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.     

A numerical study of aerosol growth in Titan's atmosphere

We present a simple model for the formation and growth of photochemical aerosols in the atmosphere of Titan. We show that, in general, an optically thick layer of particles in the size range required by models of Titan cannot be obtained at pressures less than about 2 mbar. Since the thin model of Titan's atmosphere requires that the inversion not extend below pressures of 0.11 mbar (D. M. Hunten and J. J. Caldwell, 1978, preprint), it seems to be ruled out by the calculations.     

The eruptive evolution of the Galilean satellites: Implications for the ancient magnetic field of Jupiter

The hypothesis considering the Jupiter-Sun system as a limiting case of a close binary star implies the initial relative ice abundances in all the Galilean satellites to be essentially equal. The satellites move in the Jovian magnetosphere; thus the unipolar current flowing through their bodies subjected their ices to volumetric electrolysis. Explosions of the electrolysis products resulted in a loss of ices. While Callisto did not explode at all, Ganymede exploded once, Europa twice, and Io two or three times. An analysis of the magnetic field changes needed to create the modern ice abundances in the satellite shows:

1. the initial field of Jupiter was ～10² times stronger when compared with the present-day field, and
2. the field had to decrease exponentially with τ_2| ≈ (0.6?1), which means its relic nature.

     

Population pressure and land use change: from tree crops to sawah in Northwestern Kalimantan,Indonesia

The author describes the role of population pressure in the current transition from tree crops to wet rice cultivation (sawah) in Northwestern Kalimantan, Indonesia. He contends that this change is occurring "because the senescent trees no longer produce enough commodities to exchange for rice to feed an enlarged population." The historical background is described, policies of the Indonesian government are discussed, and data are presented on the rate of population growth     

Systematic reductions of 19th century planetary observations

Systematic reductions of nineteenth century observations to the system of the FK4 are discussed. Reductions made on a nightly basis are described and compared with the results obtained through the use of conventional tables. The series of observations made at the Paris Observatory from 1837 to 1881 was used to compare the two methods, and a combined system of 24 000 FK4, FK4 Sup and AGK 3R positions and proper motions provided the reference stars. The results show that for Uranus the mean error of a single observation in right ascension is ±1..33 when tables are used for the reductions, and ±1.12 when nightly reductions are made, while in declination the corresponding mean errors are ±0.88 and ±0.80. The observations of Neptune show an even greater difference between the two methods; the mean errors for the tabular and nightly reductions are ±1.57 and ±1.09 in right ascension and ±0.88 and ±0.75 in declination. Secular rates in the (0–C)'s of Uranus of –0.029/year in right ascension and ±0.030/year in declination are present when the observations are reduced with tables. These rates are reduced to –0.007/year and +0.015/year, respectively, when nightly reductions are made.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

A polarimetric investigation of the eclipsing binary XY ursae majoris

On three nights in February 1976 we carried out polarimetric measurements, in V, of the short periodic eclipsing binary XY UMa, covering a complete cycle. The results are as follows:

1. Within all phase intervals the linear polarization does not exceed 0.1%.
2. In the phase range 0 ^p .95–1 ^p .35 the scatter of the Stokes parametersQ andU is about twice that within the phase interval 0 ^p .35–0 ^p .95.
3. A periodogram analysis of these data revealed a period of 21000 s, which is equal to half the orbital periodP _o=0^d.47899 within 1.5%.

From these we derive the conclusions that no circumstellar envelope can be made responsible for the observed long-term changes of the light curve and system brightness, supporting the earlier spectroscopic finding. The different scatter of the Stokes parameters at different phase intervals and theP _o/2 periodicity are in favor of the star spot model for XY UMa proposed by one of the authors (E. G.).     

Optimal curve fitting procedures applied to the light curves of classical cepheids

Optimal curve fitting procedures based on the well known Baade/Wesselink methodology have been applied to Stebbinset al.'s 6-colour photometry of the classical cepheids Cep and Aql. Radial velocity data have been represented by a Fourier series, while the brightness temperature at the effective wavelength of observation forms a convenient temperature variable in the fitting function. This fitting function requires the specification of six parameters which thus play the role of unknowns in the optimization problem, though, in fact, all six parameters cannot be independently determined.The formulation involves a simple connection between colours and brightness temperatures, and model stellar atmosphere calculations can provide such a connection. The model stellar atmosphere data of Carbon and Gingerich (1969), which take careful account of line blanketing effects are, to some extent, supported by the results for Aql, though the position is less certain in the case of Cep. On the basis of the Carbon and Gingerich data, and if we take into account various estimates of the interstellar reddening, the absolute magnitudes of Cep and Aql areM _v=–3.57 andM _v=–3.79, respectively; but optimal curve fits would decrease both these values by about 0^m.09.     

Some comments on the Oort cloud

The arguments used by Lyttleton to prove the nonexistence of the Oort cloud are reviewed, and it is shown that Oort's hypothesis remains consistent with observation. The 1950 model of the cloud cannot be correct and, by use of the results from a number of more recent papers, an improved model is described and compared with observations. It is emphasized that comparison of the predictions of theory with observations should concentrate on thea-distribution, as the 1/a-distribution masks much of the detailed structure of the theory. An order of magnitude argument is given which shows that 20% of so-called new comets have passed through the planetary system before, and the implications of this to the statistics of near-parabolic comet orbits are briefly investigated.