Photometry, light curve solution and period study of contact binary BX And

The photometry of the binary star BX And (HIP 10027) is performed during several nights in October and November 2019, and October 2020 using B, V, and R Johnson-Cousins filters in Dr. Mojtahedi Observatory of the University of Birjand. Astronomical image processing and data reduction are performed by the IRIS software and light curves are obtained. These curves, along with the radial velocity data of the binary star, are analyzed by the Phoebe program to determine the physical and geometric parameters of the system. The evolutionary state of this system is investigated using the Hertzsprung-Russell (H-R) and density vs color index diagrams. The O-C curve is plotted using the eclipse times obtained in this study and those reported in the literature. By fitting a quadratic function to this curve, a new linear ephemeris is obtained for the system, and the mass transfer rate between the components of the system is determined. A periodic behavior is observed in the residuals, after subtracting the quadratic function from the O-C curve. These periodic changes are attributed to the presence of a third component in the system. The parameters of the third component are determined by fitting the light-time function to the residuals curve.

Capsizing Performance of Dead Ship Stability for Damaged Ships

This study proposes a method for combining capsizing probability and flooding process to investigate the time-domain dead ship stability of a damaged ship. It focuses on a nonlinear righting lever GZ curve solution in the following aspects: one aspect subjects the influence of damaged tanks on a hull shape to the wind and wave, and the other aspect is based on a real-time calculation of the GZ curve. According to 1‐degree-of-freedom rolling equation, the damaged capsizing probability model is established through fourth-order Runge-Kutta algorithm and Monte Carlo simulation. Also, the model solution is applied on the basis of Visual Basic 6.0 language, and the results are compared with the NAPA platform. The most significant development in this study is combining time-domain flooding process and capsizing probability calculation. To verify the proposed methods, two damaged fishery bureau vessels are used as the sample ships. Results of time-domain capsizing probability under different loading conditions are compared, and the difference and its possible reasons are analyzed.

V1187 Herculis: A Red Novae progenitor, and the most extreme mass ratio binary known

Complete BVRCIC light curves of V1187 Her were obtained in May 2017 at the Dark Sky Observatory in North Carolina with the 0.81-m reflector of Appalachian State University. Earlier, spectra were taken at the Dominion Astrophysical Observatory with the 1.8-m telescope. The spectral type was found to be F8±1 V (6250 K), so the binary is of solar-type. V1187 Her was previously identified as a low amplitude (V < 0.2 mag), short period, overcontact eclipsing binary (EW) with a period of 0.310726 d. Strikingly, despite its low amplitude, the early light curves show total eclipses (eclipse duration ≍31.5 minutes), which is a characteristic of an extreme mass ratio binary. A period study covering 11 years reveals a continuous period decrease dP/dt=–4.7×10–9 d yr–1. The multi-band Wilson-Devinney light curve solution gives a fill-out of 79% and a mass ratio of only 0.0440±0.0001. There is a cool spot region on the secondary component, which is 400 K hotter than the primary. The inclination is only 66.85±0.05 despite the system’s total eclipses.

Pythagorean-hodograph cycloidal curves

In the paper, Pythagorean-hodograph cycloidal curves as an extension of PH cubics are introduced. Their properties are examined and a constructive geometric characterization is established. Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined. The asymptotic approximation order analysis carried out indicates clearly which interpolatory curve solution should be selected in practice. This makes the curves introduced here a useful practical tool, in particular in algorithms that guide CNC machines.