Chaotic coexistence of librational and rotational dynamics in the averaged planar three-body problem

Through an appropriate change of reference frame and rescalings of the variables and the parameters introduced, the Hamiltonian of the three-body problem is written as a perturbed Kepler problem. In this system, new Delaunay variables are defined and a suitable configuration of the phase space and the mass parameters is chosen. In such a system, wide regions of librational and rotational motions where orbits are regular and stable are found. Close to the separatrix of these regions, the existence of chaotic motions presenting a double rotational and librational dynamics is proved, numerically, through Poincare sections and the use of FLI

On the propagation of a perturbation in an anharmonic system

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.Comment: 14 page

Euler integral as a source of chaos in the three–body problem

In this paper we address, from a purely numerical point of view, the question, raised in Pinzari (2019), Pinzari (2020), and partly considered in Pinzari (2020), Di Ruzza et al. (2020), Chen and Pinzari (2021), whether a certain function, referred to as “Euler Integral”, is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the “unperturbed separatrix”, which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the Euler Integral (which are in fact small), we detect the existence of chaos closely to the unperturbed separatrix. The latter result is obtained through a careful use of the machinery of covering relations, developed in Gierzkiewicz and Zgliczyński (2019), Zgliczynski and Gidea (2004), Wilczak and Zgliczynski (2003)

On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects

The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the planar circular case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple two-dimensional map, that is invariant with respect to the mass parameter of the planet, and turns out to be a remarkable tool to investigate the distribution of the co-orbitals objects of interest. The study is based on the data corresponding to the ephemerides computed by the JPL Horizons system for asteroids with a sufficient low orbital inclination with respect to the Sun–planet orbital plane. These objects are cataloged according to their current dynamics, together with the transitions that occur in the given time frame from a given type of co-orbital motion to another. The results provide a general catalog of co-orbital asteroids in the solar system, the first one to our knowledge, and an efficient mean to study transitions

The relativity experiment of MORE: global full-cycle simulation and results

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. In particular, the Mercury Orbiter Radioscience Experiment (MORE) intends, as one of its goals, to perform a test of General Relativity. This can be done by measuring and constraing the post-Newtonian (PN) parameters to an accuracy significantly better than current one. In this work we perform a global full-cycle simulation of the BepiColombo Radio Science Experiments (RSE) in a realistic scenario, focussing on the relativity experiment but solving simultaneously for all the parameters of interest for RSE in a global least squares fit within a constrained multiarc strategy. The results on the achievable accuracy for each PN parameter will be presented and discussed

The BepiColombo MORE gravimetry and rotation experiments with the ORBIT14 software

The BepiColombomission to Mercury is an ESA/JAXAcornerstone mission, consisting of two spacecraft in orbit around Mercury addressing several scientific issues. One spacecraft is the Mercury Planetary Orbiter, with full instrumentation to perform radio science experiments. Very precise radio tracking from Earth, on-board accelerometer and optical measurements will provide large data sets. From these it will be possible to study the global gravity field of Mercury and its tidal variations, its rotation state and the orbit of its centre of mass. With the gravity field and rotation state, it is possible to constrain the internal structure of the planet. With the orbit of Mercury, it is possible to constrain relativistic theories of gravitation. In order to assess that all the scientific goals are achievable with the required level of accuracy, full cycle numerical simulations of the radio science experiment have been performed. Simulated tracking, accelerometer and optical camera data have been generated, and a long list of variables including the spacecraft initial conditions, the accelerometer calibrations and the gravity field coefficients have been determined by a least-squares fit. The simulation results are encouraging: The experiments are feasible at the required level of accuracy provided that some critical terms in the accelerometer error are moderated. We will show that BepiColombo will be able to provide at least an order of magnitude improvement in the knowledge of Love number k2, libration amplitudes and obliquity, along with a gravity field determination up to degree 25 with a signal-to-noise ratio of 10

The radio science experiment with BepiColombo mission to Mercury

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radio science Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. Using radio observables (range and range-rate) performed with very accurate tracking from ground stations, together with optical observations from the on-board high resolution camera (SIMBIO-SYS) and accelerometer readings from the on-board accelerometer (ISA), MORE will be able to measure with unprecedented accuracy the global gravity field of Mercury and the rotation state of the planet. In this work we present the results of a numerical full-cycle simulation of the gravimetry and rotation experiments of MORE: we discuss the accuracies which can be achieved, focussing in particular on the possible benefits from the use of optical observations in support to the tracking measurements

The BepiColombo MORE gravimetry and rotation experiments with the ORBIT14 software

open6noopenG. Schettino, S. Di Ruzza, S. Cicalò, G. Tommei; A. Milani Comparetti; E.M. AlessiSchettino, G.; DI RUZZA, Sara; Cicalò, S.; Tommei, G.; Milani Comparetti, A.; Alessi, E. M

Operational experience, improvements, and performance of the CDF Run II silicon vertex detector

The Collider Detector at Fermilab (CDF) pursues a broad physics program at Fermilab's Tevatron collider. Between Run II commissioning in early 2001 and the end of operations in September 2011, the Tevatron delivered 12 fb-1 of integrated luminosity of p-pbar collisions at sqrt(s)=1.96 TeV. Many physics analyses undertaken by CDF require heavy flavor tagging with large charged particle tracking acceptance. To realize these goals, in 2001 CDF installed eight layers of silicon microstrip detectors around its interaction region. These detectors were designed for 2--5 years of operation, radiation doses up to 2 Mrad (0.02 Gy), and were expected to be replaced in 2004. The sensors were not replaced, and the Tevatron run was extended for several years beyond its design, exposing the sensors and electronics to much higher radiation doses than anticipated. In this paper we describe the operational challenges encountered over the past 10 years of running the CDF silicon detectors, the preventive measures undertaken, and the improvements made along the way to ensure their optimal performance for collecting high quality physics data. In addition, we describe the quantities and methods used to monitor radiation damage in the sensors for optimal performance and summarize the detector performance quantities important to CDF's physics program, including vertex resolution, heavy flavor tagging, and silicon vertex trigger performance.Comment: Preprint accepted for publication in Nuclear Instruments and Methods A (07/31/2013