Resonant asteroids between the main belt and Jupiter's orbit

Selected orbits of asteroids close to the 3/2 and 4/3 resonances in the outer belt are studied by extended numerical integrations of the four-body problem Sun-Jupiter-Saturn-asteroid. Jupiter's variable eccentricity causes strong or dominant effects in the asteroidal eccentricity, rate of perihelion, and critical argument. However, a suitable transformation removes most of these effects by the transition to respective new quantities. Cases of circulation can change to permanent libration in the new critical argument. This happens in the case of (1256) Normannia, one of the two objects found to be circulating near the 3/2 resonance in former work. The other object, (334) Chicago, remains a case of circulation and shows significant deviations from quasi-periodic motion, contrary to all the other studied Hildas (3/2 cases) and to (279) Thule (4/3). Temporary libration with respect to a resonance of high order is visible in the long-period evolution of Chicago's orbit. There are cases of some analogy further inward in the belt: (903) Nealley changes to permanent libration at the 2/1 resonance by the use of the new critical argument, and (522) Helga's orbit shows a non-quasi-periodic behaviour.     

Libration of arguments of circumbinary-planet orbits at resonance

The paper refers to fictitious resonant orbits of planet type that surround both components of a binary system. In case of 16 studied examples a suitable choice of the starting values leads to a process of libration of special angular arguments and to an evolution with an at least temporary stay of the planet in the resonant orbit. The ratio of the periods of revolution of the binary and a planet is equal to 1:5. Eight orbits depend on the ratio 1:5 of the masses of the binary components, but two other ratios appear as well. The basis of this study is the planar, elliptic or circular restricted problem of three bodies, but remarks at the end of the text refer to a four-body problem.     

Gene flow and demographic history of the mangrove crab Neosarmatium meinerti: A case study from the western Indian Ocean

Most marine organisms are characterized by at least one planktonic phase during their life history, potentially allowing interconnection of populations separated by several hundred kilometers. For many years, the idea that marine species are genetically homogenous throughout their range of distribution, due to passive larval transport, has been a paradigm. Nowadays, a growing number of studies underline the existence of boundaries in the marine realm and highlight how larval dispersal is a complex process depending on biotic as well as abiotic factors. Marine fragmented habitats, such as atolls, mangroves and estuaries, are optimal systems for investigating the marine dispersion process under a metapopulation approach, since populations can be geographically defined a priori as opposed to those occupying open marine environments. Within this frame, the present paper investigates the population genetic structure and the demographic history of the mangrove crab Neosarmatium meinerti within the western Indian Ocean by partial sequences of the mitochondrial DNA cytochrome oxidase subunit I. A total of 167 specimens were sampled from six mangrove sites distributed along the East African coast, from Kenya to South Africa, also including a mangrove forest located on Mahé Island, Seychelles. A sharp genetic break between the mainland and the Seychelles is recorded, revealing the existence of two historically distinct groups that can be defined as independent evolutionary units. Gene flow along the East African coast appears to be high enough to form a single metapopulation, probably by means of stepping stone populations. Otherwise, this mainland metapopulation is currently under expansion through a gradual moving front from the subtropical toward the equatorial populations.     

Some recent work on the orbital theory of asteroids

This is a brief report on three theoretical projects about asteroids. The results presented here were recently obtained at the Astronomisches Rechen-Institut in Heidelberg, and it is planned to publish them in astronomy and Astrophysics in detail. The first project is a continuation of former work on asteroids with a mean motion commensurable to that of Jupiter (compare Schubart, 1968). In the two other cases the problem consists in the best possible determination of the value of a planetary mass in units of solar mass.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.     

Additional effects of resonance in Hilda-asteroid orbits by the combined action of Jupiter and Saturn

Inside the 3/2 mean motion resonance some Hilda-type orbits show effects of a three-body resonance that includes the frequency of the libration due to the 3/2 resonance. A graphical method presents numerical results for such orbits and demonstrates in 6 cases a process of temporary libration, that is ruled by the additional resonance together with the secular period of the eccentricities of Jupiter and Saturn.     

Numerical studies of chaotic Hilda-type orbits

Earlier work indicates a comparatively rapid chaotic evolution of the orbits of some Hilda asteroids that move at the border of the domain occupied by the characteristic parameters of the objects at the 3/2 mean motion resonance. A simple Jupiter–Saturn model of the forces leads to numerical results on some of these cases and allows a search for additional resonances that can contribute to the chaotic evolution. In this context the importance of the secondary resonances that depend on the period of revolution of the argument of perihelion is pointed out. Among the studied additional resonances there are three-body resonances with arguments that depend on the mean longitudes of Jupiter, Saturn, and asteroid, but on slowly circulating angular elements of the asteroid as well, and the frequency of these arguments is close to a rational ratio with respect to the frequency of the libration due to the basic resonance.     

Contrasting genetic diversity with phenotypic diversity in coloration and size in Xantho poressa (Brachyura: Xanthidae), with new results on its ecology

The ecology of Xantho poressa (Olivi, 1792) (Brachyura) was studied during field trips to the Mediterranean Sea, the Black Sea and the Spanish Atlantic Ocean. Our results reveal that X. poressa lives from the intertidal to the shallow subtidal zone, and inhabits relatively protected rocky shores, often with pebble underground, from juvenile to adult stages. A mark–recapture experiment revealed a high population density in this habitat. All stages, but predominantly juveniles, show a variability of colour patterns, which allow the crabs to blend in with the rocky substratum, thereby hiding from predators as passive defence. Adulthood can be reached with a carapace length smaller than 6 mm. The morphometric analysis of the species revealed allometric growth in carapace shape. Variability in overall size could be observed at different collecting sites. Neither the colour morphs nor the size differences could be attributed to differences of Cytochrome Oxidase subunit I mitochondrial DNA sequences, suggesting that ecological rather than genetic patterns are responsible for the different phenotypes.     

The planetary masses and the orbits of the first four minor planets

Numerical tests are the basis of a study about the effects caused in the orbits of the planets (1)–(4) by possible errors in the system of planetary masses. The masses of five major and three minor planets are considered. Especially, the effects caused by (1) Ceres in the orbit of (2) Pallas since the time of discovery are found to be large enough for a determination of the mass of Ceres. A first result for this mass is (6.7±0.4)×10^–10 solar masses.     

Numerical determination of proper inclinations of Hilda-type asteroids

Proper inclination and proper eccentricity are constants of integration in the theory of secular perturbations of an asteroid. This theory is based on simplified differential equations, and therefore it is not applicable to Hilda-type motion, a case of 3/2 resonance with respect to Jupiter. Numerical integration is necessary for an analogous study of the eccentric Hilda-type orbits. Values of proper eccentricity of real Hildas had resulted from such a study. Here the conditions of nature are approximated stepwise by proceeding from a simplified model to the rigorous problem Sun-Jupiter-Saturn-asteroid. This procedure leads to a way of determining proper inclinations of Hildas. Long-period integrations do not show variations of these characteristic values.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.This paper is dedicated to Professor Victor Szebehely.     

Low-eccentricity motion of asteroids near the 2/1 Jovian resonance

(903) Nealley moves on an orbit of low eccentricity with a mean motion that is slightly larger than the 2/1 value of resonance. This orbit and some related fictious orbits are studied by numerical integrations of the four-body problem Sun-Jupiter-Saturn-asteroid over an interval of 110000 yr. The author's experience on related cases of resonance allows a study of the variation of suitably defined orbital parameters. The long-term evolution of the orbits is compared with earlier predictions. Some of the librating orbits are temporarily captured in a secondary resonance that refers to three-dimensional motion and is demonstrated by a special example.