Some integrable cases of the two-body problem with mass depending both on time and distance

an extension of the Gylden-Meshcherskii problem when the mass depends both on time and distance between two bodies is considered. certain mass loss laws as well as the Meshcherskii position vector and time transformation are used to convert the problem into the cases with equations of motion arising from integrable potentials.     

The Morávka meteorite fall: 1. Description of the events and determination of the fireball trajectory and orbit from video records

Abstract— The Morávka (Czech Republic) meteorite fall occurred on May 6, 2000, 11:52 UT, during the daytime. Six H5–6 ordinary chondrites with a total mass of 1.4 kg were recovered. The corresponding fireball was witnessed by thousands of people and also videotaped by 3 casual witnesses. Sonic booms were recorded by 16 seismic stations in the Czech Republic and Poland and by one infrasonic station in Germany. A total of 2.5% of the fireball eyewitnesses reported electrophonic sounds. Satellites in Earth orbit detected part of the fireball light curve. In this first paper from a series of 4 papers devoted to the Morávka meteorite fall, we describe the circumstances of the fall and determine the fireball trajectory and orbit from calibrated video records. Morávka becomes one of only 6 meteorites with a known orbit. The slope of the trajectory was 20.4° to the horizontal, the initial velocity was 22.5 km/s, and the terminal height of the fireball was 21 km. The semimajor axis of the orbit was 1.85 AU, the perihelion distance was 0.982 AU, and the inclination was 32.2°. The fireball reached an absolute visual magnitude of ?20 at a height of 33 km.     

A possible presence of HeH+ in white dwarfs

The equivalent width calculations for the fundamental vibration rotation band lines of HeH⁺ have been carried out for a non-DA white dwarf model with an effective temperature of 12 000 K. BothP andR branch lines with rotational quantum numbersJ=3 to 18 were included in the calculations. A search for these lines in helium rich white dwarfs is suggested.     

Models for the magnitude‐distribution of brightest cluster galaxies

The brightest, or first-ranked, galaxies (BCGs) in rich clusters show a very small dispersion in luminosity, making them excellent standard candles. This small dispersion raises questions about the nature of BCGs. Are they simply the extremes of normal galaxies formed via a stochastic process, or do they belong to a special class of atypical objects? If they do, are all BCGs special, or do normal galaxies compete for the first rank? To answer these questions, we undertake a statistical study of BCG magnitudes using results from extreme value theory. Two-population models do better than one-population models. A simple scenario where a random boost in the magnitude of a fraction of bright normal galaxies forms a class of atypical galaxies best describes the observed distribution of BCG magnitudes.     

Measurement of radiative lifetimes and determination of transition probabilities of astrophysical interest in Ho iii

Lifetimes of six levels belonging to the 4f¹⁰6p configuration of Ho  iii have been measured for the first time using the time-resolved laser-induced fluorescence method. They are compared with multiconfigurational pseudo-relativistic Hartree–Fock calculations. A very good agreement is found. Using the experimental lifetimes and theoretical branching fractions, a first set of transition probabilities of astrophysical interest has been obtained for this ion.