A volume-averaged nodal projection method for the Reissner-Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

First observations and magnitude measurement of Starlink's Darksat

Measure the Sloan g' magnitudes of the Starlink's STARLINK-1130 (Darksat) and 1113 LEO communication satellites and determine the effectiveness of the Darksat darkening treatment at 475.4\,nm. Two observations of the Starlink's Darksat LEO communication satellite were conducted on 2020/02/08 and 2020/03/06 using a Sloan r' and g' filter respectively. While a second satellite, STARLINK-1113 was observed on 2020/03/06 using a Sloan g' filter. The initial observation on 2020/02/08 was a test observation when Darksat was still manoeuvring to its nominal orbit and orientation. Based on the successful test observation, the first main observation was conducted on 2020/03/06 along with an observation of the second Starlink satellite. The calibration, image processing and analysis of the Darksat Sloan g' image gives an estimated Sloan g' magnitude of $7.46\pm0.04$ at a range of 976.50\,km. For STARLINK-1113 an estimated Sloan g' magnitude of $6.59\pm0.05$ at a range of 941.62\,km was found. When scaled to a range of 550\,km and corrected for the solar and observer phase angles, a reduction by a factor of two is seen in the reflected solar flux between Darksat and STARLINK-1113. The data and results presented in this work, show that the special darkening coating used by Starlink for Darksat has darkened the Sloan g' magnitude by $0.77\pm0.05$\,mag, when the range is equal to a nominal orbital height (550\,km). This result will serve members of the astronomical community modelling the satellite mega-constellations, to ascertain their true impact on both the amateur and professional astronomical communities. Concurrent and further observations are planned to cover the full optical and NIR spectrum, from an ensemble of instruments, telescopes and observatories.Comment: Accepted for publication in A&A Letters. 5 pages, 2 figures and 4 table

Spectroscopic Observations of New Oort Cloud Comet 2006 VZ13 and Four Other Comets

Spectral data are presented for comets 2006 VZ13 (LINEAR), 2006 K4 (NEAT), 2006 OF2 (Broughton), 2P/Encke, and 93P/Lovas I, obtained with the Cerro-Tololo Inter-American Observatory 1.5-m telescope in August 2007. Comet 2006 VZ13 is a new Oort cloud comet and shows strong lines of CN (3880 angstroms), the Swan band sequence for C_2 (4740, 5160, and 5630 angstroms), C_3 (4056 angstroms), and other faint species. Lines are also identified in the spectra of the other comets. Flux measurements of the CN, C_2 (Delta v = +1,0), and C_3 lines are recorded for each comet and production rates and ratios are derived. When considering the comets as a group, there is a correlation of C_2 and C_3 production with CN, but there is no conclusive evidence that the production rate ratios depend on heliocentric distance. The continuum is also measured, and the dust production and dust-to-gas ratios are calculated. There is a general trend, for the group of comets, between the dust-to-gas ratio and heliocentric distance, but it does not depend on dynamical age or class. Comet 2006 VZ13 is determined to be in the carbon-depleted (or Tempel 1 type) class.Comment: 8 pages, 6 figures, 6 tables; Accepted by MNRA

A search for evidence of irradiation in Centaurus X-4 during quiescence

We present a study of the neutron star X-Ray Transient Cen X-4. Our aim is to look for any evidence of irradiation of the companion with a detailed analysis of its radial velocity curve, relative contribution of the donor star and Doppler tomography of the main emission lines. To improve our study all our data are compared with a set of simulations that consider different physical parameters of the system, like the disc aperture angle and the mass ratio. We conclude that neither the radial velocity curve nor the orbital variation of the relative donor's contribution to the total flux are affected by irradiation. On the other hand, we do see emission from the donor star at H${\alpha}$ and HeI 5876 which we tentatively attribute to irradiation effects. In particular, the H${\alpha}$ emission from the companion is clearly asymmetric and we suggest is produced by irradiation from the hot-spot. Finally, from the velocity of the HeI 5876 spot we constrain the disc opening angle to alpha=7-14 deg.Comment: 4 pages, 5 figures, accepted for publication in A&A as a R

Optical-to-NIR magnitude measurements of the Starlink LEO Darksat satellite and effectiveness of the darkening treatment

Four observations of Starlink's LEO communication satellites, Darksat and STARLINK-1113, were conducted on two nights with two telescopes. The Chakana 0.6\,m telescope at the Ckoirama observatory (Chile) observed both satellites on 5\,Mar\,2020 (UTC) and 7\,Mar\,2020 (UTC) using a Sloan r' and Sloan i' filter, respectively. The ESO VISTA 4.1\,m telescope with the VIRCAM instrument observed both satellites on 5\,Mar\,2020 (UTC) and 7\,Mar\,2020 (UTC) in the NIR J-band and Ks-band, respectively. The calibration, image processing, and analysis of the Darksat images give r\,$\approx$\,5.6\,mag, i\,$\approx$\,5.0\,mag, J\,$\approx$\,4.2\,mag, and Ks\,$\approx$\,4.0\,mag when scaled to a range of 550\,km (airmass $=1$) and corrected for the solar incidence and observer phase angles. In comparison, the STARLINK-1113 images give r\,$\approx$\,4.9\,mag, i\,$\approx$\,4.4\,mag, J\,$\approx$\,3.8\,mag, and Ks\,$\approx$\,3.6\,mag when corrected for range, solar incidence, and observer phase angles. The data and results presented in this work show that the special darkening coating used by Starlink for Darksat has darkened the Sloan r' magnitude by 50\,\%, Sloan i' magnitude by 42\,\%, NIR J magnitude by 32\,\%, and NIR Ks magnitude by 28\,\%. The results show that both satellites increase in reflective brightness with increasing wavelength and that the effectiveness of the darkening treatment is reduced at longer wavelengths. This shows that the mitigation strategies being developed by Starlink and other LEO satellite operators need to take into account other wavelengths, not just the optical. This work highlights the continued importance of obtaining multi-wavelength observations of many different LEO satellites in order to characterise their reflective properties and to aid the community in developing impact simulations and developing mitigation tools.Comment: Accepted for publication in A&A, 10 pages, 10 figures, 3 table

739 observed NEAs and new 2-4m survey statistics within the EURONEAR network

We report follow-up observations of 477 program Near-Earth Asteroids (NEAs) using nine telescopes of the EURONEAR network having apertures between 0.3 and 4.2 m. Adding these NEAs to our previous results we now count 739 program NEAs followed-up by the EURONEAR network since 2006. The targets were selected using EURONEAR planning tools focusing on high priority objects. Analyzing the resulting orbital improvements suggests astrometric follow-up is most important days to weeks after discovery, with recovery at a new opposition also valuable. Additionally we observed 40 survey fields spanning three nights covering 11 sq. degrees near opposition, using the Wide Field Camera on the 2.5m Isaac Newton Telescope (INT), resulting in 104 discovered main belt asteroids (MBAs) and another 626 unknown one-night objects. These fields, plus program NEA fields from the INT and from the wide field MOSAIC II camera on the Blanco 4m telescope, generated around 12,000 observations of 2,000 minor planets (mostly MBAs) observed in 34 square degrees. We identify Near Earth Object (NEO) candidates among the unknown (single night) objects using three selection criteria. Testing these criteria on the (known) program NEAs shows the best selection methods are our epsilon-miu model which checks solar elongation and sky motion and the MPC's NEO rating tool. Our new data show that on average 0.5 NEO candidates per square degree should be observable in a 2m-class survey (in agreement with past results), while an average of 2.7 NEO candidates per square degree should be observable in a 4m-class survey (although our Blanco statistics were affected by clouds). At opposition just over 100 MBAs (1.6 unknown to every 1 known) per square degree are detectable to R=22 in a 2m survey based on the INT data, while our two best ecliptic Blanco fields away from opposition lead to 135 MBAs (2 unknown to every 1 known) to R=23.Comment: Published in Planetary and Space Sciences (Sep 2013

Transit timing variations in the WASP-4 planetary system*

Abstract Transits in the planetary system WASP-4 were recently found to occur 80 s earlier than expected in observations from the TESS satellite. We present 22 new times of mid-transit that confirm the existence of transit timing variations, and are well fitted by a quadratic ephemeris with period decay dP/dt = −9.2 ± 1.1 ms yr−1. We rule out instrumental issues, stellar activity and the Applegate mechanism as possible causes. The light-time effect is also not favoured due to the non-detection of changes in the systemic velocity. Orbital decay and apsidal precession are plausible but unproven. WASP-4 b is only the third hot Jupiter known to show transit timing variations to high confidence. We discuss a variety of observations of this and other planetary systems that would be useful in improving our understanding of WASP-4 in particular and orbital decay in general

The stellar occultation by Makemake on 2011 April 23

We have taken advantage of a stellar occultation by the dwarf planet Makemake on 2011 April 23, to determine several of its main physical properties. We present results from a multisite campaign with 8 positive occultation detections from 5 different sites, including data from the 8-m VLT and 3.5-m NTT telescopes in Chile, which have very high temporal resolution. Because the star was significantly fainter than Makemake (setting a record in the magnitude of a star whose occultation has been detected), the occultation resulted in a drop of just ~0.3 mag in the lightcurves. From the lightcurves we have been able to determine the size and shape of the body, its geometric albedo and constraints on its atmosphere