On the stability of the satellites of asteroid 87 Sylvia

The triple asteroidal system (87) Sylvia is composed of a 280-km primary and two small moonlets named Romulus and Remus ( Marchis et al. 2005b ). Sylvia is located in the main asteroid belt, with semi-major axis of about 3.49 au, eccentricity of 0.08 and 11° of orbital inclination. The satellites are in nearly equatorial circular orbits around the primary, with orbital radius of about 1360 km (Romulus) and 710 km (Remus). In this work, we study the stability of the satellites Romulus and Remus. In order to identify the effects and the contribution of each perturber, we performed numerical simulations considering a set of different systems. The results from the three-body problem, Sylvia–Romulus–Remus, show no significant variation of their orbital elements. However, the inclinations of the satellites present a long-period evolution with amplitude of about 20° when the Sun is included in the system. Such amplitude is amplified to more than 50° when Jupiter is included. These evolutions are very similar for both satellites. An analysis of these results shows that Romulus and Remus are librating in a secular resonance and their longitude of the nodes are locked to each other. Further simulations show that the amplitude of oscillation of the satellites' inclination can reach higher values depending on the initial values of their longitude of pericentre. In those cases, the satellites get caught in an evection resonance with Jupiter, their eccentricities grow and they eventually collide with Sylvia. However, the orbital evolutions of the satellites became completely stable when the oblateness of Sylvia is included in the simulations. The value of Sylvia's J ₂ is about 0.17, which is very high. However, even just 0.1 per cent of this value is enough to keep the satellite's orbital elements with no significant variation.     

Rare-earth data on monzonoritic rocks related to anorthosites and their bearing on the nature of the parental magma of the anorthositic series

Major and trace elements have been determined in monzonoritic rocks (hypersthene-monzodiorite or jotunite) from two intrusions belonging to the South Rogaland anorthositic complex (Norway). The rare-earth abundance pattern reveals no Eu anomaly, or only a very small one. This fact together with field observations suggest that these rocks represent the parental magma of the anorthositic suite. High Ti and P abundances, low Si content, high Fe/Mg and K₂O/SiO₂ ratios are characteristics of the major element geochemistry. Absolute amounts of some trace elements abundances vary distinctly between the two intrusions. K/Rb ratios as high as 1700 are observed. Partial fusion of upper mantle kaersutite is proposed as a possible mechanism of magma generation. Partition coefficients between plagioclase phenocrysts and liquid are determined.     

Summer and winter differences in zooplankton biomass,distribution and size composition in the KwaZulu-Natal Bight,South Africa

Zooplankton biomass and distribution in the KwaZulu-Natal Bight were investigated in relation to environmental parameters during summer (January–February 2010) and winter (July–August 2010). Mean zooplankton biomass was significantly higher in winter (17.1 mg dry weight [DW] m^–3) than in summer (9.5 mg DW m^?3). In summer, total biomass was evenly distributed within the central bight, low off the Thukela River mouth and peaked near Durban. In winter, highest biomass was found offshore between Richards Bay and Cape St Lucia. Zooplankton biomass in each size class was significantly, negatively related to sea surface temperature and integrated nitrate, but positively related to surface chlorophyll a and dissolved oxygen. Zooplankton biomass was significantly related to bottom depth, with greatest total biomass located inshore (<50 m). Distribution across the shelf varied with zooplankton size. Seasonal differences in copepod size composition suggest that a smaller, younger community occupied the cool, chlorophyll-rich waters offshore from the St Lucia upwelling cell in winter, and a larger, older community occurred within the relatively warm and chlorophyll-poor central bight in summer. Nutrient enrichment from quasi-permanent upwelling off Durban and Richards Bay appears to have a greater influence on zooplankton biomass and distribution in the bight than the strongly seasonal nutrient input from the Thukela River.     

A New Framework for Solving the Spatial Network Problems Based on Line Graphs

In this article we define inverse line graphs of directed graphs as a new framework for solving some classical network analysis problems. The extraction method and theories of inverse line graphs are explained in this article. It is shown that by changing the analysis space from the original directed graph to the inverse line graph, complex problems can be changed into simpler problems. We show the usefulness of the proposed framework in two particular applications: shortest path computations and the more general route planning. Considering the implementation result, we expect that this framework could be used in many more network analysis problems.