Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative-velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and the Earth is possible, at least for the case of a two-dimensional system. Simulations assuming an initial uniform distribution of orbital eccentricities on the interval from 0 to e_max are found to produce final states containing too many bodies with masses which are too small when e_max < 0.10, while simulations with e_max > 0.20 result in too many catastrophic collisions between bodies thus preventing rapid accretion of planetary-size bodies. The e_max = 0.15 simulation ends with a state surprisingly similar to that of the present terrestrial planets and, therefore, provides a rough estimate of the range of radial sampling to be expected for the terrestrial planets.     

O VI (λ = 1032 Å) profiles in and above an active region prominence,compared to quiet Sun center and limb profiles

O vi ( = 1032 Å) profiles have been measured in and above a filament at the limb, previously analyzed in H i, Mg ii, Ca ii resonance lines (Vial et al., 1979). They are compared to profiles measured at the quiet Sun center and at the quiet Sun limb.Absolute intensities are found to be about 1.55 times larger than above the quiet limb at the same height (3); at the top of the prominence (15 above the limb) one finds a maximum blue shift and a minimum line width. The inferred non-thermal velocity (29 km s^–1) is about the same as in cooler lines while the approaching line-of-sight velocity (8 km s^–1) is lower than in Ca ii lines.The O vi profile recorded 30 above the limb outside the filament is wider (FWHM = 0.33 Å). It can be interpreted as a coronal emission of O vi ions with a temperature of about 10⁶ K, and a non-thermal velocity (NTV) of 49 km s^–1. This NTV is twice the NTV of quiet Sun center O vi profiles. Lower NTV require higher temperatures and densities (as suggested by K-coronameter measurements). Computed emission measures for this high temperature regime agree with determinations from disk intensities of euv lines.     

A new satellite of Saturn: Dione B

On March 1, 1980, observations of Saturn from Pic-du-Midi Observatory using a Lallemand electronographic camera led to the discovery of a new satellite (V magnitude ? + 17.5) whose orbital period is surprisingly similar to that of Dione.     

Contemporary urbanization and an optimal size for Soviet cities

This article is an English translation of the work cited in 46: 3092. The authors review the conclusions of Pivovarov (see 44: Title 3118) concerning the nature of the urbanization process and optimal city size in the USSR. The relationship between urbanization and the characteristics of a given socioeconomic system is examined, and the possibility of determining optimal size for cities of different functional types is evaluated     

A geographical interpretation of an attempt at migratory regionalization in Italy

In the first part, the authors review a group of studies dealing with the identification of regional differences in Italian migratory patterns, especially using the concept of migration field. The second part is devoted to a study of the hierarchical clustering of Italian provinces using 1973 inter-provincial migratory flow data. (summary in ENG, FRE)     

Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.