A Monte Carlo investigation of Jovian perturbations on short-period comet orbits

We present statistical distributions of Jovian perturbations on short-period comet orbits resulting from accurate numerical integrations. Our sample of 60, 000 cometary orbits with low inclinations and random orientations is characterized by perihelia between 0 and 7 AU and aphelia between 4 and 13 AU. The perturbations considered are those experienced because of Jupiter's gravitation per orbital revolution by the comets. Regularization and accurate step-length control in the numerical integration gives statistical results appreciably different from those computed by Rickman and Vaghi (1978). Their use of a crude method of integration led to erroneous results for close encounters. Strong asymmetries of the $\text{δ(}\text{1}\text{a}\text{)}$ distributions, in particular for the extreme tails, are observed for perihelion- or aphelion-tangent orbits. These orbits are also shown to experience the strongest energy perturbations on the average. Some results concerning the perturbations of Tisserand parameters are indicated. The perturbation distributions for the angular elements are described and discussed. The role of the minimum distance from Jupiter as an indicator of perturbations is investigated.     

Radius of convergence of Lie series for some elliptic elements

For equatorial orbits about an oblate body, we show that the Lie series for the elliptic elementse,f,l and diverge when the oblateness exceeds a critical multiple of the transformed eccentricity constant. The use of similar truncated series expansions for such elliptic elements by Brouwer accounts for the first-order errors at low eccentricity in his derived coordinates for an artificial satellite.     

A survey of coronal holes and their solar wind associations throughout sunspot cycle 20

To gain insight into the relationships between solar activity, the occurrence and variability of coronal holes, and the association of such holes with solar wind features such as high-velocity streams, a study of the period 1963–1974 was made. This period corresponds approximately with sunspot cycle 20. The primary data used for this work consisted of X-ray and XUV solar images obtained from rockets. The investigation revealed that:

1. The polar coronal holes prominent at solar minimum, decreased in area as solar activity increased and were small or absent at maximum phase. This evolution exhibited the same phase difference between the two hemispheres that was observed in other indicators of activity.
2. During maximum, coronal holes occurred poleward of the sunspot belts and in the equatorial region between them. The observed equatorial holes were small and persisted for one or two solar rotations only; some high latitude holes had lifetimes exceeding two solar rotations.
3. During 1963–74 whenever XUV or X-ray images were available, nearly all recurrent solar wind streams of speed ?500 km s^?1 were found associated with coronal holes at less than 40° latitude; however some coronal holes appeared to have no associated wind streams at the Earth.

     

Studies of solar flares using optical,X-ray and radio data

I have studied a number of flares for which good X-ray and optical data were available. An average lag of 5.5 s between hard X-ray (HXR) start and H start, and HXR peak and Ha peak was found for 41 flares for which determination was possible. Allowing for time constants the time lag is zero. The peak H lasts until 5–6 keV soft X-ray (SXR) peak. The level of H intensity is determined by the SXR flux.Multiple spikes in HXR appear to correspond to different occurrences in the flare development. Flares with HXR always have a fast H rise. Several flares were observed in the 3835 band; such emission appears when the 5.1–6.6 keV flux exceeds 5 × 10⁴ ph cm^-2 s^-1 at the Earth. Smaller flares produce no 3835 emission; we conclude that coronal back conduction cannot produce the bright chromospheric network of that wavelength.The nearly simultaneous growth of H emission at distant points means an agent travelling faster than 5 × 10³ km s^-1 is responsible, presumably electrons.In all cases near the limb an elevated Ha source is seen with the same time duration as HXR flux; it is concluded that this H source is almost always an elevated cloud which is excited by the fast electrons. A rough calculation is given. Another calculation of H emission from compressed coronal material shows it to be inadequate.In several cases homologous flares occur within hours with the same X-ray properties.Radio models fit, more or less, with field strengths on the order of 100G. A number of flares are discussed in detail.     

The strength of the Sun's polar fields

The magnetic field strength within the polar caps of the Sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. In this paper we report measurements of the polar fields made at the Stanford Solar Observatory using the Fe i line 525.02 nm. We find that the average flux density poleward of 55° latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 × 10¹⁴ Wb. We also show that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.     

California's population geography: lessons for a fourth grade class

Purpose of this paper is to present a model for teaching fourth grade children some aspects of the population geography of California from a nontextual approach. The objective is to interest and instruct children in the mobility of the people, and on the reasons why so many families have moved to California from other states. Students should be alerted not only to internal migration problems, but to the excess of births over deaths. Materials necessary for the lessons are transparencies, overhead projector, marking pencils, chalk and chalkboard. After showing the students that California population has approximately doubled every 20 years, the students should be encouraged to find reasons explaining why people have moved to the state, should be able to categorize those reasons under the terms industrial/manufacturing, agricultural, urban or recreational, should learn how to plot population distribution on a California regional outline map, and should attempt to explain why certain parts of California are more popular than others. The teaching model described in this paper may be replicated with modfications for any grade level and area of study.     

Lithologic transition and bed thickness periodicities in turbidite successions of the Antola Formation, Northern Apennines, Italy

The Antola Formation of Upper Cretaceous age crops out extensively in the Northern Apennines and consists of graded units of calcareous sandstones, sandstones, marlstones, and shales. It can be subdivided into the Cerreto, Antola Marlstone, Bruggi, and S. Donato Members on the basis of bed thicknesses and percentage of shales. Although the whole formation is interpreted as a deep-sea basin plain deposit, the members constitute lateral facies subdivisions which range from proximal, thick-bedded turbidities that show a prevalence of thinning upward cycles in bed thicknesses to distal turbidites that show predominantly thickening upward cycles and have a high percentage of shale. Repetitive patterns in the lithological sequence of the turbidite association are generally distinctive and are satisfactorily described as first order Markov chains. Only the Antola Marlstone Member has an additional second order Markov property. Imaginary eigenvalues of the transition probability matrices of all but the Bruggi Member demonstrate a strong cyclic character in the lithologic ordering within the formation. The behaviour of the Antola Marlstone and of the Bruggi may reflect the influence of a secondary ophiolitic intra-basinal source of clastics that contributed sandy turbidites and olistostromes. Systematic long-term variations in the sequence of bed thickness development in some sections of the Antola Formation are often subtle and equivocal, and pose special problems in interpretation. Fourier analysis was applied to the task of partitioning fundamental wavelengths from “background noise” introduced by essentially random depositional processes. In all members there is (1) strong short-term wavelength of two to three beds indicative of alternating thin and thick beds and judged to be typical of turbidite sequences; (2) an intermediate wavelength ranging from about five beds (proximal facies), eight beds (distal) to nine beds (very distal), which have both thinning and thickening upward trends, interpreted respectively as valley fill due to shifting talwegs of low density turbidity currents, and to progradational, flat turbidite lobes; (3) a poorly defined long-term wave-length of from thirty to greater than sixty beds that may be related to an unspecified trend in the evolution of the sedimentary basin. Phase angles associated with the coniputed power spectra give indications as to the asymmetry (thickening or thinning upward) or symmetry of the representative units.     

A trough cross-stratified glaucarenite: a Cambrian tidal inlet accumulation

The upper part of the Riley Formation, Cambrian of central Texas, is primarily composed of a sequence of thoroughly trough cross-stratified deposits. The dominant lithologies range from fossiliferous glaucarenite to highly glauconitic bio-sparrudite. These cross-stratified deposits accumulated within a tidal inlet and associated lagoonal tributary and distributary channels. Tidal inlet-fill strata are underlain by shallow, open marine oosparites and biomicrites and are overlain by parallel bedded glaucarenites which accumulated as part of a barrier island complex. The parallel bedded deposits exhibit large scale, gently inclined strata, ripple cross-stratification, and a minor amount of vertical burrows. Some glaucarenite units within the tidal inlet-fill have local concentrations of skeletal material, primarily trilobite carapaces. These concentrations are most abundant in the bottoms of troughs. Cementation by bladed to fibrous spar between the carapaces has resulted in the nodular appearance of these skeletal accumulations. Calcite clasts, with relict evaporite textures, occur within the carbonate nodules and surrounding glaucarenite. These clasts were eroded from the shallow subsurface of the barrier island as the tidal inlet migrated. The presence of the former evaporite clasts attest to an arid climate at the time of their formation.     

Fair weather and storm sand transport on the Long Island, New York, inner shelf

Both spring-summer and fall-winter sand transport have been observed on the Long Island, New York, inner shelf at water depths of 20-22 m using a radio-isotope sand tracer system. The extent of dispersal of the tagged, fine sand was measured at 3 week intervals in two 70 day experiments. In the late spring and early summer, movement was primarily diffusive in nature, extending 100 m around the line of tracer injection, while late fall-winter patterns had strong advective features, including an ellipsoidal outline extending approximately 1500 m westward of the injection points after the passage of several storms with strong northeasterly winds. Near-bottom current observations made with Savonius rotor sensors identify the event responsible for the bulk of the transport over the 135 day observation period as a storm flow of 2 days duration. Tracer and current observations together suggest that westward winter storm flow along the Long Island shelf is the major mechanism of sand transport at these depths on a yearly time scale. A least-squares fit of several of the observed winter patterns with a plume model yields average sediment mass flux lower bounds of 3.2 × 10^?3 gm/cm/sec and 1.7 × 10^?1 gm/cm/sec for ‘typical’ and extreme winter storm activity.