An asymptotic solution for the Trojan case of the plane elliptic restricted problem of three bodies

The planar motion of a Trojan asteroid is considered within the framework of the elliptic restricted three-body problem. The solution is derived asymptotically to second order taking the square root of the Jupiter-Sun mass ratio and the orbital eccentricity of Jupiter as first order quantities. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter including both short and long periodic terms resulting from the orbital accentricity of Jupiter.     

The three-dimensional motion of Trojan asteroids

The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time-scales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian pointsL ₄,L ₅, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed.     

Observed Trends in Severe Weather Conditions Based on Humidex,Wind Chill,and Heavy Rainfall Events in Canada for 1953–2012

Observed trends in severe weather conditions based on public alert statements issued by Environment Canada are examined for Canada. Changes in extreme heat and extreme cold events represented by various humidex and wind chill indices are analyzed for 1953–2012 at 126 climatological stations. Changes in heavy rainfall events based on rainfall amounts provided by tipping bucket rainfall gauges are analyzed for 1960–2012 at 285 stations. The results show that extreme heat events, defined as days with at least one hourly humidex value above 30, have increased significantly at more than 36% of the stations, most of which are located south of 55°N; days with nighttime hourly humidex values remaining above 20 have increased significantly at more than 52% of the stations, most of which are located south of 50°N. Extreme cold events represented by days with at least one hourly wind chill value below ?30 have decreased significantly at more than 76% of the stations across the country. No consistent changes were found in heavy rainfall events. Because city residents are very vulnerable to severe weather events, detailed results on changes in extreme heat, extreme cold, and heavy rainfall events are also provided for ten urban centres.     

Earliest Triassic microbialites in Çürük Dag,southern Turkey: composition,sequences and controls on formation

The Permian–Triassic Boundary sequence at Çürük Dag, near Antalya, Turkey, begins with a major erosion surface interpreted as being the Late Permian lowstand, on which lies ca 0·4 m of grainstone/packstone composed of ooids, peloids and bioclasts. Most ooids are superficial coats on fragments of calcite crystals presumed to be eroded from crystal fans which are no longer present. The erosion surface is smooth and shows no evidence of dissolution; the grainstone/packstone contains intraclasts of the underlying wackestone, proving erosion. Next are 15 m of microbialite comprised of interbedded stromatolites, thrombolites, plus beds of planar limestones with small‐scale erosion. The latter comprise a complex interlayering of stromatolitic, thrombolitic and peloidal fabrics and precipitated crystal fans, which form a hybrid of microbialite and inorganic carbonate, together with bioclastic debris and micrite. The Çürük Dag microbialite sequence is repetitious; the lower part is more complex, with abundant stromatolites and hybrid microbialites. Some of the stromatolites are themselves hybrids composed of peloids and crystal fans. In the upper part of the sequence stromatolites are missing and the rock is composed mostly of recrystallized thrombolites that develop upwards from tabular to domal form. The domes form directly below small breaks in microbialite growth where very thin shelly micrites and grainstones/packstones are deposited. Repetition of facies may be controlled by sea‐level change; a deepening‐up model is consistent with the evidence. Stromatolites (with abundant crystal fans) dominate in shallower water, deepening through hybrid microbialite and interlayered sediments to thrombolite, probably no more than a few tens of metres deep, followed by breaks and renewal of microbialite growth. An interpretation of open marine fully oxygenated waters for microbialite growth is consistent with ongoing parallel work that has identified Bairdioid ostracods in the microbialite, a group known to be open marine. However, other researchers have proposed low oxygen conditions for Permian–Triassic boundary facies globally, so work continues to confirm whether the Çürük Dag microbialite grew in dysoxic or normally oxygenated conditions. The principal stimulus for post‐extinction microbialites is likely to be carbonate supersaturation of the oceans. The microbialite sequence is overlain by a further 25 m of grainstone/packstone (without microbialite), followed by Early Triassic shales. Overall, microbialites form a thin aggradational sequence during an overall relative sea‐level rise, consistent with global eustatic rise following the Late Permian lowstand.     

Integration of sedimentology and ground‐penetrating radar for high‐resolution imaging of a carbonate platform

Ground‐penetrating radar has not been applied widely to the recognition of ancient carbonate platform geometries. This article reports the results of an integrated study performed on an Upper Jurassic outcrop from the south‐east Paris basin, where coral bioherms laterally change into prograding depositional sequences. Ground‐penetrating radar profiles illustrate the different bedding planes and major erosional unconformities visible at outcrop. A ground‐penetrating radar profile conducted at the base of the cliff displays a palaeotopographic surface on which the outcropping bioherms settled. The excellent penetration depths of the ground‐penetrating radar (20 m with a monostatic 200 MHz antenna) images the carbonate platform geometries, ranging between outcrop workscale (a few metres) and seismic scale (several hundreds of metres). This study supports recent evidence of icehouse conditions and induced sea‐level fluctuations controlling the Upper Jurassic carbonate production.     

Electron acceleration within coronal loops: A wave-particle process?

A simple model as given which aims at explaining how electrons could be accelerated within solar coronal loops due to their trapping by quasi-monochromatic whistler waves.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.