The formal integrals of the restricted planar problem of the three bodies

The first integrals of motion of the restricted planar circular problem of three bodies are constructed as the formal power series in r^1/2, r being the distance of a moving particle from the primary. It is shown that the coefficients of these series are trigonometric polynomials of an angular variable. Some particular solutions have been found in a closed form. The proposed method for constructing the formal integrals can be generalized to a spatial problem of three bodies.     

A 2000-YEAR CONTEXT FOR MODERN CLIMATE CHANGE

ABSTRACT. Although considerable attention has been paid to the record of temperature change over the last few centuries, the range and rate of change of atmospheric circulation and hydrology remain elusive. Here, eight latitudinally well-distributed (pole-equator-pole), highly resolved (annual to decadal) climate proxy records are presented that demonstrate major changes in these variables over the last 2000 years. A comparison between atmospheric ¹⁴C and these changes in climate demonstrates a first-order relationship between a variable Sun and climate. The relationship is seen on a global scale.     

Coulometric TCO2 analyses for marine studies; an introduction

Progress in the introduction of coulometry for the analysis of total carbon dioxide (TCO₂) in marine waters is described. An extractor—stripper removes CO₂ that is measured coulometrically by the quantity of electricity (coulombs) used to electrogenerate OH^? ions for the titration of the acid formed by the reaction of CO₂ and ethanolamine. The equivalence point is detected photometrically with thymolphthalein as the indicator, and Faraday's Law relates coulombs to equivalents of titrant generated and CO₂ determined so that there are no standard curves needed or titrants to standardize or store. Accuracy was determined by adding gelatin capsules containing 100–1500 μg C of pure CaCO₃ into the stripper, and accuracies of better than ± 1 μg C were achieved. The best precision for natural seawater (± 1 standard error) of ± 0.5 μmol l^?1 was found for 17 samples of Bermuda coastal waters having a mean TCO₂ of 2007.2 μmol l^?1 (0.05% CV). Sources of error and precautions are discussed. This method, which has been used successfully at sea, can be used to study a variety of marine phenomena involving TCO₂.     

Spectrophotometric Variability of Mira

Data from the Pulkovo spectrophotometric data base on the absolute quasimonochromatic fluxes from oCet in the 320–1080 nm range are used to determine the physical parameters of this star in different phases of its light curve. The continuum emission layer is found to expand between the phases of the cycle corresponding to the rising and falling branches of the light curve. The average expansion velocity is 32 km/s. By the time the star’s brightness has fallen by roughly three magnitudes, its radius has increased by almost a factor of three. Over this same time the temperature of the layer has fallen from 3000 K to 2200 K. For this expansion velocity, the calculated mass rate loss is ⊙ M /year.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 175–189 (May 2005).     

The internal magnetic field of the Sun and peculiarities of the solar activity cycles

The existence of prolonged periods of abnormally low solar activity (such as the Maunder minimum) is explained within the framework of Leighton's model of a solar cycle with a hypothetical internal magnetic field of the Sun taken into account.