in the literature. Possible violations could arise from quantum physics applied to gravity or the presence of vector and tensor fields mediating the gravitational interaction together with the metric tensor of General Relativity. We present our results in the latter case. We analyzed the orbit of the LAGEOS and LAGEOS II satellites over a period of almost three decades. The effects of the possible preferred frame represented by the cosmic microwave background radiation on the mean argument of latitude of the satellites orbit were considered. These effects would manifest themselves mainly through the post-Newtonian parameter $α_1$, a parameter that has a null value in General Relativity. We constrain this parameterized post-Newtonian parameter down to the level of $α_1 \le 2\times10^{-5}$, improving a previous limit obtained through the Lunar Laser Ranging technique.

gr-qc↗

The dynamics around the collinear points of the elliptic three-body problem: A normal form approach

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we imple ment a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions.

math.DS↗

Bifurcation sequences in the secular 3D planetary 3-Body problem: a geometric approach

We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body problem. Stemming from the analysis in [17], we examine various normal form models as regards the extent to which they lead to a phase space dynamics qualitatively similar as that in the complete system. For fixed total angular momentum, the phase space in Hopf variables is the 3D sphere, and the complete sequence of bifurcations of new periodic orbits can be recovered through formulas yielding the tangencies or degenerate intersections between the sphere and the surfaces of a constant second integral of motion of the normal form flow. In particular, we find the critical values of the second integral giving rise to pitchfork and saddle-node bifurcations of new periodic orbits in the system. This analysis renders possible to predict the most important structural changes in the phase space, as well as the emergence of new possible stable periodic planetary orbital configurations which can take place as the mutual inclination between the two planets is allowed to increase.

math-ph↗

Dynamical Stability of the Laplace Resonance

We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all resonant arguments are librating. The sequence of equilibria exists all along the possible states balancing resonance offsets and forced eccentricities. Possible additional new-de Sitter equilibria may exist when at least one of the forced eccentricities is large (the paradigmatic case is Gliese-876). In the present work, these families of equilibria are traced up to crossing exact commensurability, where approximate first-order solutions diverge. Explicit exact location of the equilibria are determined allowing us to verify the Lyapunov stability of the standard de Sitter equilibrium and of the stable branches of the additional ones.

astro-ph.EP↗

Normal forms for the Laplace resonance

We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second order in the eccentricities. The reduced Hamiltonian, constructed by a transformation to resonant coordinates, is then submitted to a suitable ordering of the terms and to the study of its equilibria. Henceforth, resonant normal forms are computed. The main result is the identification of two different classes of equilibria. In the first class, only one kind of stable equilibrium is present: the paradigmatic case is that of the Galilean system. In the second class, three kinds of stable equilibria are possible and at least one of them is characterised by a high value of the forced eccentricity for the `first planet': here the paradigmatic case is the exo-planetary system GJ-876, in which the combination of libration centers admits triple conjunctions otherwise not possible in the Galilean case. The normal form obtained by averaging with respect to the free eccentricity oscillations, describes the libration of the Laplace argument for arbitrary amplitudes and allows us to determine the libration width of the resonance. The agreement of the analytic predictions with the numerical integration of the toy models is very good.

astro-ph.EP↗

Bifurcation of frozen orbits in a gravity field with zonal harmonics

We propose a methodology to study the bifurcation sequences of frozen orbits when the 2nd-order fundamental model of the satellite problem is augmented with the contribution of octupolar terms and relativistic corrections. The method is based on the analysis of twice-reduced closed normal forms expressed in terms of suitable combinations of the invariants of the Kepler problem, able to provide a clear geometric view of the problem.

math-ph↗

Proper Elements for Space Debris

Proper elements are quasi-invariants of a Hamiltonian system, obtained through a normalization procedure. Proper elements have been successfully used to identify families of asteroids, sharing the same dynamical properties. We show that proper elements can also be used within space debris dynamics to identify groups of fragments associated to the same break-up event. The proposed method allows to reconstruct the evolutionary history and possibly to associate the fragments to a parent body. The procedure relies on different steps: (i) the development of a model for an approximate, though accurate, description of the dynamics of the space debris; (ii) the construction of a normalization procedure to determine the proper elements; (iii) the production of fragments through a simulated break-up event. We consider a model that includes the Keplerian part, an approximation of the geopotential, and the gravitational influence of Sun and Moon. We also evaluate the contribution of Solar radiation pressure and the effect of noise on the orbital elements. We implement a Lie series normalization procedure to compute the proper elements associated to semi-major axis, eccentricity and inclination. Based upon a wide range of samples, we conclude that the distribution of the proper elements in simulated break-up events (either collisions and explosions) shows an impressive connection with the dynamics observed immediately after the catastrophic event. The results are corroborated by a statistical data analysis based on the check of the Kolmogorov-Smirnov test and the computation of the Pearson correlation coefficient.

astro-ph.EP↗

Dark gravitomagnetism with LISA and gravitational waves space detectors

We present here the proposal to use the LISA interferometer for detecting the gravito-magnetic field due to the rotation of the Milky Way, including the contribution given by the dark matter halo. The galactic signal would be superposed to the gravitomagnetic field of the Sun. The technique to be used is based on the asymmetric propagation of light along the closed contour of the space interferometer (Sagnac-like approach). Both principle and practical aspects of the proposed experiment are discussed. The strategy for disentangling the sought for signal from the kinematic terms due to proper rotation and orbital motion is based on the time modulation of the time of flight asymmetry. Such modulation will be originated by the annual oscillation of the plane of the interferometer with respect to the galactic plane. Also the effect of the gravitomagnetic field on the polarization of the electromagnetic signals is presented as an in principle detectable phenomenon.

gr-qc↗

On the detuned 2:4 resonance

We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1:2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations. For cubic potentials this concerns the short axial orbits and in galactic dynamics the resulting stable periodic orbits are called "banana" orbits. Galactic potentials are symmetric with respect to the co-ordinate planes whence the potential -- and the normal form -- both have no cubic terms. This $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetry turns the 1:2 resonance into a higher order resonance and one therefore also speaks of the 2:4 resonance. In this paper we study the 2:4 resonance in its own right, not restricted to natural Hamiltonian systems where $H = T + V$ would consist of kinetic and (positional) potential energy. The short axial orbit then turns out to be dynamically stable everywhere except at a simultaneous bifurcation of banana and "anti-banana" orbits, while it is now the long axial orbit that loses and regains stability through two successive period-doubling bifurcations.

nlin.CD↗

An improved measurement of the Lense-Thirring precession on the orbits of laser-ranged satellites with an accuracy approaching the 1% level

We present a new measurement of the Lense-Thirring effect on the orbits of the geodetic satellites LAGEOS, LAGEOS II and LARES. This secular precession is a general relativity effect produced by the gravitomagnetic field of the Earth generated by its rotation. The effect is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein's theory of gravitation. This measurement stands out, compared to previous measurements in the same context, for its precision ($\simeq7.4\times10^{-3}$) and accuracy ($\simeq16\times10^{-3}$), i.e. for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. For this new measurement, we have largely exploited the results of GRACE mission to significantly improve the description of the gravitational field of the Earth, by also modeling its time dependence. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects.

gr-qc↗

Structure of the center manifold of the L1 and L2 collinear libration points in the restricted three-body problem

We present a global analysis of the center manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1 commensurability leads to the construction of a detuned Birkhoff-Gustavson normal form. The bifurcation sequences of the main orbit families are investigated by a geometric theory based on the reduction of the symmetries of the normal form, invariant under spatial mirror symmetries and time reversion. This global picture applies to any values of the mass parameter.

nlin.CD↗

Liquid actuated gravity experiments

We describe a new actuation technique for gravity experiments based on a liquid field mass. The Characterizing idea is to modulate the gravity force acting on a test mass by controlling the level of a liquid in a suitable container. This allows to obtain a periodical gravity force without moving parts (except the liquid level) close to the TM. We describe in detail the most relevant aspects of the liquid actuator and discuss how it can be used in gravity experiments. In particular we analyse an application to test the inverse square law in the mm to cm distance region.

physics.ins-det↗

Accurate modelling of the low-order secondary resonances in the spin-orbit problem

We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To this end we extend the perturbative approach introduced in Gkolias et. al. (2016), based on normal form series computations. This allows to recover analytically all non-trivial features of the phase space topology and bifurcations associated with these resonances. Applications include the characterization of spin states of irregular planetary satellites or double systems of minor bodies with irregular shapes. The key ingredients of our method are: i) the use of a detuning parameter measuring the distance from the exact resonance, and ii) an efficient scheme to `book-keep' the series terms, which allows to simultaneously treat all small parameters entering the problem. Explicit formulas are provided for each secondary resonance, yielding i) the time evolution of the spin state, ii) the form of phase portraits, iii) initial conditions and stability for periodic solutions, and iv) bifurcation diagrams associated with the periodic orbits. We give also error estimates of the method, based on analyzing the asymptotic behavior of the remainder of the normal form series.

astro-ph.EP↗

Satellite Laser Ranging and General Relativity measurements in the field of the Earth: state of the art and perspectives

Recent results of the LARASE research program in terms of models improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure of the satellite and of its physical characteristics in order to be correctly accounted for. In the field of gravitational measurements, we introduce a new and precise measurement of the relativistic Lense-Thirring precession. The role of the errors related to the knowledge of the gravitational field of the Earth in this kind of measurements is also discussed. Finally, the main results in relativistic measurements and constraints obtained during the last few years by means of the laser tracking of passive satellites are summarized. The key role of the Satellite Laser Ranging technique in these activities is highlighted, together with the sinergy it produces between space geodesy and fundamental physics measurements.

gr-qc↗

Element history of the Laplace resonance: a dynamical approach

We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In particular, we construct approximate models for the evolution of the librating argument over the period of 100 years, focusing on its principal amplitude and frequency, and on the observed mean motion combinations associated with the quasi-resonant interactions. First, we numerically propagated the Cartesian equations of motion of the Jovian system for the period under examination, and by comparing the results with a suitable set of ephemerides, we derived the main dynamical effects on the target quantities. Using these effects, we built an alternative Hamiltonian formulation and used the normal forms theory to locate the resonance and to compute its main amplitude and frequency. From the Cartesian model we observe that on the timescale considered and with ephemerides as initial conditions, both the librating argument and the diagnostics are well approximated by considering the mutual gravitational interactions of Jupiter and the Galilean moons (including Callisto), and the effect of Jupiter's J2 harmonic. Under the same initial conditions, the Hamiltonian formulation in which Callisto and J2 are reduced to their secular contributions achieves larger errors for the quantities above, particularly for the librating argument. By introducing appropriate resonant variables, we show that these errors can be reduced by moving in a certain action-angle phase plane, which in turn implies the necessity of a tradeoff in the selection of the initial conditions. In addition to being a good starting point for a deeper understanding of the Laplace resonance, the models and methods described are easily generalizable to different types of multi-body mean motion resonances. They are also prime tools for studying the dynamics of extrasolar systems.

astro-ph.EP↗

The dynamics of the de Sitter resonance

We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree of freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase-plane of the normal form, we can identify a \sl Laplace-like \rm configuration, which highlights many substantial aspects of the observed one.

astro-ph.EP↗

Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces

In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be due to, for example, a variation of the moments of inertia or to tidal interactions. In this work, we consider a simplified model describing the rotational dynamics, known as the spin-orbit problem, where we assume that the orbital motion is provided by a fixed Keplerian ellipse. We consider different examples in which a non-conservative force acts on the model and we propose an analytical method, which reduces the system to a Hamiltonian framework. In particular, we compute a time parametrisation in a series form, which allows us to transform the original system into a Hamiltonian one. We also provide applications of our method to study the rotational motion of a body with time-varying moments of inertia, e.g. an artificial satellite with flexible components, as well as subject to a tidal torque depending linearly on the velocity.

astro-ph.EP↗