Location, orbit and energy of a meteoroid impacting the moon during the Lunar Eclipse of January 21, 2019

During lunar eclipse of January 21, 2019 a meteoroid impacted the Moon producing a visible light flash. The impact was witnessed by casual observers offering an opportunity to study the phenomenon from multiple geographical locations. We use images and videos collected by observers in 7 countries to estimate the location, impact parameters (speed and incoming direction) and energy of the meteoroid. Using parallax, we achieve determining the impact location at lat. $-29.43^{+0.30}_{-0.21}$, lon. $-67.89^{+0.07}_{-0.09}$ and geocentric distance as 356553 km. After devising and applying a photo-metric procedure for measuring flash standard magnitudes in multiple RGB images having different exposure times, we found that the flash, had an average G-magnitude $\langle G\rangle = 6.7\pm0.3$. We use gravitational ray tracing (GRT) to estimate the orbital properties and likely radiant of the impactor. We find that the meteoroid impacted the moon with a speed of $14^{+7}_{-6}$ km/s (70% C.L.) and at a shallow angle, $\theta < 38.2$ degrees. Assuming a normal error for our estimated flash brightness, educated priors for the luminous efficiency and object density, and using the GRT-computed probability distributions of impact speed and incoming directions, we calculate posterior probability distributions for the kinetic energy (median $K_{\rm med}$ = 0.8 kton), body mass ($M_{\rm med}$ = 27 kg) and diameter ($d_{\rm med}$ = 29 cm), and crater size ($D_{\rm med}$ = 9 m). If our assumptions are correct, the crater left by the impact could be detectable by prospecting lunar probes. These results arose from a timely collaboration between professional and amateur astronomers which highlight the potential importance of citizen science in astronomy.Comment: 19 pages, 11 figures, 4 tables. Data and scripts available in https://github.com/seap-udea/MoonFlashes. Accepted for publication in MNRA

Jets, knots and tails in planetary nebulae: NGC 3918, K 1-2 and Wray 17-1

We analyze optical images and high-resolution, long-slit spectra of three planetary nebulae which possess collimated, low-ionization features. NGC 3918 is composed of an inner, spindle-shaped shell mildly inclined with respect to the plane of the sky. Departing from the polar regions of this shell, we find a two-sided jet expanding with velocities which increase linearly with distance from 50 to 100 km/s. The jet is probably coeval with the inner shell (with the age of approximately 1000 D yr, where D is the distance in kpc), suggesting that its formation should be ascribed to the same dynamical processes which also shaped the main nebula, and not to a more recent mass loss episode. We discuss the formation of the aspherical shell and jet in the light of current hydrodynamical and magnetohydrodynamical theories. K 1-2 is a planetary nebula with a close binary nucleus which shows a collimated string of knots embedded in a diffuse, elliptical shell. The knots expand with a velocity similar to that of the elliptical nebula (25 km/s), except for an extended tail located out of the main nebula, which linearly accelerates up to 45 km/s. We estimate an inclination on the line of the sight of 40 degres for the string of knots; once the orientation of the orbit is also determined, this information will allow us to test the prediction of current theories of the occurrence of polar jets from close binary systems. Wray 17-1 has a complex morphology, showing two pairs of low-ionization structures located in almost perpendicular directions from the central star, and embedded in a large, diffuse nebula. The two pairs show notable similarities and differences, and their origin is very puzzling.Comment: 20 pages plus 10 figures. ApJ recently published (ApJ 523, 721 (1999)

On the analytic-numeric treatment of weakly singular integrals on arbitrary polygonal domains

An alternative analytical approach to calculate the weakly singular free-space static potential integral associated to uniform sources is presented. Arbitrary oriented flat polygons are considered as integration domains. The technique stands out by its mathematical simplicity and it is based on a novel integral transformation. The presented formula is equivalent to others existing in literature, being also concise and suitable within a singularity subtraction framework. Generalized Cartesian product rules built on the double exponential formula are utilized to integrate numerically the resulting analytical 2D potential integral. As a consequence, drawbacks associated to endpoint singularities in the derivative of the potential are tempered. Numerical examples within a surface integral equation-Method of Moments framework are finally provided

Noether's Theorem and time-dependent quantum invariants

The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the non-stationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are obtained also from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated, and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares, UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994

On the Mechanism of the Copper-Catalyzed Enantioselective 1,4-Addition of Grignard Reagents to α,β-Unsaturated Carbonyl Compounds

The mechanism of the enantioselective 1,4-addition of Grignard reagents to α,β-unsaturated carbonyl compounds promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochemical analysis. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examined. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodynamic activation parameters were determined from the temperature dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.