Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

Seven Asteroids Studied from Modra Observatory in the Course of Binary Asteroid Photometric Campaign

We report lightcurves for five asteroids from the inner main belt—(1703) Barry, (2590) Mourão, (4022) Nonna, (5171) Augustesen, (23031) 1999 XX₇—and for two near-Earth asteroids—(100004) 1983 VA, (144922) 2005 CK₃₈—obtained at Modra Observatory as a part of binary asteroid photometric campaign. Estimated synodic rotational periods and amplitudes of their composite lightcurves were as follows: 107.1 ± 0.5 h, 0.5 mag for (1703) Barry; 15.59 ± 0.01 h, 0.49 mag for (2590) Mourão; 2.5877 ± 0.0005 h, 0.08 mag for (4022) Nonna; 474 ± 10 h, 0.8 mag for (5171) Augustesen; 3.075 ± 0.001 h, 0.43 mag for (23031) 1999 XX₇; 3.1643 ± 0.0009 h, 0.11 mag for (100004) 1983 VA; 4.7894 ± 0.0005 h, 0.27 mag for (144922) 2005 CK₃₈. The slow rotator (5171) Augustesen and possibly also (1703) Barry appear to be tumblers, though their precession periods can not be estimated from the available data.     

Observational Evidence for Rising Penumbral Flux Tubes?

On 13 May 2000 parts of a penumbra were observed in an active region NOAA 8990 with the La Palma Stokes Polarimeter attached to the Swedish Vacuum Solar Telescope. The stratification over the solar atmosphere of different physical parameters is retrieved from these data by using the Stokes inversion based on response functions. The results confirm the previous findings of the penumbral structure. In general, the magnetic field becomes weaker and more horizontal with increasing distance from the umbra and the line-of-sight velocities are increasing towards the outer boundary of the penumbra. The results also suggest the existence of the unresolved fine structure of the penumbra. The stratifications of the temperature and of the magnetic field strength indicate the presence of rising flux tubes, which were predicted theoretically by Schlichenmaier, Jahn and Schmidt (1998, Astron. Astrophys. 337, 897).     

Life history of the bathyal octopus Pteroctopus tetracirrhus (Mollusca,Cephalopoda) in the Mediterranean Sea

The life cycle of the deep-sea octopus Pteroctopus tetracirrhus was studied from monthly samples obtained throughout the year in different areas of the western Mediterranean (mainly around the Balearic Islands and along the coast of the Iberian Peninsula). A total of 373 individuals (205 females, 168 males) were analyzed; females ranged from 4.5 to 14.0 cm mantle length (ML) and males from 4.5 to 11.5 cm ML. There were few small-sized octopuses (<7 cm ML) in the samples, which might indicate that these individuals inhabit rocky grounds that are not accessible to trawlers or waters deeper than the maximum depth sampled (800 m). The species occurred more frequently around the Balearic Islands than along the Iberian Peninsula as they appeared in 20% and 7%, respectively, of the hauls in these areas. The octopus inhabits the lower continental shelf and upper slope in both areas, primarily between 200 and 500 m depth. Modal lengths were followed from autumn, when recruits were caught by trawlers, to summer, when reproduction took place. Females grew from 8 to 10 cm ML from winter to spring, but this modal size did not increase further in summer; males grew from 7 to 9 cm ML from winter to spring. The total disappearance of large individuals after summer suggests a life cycle lasting a single year. The evolution of the monthly mean sizes showed that the growth was best described by log-linear functions in both sexes. The length at first maturity was clearly higher in females (12 cm ML) than in males (8 cm ML). A total of 30 different prey items, belonging to four major taxonomic groups (crustaceans, osteichthyes, cephalopods and gastropods), were identified in the stomach contents. The diet of the octopus was based on crustaceans and teleosts, which accounted for 75% and 23% of the prey items, respectively. Cephalopods and gastropods were accessory prey as they only represented 1.6% and 0.7%, respectively, of the total. The octopus showed a marked preference for the benthic fish Symphurus nigrescens and the endobenthic crustacean Alpheus glaber. The bathymetric distribution of P. tetracirrhus coincides with those of these two main prey, which suggests that the distribution of the octopus might be strongly linked to its trophic resources.     

Book reviews

Astrophysics and Space Science -     

OPserver: interactive online computations of opacities and radiative accelerations

Codes to compute mean opacities and radiative accelerations for arbitrary chemical mixtures using the Opacity Project recently revised data have been restructured in a client–server architecture and transcribed as a subroutine library. This implementation increases efficiency in stellar modelling where element stratification due to diffusion processes is depth dependent, and thus requires repeated fast opacity re-estimates. Three user modes are provided to fit different computing environments, namely, a web browser, a local workstation and a distributed grid.     

The search for hot spots associated with the Cygnus X-3 relativistic jet

We report and shortly discuss here the observational work carried out in order to test the possibility that two previously detected radio sources, in the vicinity of the well known microquasar Cygnus X-3, could be hot spot tracers of interaction between its relativistic jet and the interstellar medium (ISM). The motivation behind this search is in part justified considering recent theoretical models of high energy γ-ray emission which strongly rely on the interaction sites of galactic relativistic jets with nearby ISM clouds. The results presented in this paper include an improved radio exploration of the several arc-minute field around Cygnus X-3 using the Very Large Array (VLA), as well as deep near infrared (NIR) imaging with the Calar Alto 3.5 m telescope. We anticipate here that our observations do not appear to support the initial hot spot hypothesis. Instead, the resulting images suggest that the two radio sources, originally believed to be hot spot candidates, are most likely background or foreground objects.     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.