Modelling of Mercury’s surface composition and remote detection from the orbit with the BepiColombo Mercury Planetary Orbiter

It can be assumed that the composition of Mercury’s thin gas envelope (exosphere) is related to the composition of the planets crustal materials. If this relationship is true, then inferences regarding the bulk chemistry of the planet might be made from a thorough exospheric study. The most vexing of all unsolved problems is the uncertainty in the source of each component. Historically, it has been believed that H and He come primarily from the solar wind, while Na and K originate from volatilized materials partitioned between Mercury’s crust and meteoritic impactors. The processes that eject atoms and molecules into the exosphere of Mercury are generally considered to be thermal vaporization, photonstimulated desorption (PSD), impact vaporization, and ion sputtering. Each of these processes has its own temporal and spatial dependence. The exosphere is strongly influenced by Mercury’s highly elliptical orbit and rapid orbital speed. As a consequence the surface undergoes large fluctuations in temperature and experiences differences of insolation with longitude. We will discuss these processes but focus more on the expected surface composition and solar wind particle sputtering which releases material like Ca and other elements from the surface minerals and discuss the relevance of composition modelling

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Extended cusp-like regions and their dependence on the Polar orbit, seasonal variations, and interplanetary conditions

Extended cusp-like regions (ECRs) are surveyed, as observed by the Magnetospheric Ion Composition Sensor (MICS) of the Charge and Mass Magnetospheric Ion Composition Experiment (CAMMICE) instrument aboard Polar between 1996 and 1999. The first of these ECR events was observed on 29 May 1996, an event widely discussed in the literature and initially thought to be caused by tail lobe reconnection due to the coinciding prolonged interval of strong northward IMF. ECRs are characterized here by intense fluxes of magnetosheath-like ions in the energy-per-charge range of _1 to 10 keV e_1. We investigate the concurrence of ECRs with intervals of prolonged (lasting longer than 1 and 3 hours) orientations of the IMF vector and high solar wind dynamic pressure (PSW). Also investigated is the opposite concurrence, i.e., of the IMF and high PSW with ECRs. (Note that these surveys are asking distinctly different questions.) The former survey indicates that ECRs have no overall preference for any orientation of the IMF. However, the latter survey reveals that during northward IMF, particularly when accompanied by high PSW, ECRs are more likely. We also test for orbital and seasonal effects revealing that Polar has to be in a particular region to observe ECRs and that they occur more frequently around late spring. These results indicate that ECRs have three distinct causes and so can relate to extended intervals in (1) the cusp on open field lines, (2) the magnetosheath, and (3) the magnetopause indentation at the cusp, with the latter allowing magnetosheath plasma to approach close to the Earth without entering the magnetosphere.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Sagnac rotational phase shifts in a mesoscopic electron interferometer with spin-orbit interactions

The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result in a shift in the interference pattern proportional to the rotation rate. Here, we analyze the Sagnac effect in a mesoscopic semiconductor electron interferometer. We include in our analysis the Rashba spin-orbit interactions in the ring. Our results indicate that spin-orbit interactions increase the rotation-induced phase shift. We discuss the potential experimental observability of the Sagnac phase shift in such mesoscopic systems.

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

Disclosing the generic behavior of topological solutions: An orbit-based approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Orbit determination using GPS including perturbations due to geopotential coefficients of high degree and order and solar radiation pressure

The main target here is to determine the orbit of an artificial satellite, using signals of the GPS constellation and least squares algorithms implemented through sequential Givens rotations as a method of estimation, with the aim of improving the performance of the orbit estimation process and, at the same time, minimizing the computational procedure cost. Geopotential perturbations up to high order and direct solar radiation pressure were taken into account. It was also considered the position of the GPS antenna on the satellite body that, lately, consists of the influence of the satellite attitude motion in the orbit determination process. An application has been done, using real data from the Topex/Poseidon satellite, whose ephemeris is available at Internet. The best accuracy obtained in position was smaller than 5 meters for short period (2 hours) and smaller than 28 meters for long period (24 hours) orbit determination. In both cases, the perturbations mentioned before were taken into consideration and the analysis occurred without selective availability on the signals measurements.

A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Impact on Geographic Location Accuracy due to Different Satellite Orbit Ephemerides

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of J(2). The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.

Comment on Effect of spin-orbit interaction on the plasma excitations in a quantum wire

We comment on the recent results [Phys. Rev. B 70, 235314 (2004)] showing the dispersion relations of single-particle and collective excitations in quantum wires in the presence of the Rashba spin-orbit interaction (SOI). We claim that those calculations performed in the absence of SOI, and used as a strong reference to the interacting case, are unlikely to be correct. We show the correct omega-q plane of the system in the absence of Rashba SOI.