Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

Structural and electrochemical characteristics of Mg((55-x))Ti(x)Ni((45-y))Pt(y) metal hydride electrodes

In recent years, Mg-Ni-based metastable alloys have been attracting attention due to their large hydrogen sorption capacities, low weight, low cost, and high availability. Despite the large discharge capacity and high activity of these alloys, the accelerated degradation of the discharge capacity after only few cycles of charge and discharge is the main shortcoming against their commercial use in batteries. The addition of alloying elements showed to be an effective way of improving the electrode performance of Mg-Ni-based alloys. In the present work, the effect of Ti and Pt alloying elements on the structure and electrode performance of a binary Mg-Ni alloy was investigated. The XRD and HRTEM revealed that all the investigated alloy compositions had multi-phase nanostructures, with crystallite size in the range of 6 nm. Moreover, the investigated alloying elements demonstrated remarkable improvements of both maximum discharge capacity and cycling life. Simultaneous addition of Ti and Pd demonstrated a synergetic effect on the electrochemical properties of the alloy electrodes. Among the investigated alloys, the best electrochemical performance was obtained for the Mg(51)Ti(4)Ni(43)Pt(2) composition (in at.%), which achieved 448 mAh g(-1) of maximum discharge capacity and retained almost 66% of this capacity after 10 cycles. In contrast, the binary Mg(55)Ni(45) alloy achieved only 248 mAh g(-1) and retained 11% of this capacity after 10 cycles. (C) 2010 Elsevier By. All rights reserved.