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The nearby astrometric-spectroscopic binary star Hip 68682 has an orbital period of ∼ 9.88 yr. The dynamical state (component masses and kinematic parameters) of this system is redetermined by fitting all the observational data available to us, including the radial velocity data (RVD), the relative position data (RPD), and the Hipparcos Intermediate Astrometric Data (HIAD). The precision-weighted sum of squared residuals calculated from our results is significantly smaller than the previous ones. With the simulated data based on Chinese Space Station Telescope (CSST), the relative orbit could be improved further.Based on the known apparent magnitude information and the fitted parallax 60.59 ± 0.36 mas, we derive the absolute V magnitudes of the two components as 5.21 mag and 8.91 mag, respectively. The component masses are determined to be 0.946 ± 0.024M⊙ and 0.526 ± 0.014M⊙. These improved dynamical masses are helpful to constrain the stellar empirical mass–luminosity relation (MLR) for low mass stars. However, significant improvement of mass–luminosity relation for this mass region still needs more data.

Machine learning is an efficient method for analysing and interpreting the increasing amount of astronomical data that are available. In this study, we show a pedagogical approach that should benefit anyone willing to experiment with deep learning techniques in the context of stellar parameter determination. Using the convolutional neural network architecture, we give a step-by-step overview of how to select the optimal parameters for deriving the most accurate values for the stellar parameters of stars: Teff{T}_{{\rm{eff}}}, logg\log g, [M/H], and vesini{v}_{e}\sin i. Synthetic spectra with random noise were used to constrain this method and to mimic the observations. We found that each stellar parameter requires a different combination of network hyperparameters and the maximum accuracy reached depends on this combination as well as the signal-to-noise ratio of the observations, and the architecture of the network. We also show that this technique can be applied to other spectral-types in different wavelength ranges after the technique has been optimized.

We present results of the investigation of the star LkHα 324/B, which belongs to the starforming dark cloud LDN 988. Based on high resolution spectroscopy, we determined its fundamental parameters as Teff=11,175±130 K, log(L*/L⊙)=1.87±0.07. According to these parameters, we found that LkHα 324/B is a pre-main sequence star with mass M≈3M⊙ and age t≈2.9 Myr. Recently, it underwent the phase of actively accreting the Herbig Ae/Be star, but accretion has now ceased in the LkHα 324/B system. This is consistent with the fact that the star is surrounded by a circumstellar disk with an inner cavity, as was determined from its spectral energy distribution. Our analysis revealed the peculiar abundance pattern of LkHα 324/B typical to those of magnetic Ap stars. It possesses mild underabundance of the light elements and excess up to ∼2–4 dex (in comparison to the Sun) of the iron peak and rare earth elements. We found no evidence for abrupt vertical abundances gradients in the lines forming the region of the LkHα 324/B atmosphere, in agreement with the results of the theoretical diffusion calculations in this temperature domain. From the intensification of the magnetically sensitive lines, we deduced that LkHα 324/B probably hosts a global magnetic field of ⟨B⟩≈3.5 kG strength. We suppose that the stabilizing role of this field favored the elements’ separation by diffusion before the star reached the main sequence.

I suggest that stars introduce mass and density scales that lead to “naturalness” in the Universe. Namely, two ratios of order unity. 1) The combination of the stellar mass scale, M*(c, ℏ, G, mp, me, e, …), with the Planck mass, MPl, and the Chandrasekhar mass leads to a ratio of order unity that reads NPl*≡MPl/(M*mp2)1/3≃0.15−3, where mp is the proton mass. 2) A system with a dynamical time equals to the nuclear life times of stars, τnuc*, has a density of ρD*(c,ℏ,G,mp,me,e,…)≡(Gτnuc*2)−1. The ratio of the dark energy density to this density is Nλ* = ρΛ/ρD* ≈ 10−7−105. Although the range is large, it is critically much smaller than the 123 orders of magnitude usually referred to when ρΛ is compered to the Planck density. In the pure fundamental particles domain there is no naturalness; either naturalness does not exist or there is a need for a new physics or new particles. The “Astrophysical Naturalness” offers a third possibility: stars introduce the combinations of, or relations among, known fundamental quantities that lead to naturalness.

Photometric observations in g' and i' bands of the newly-discovered W UMa stars WISEJ004327.7+722407 and WISEJ234557.8+510456 are presented. The two targets are with shallow-contact configurations and their components are of G{K spectral type. We found that WISEJ004327.7+722407 is of A subtype while WISEJ234557.8+510456 is of W subtype. The different light levels at the quadratures were reproduced by cool spots on the bigger components. The procedure for calculation of the global parameters of eclipsing binaries by light curve solutions and GAIA distances was refined for stars with deep eclipses. The obtained global parameters reveal that at least one of the components of WISEJ004327.7+722407 and WISEJ234557.8+510456 is oversized, overluminous and too hot compared with an MS star with the same mass.

The Kepler space telescope has detected a large number of variable stars. We summarize 2261 δ Scuti and hybrid variables in the literature, and perform time-frequency analysis on these variable stars. Two non-eclipsing binary systems, KIC 5080290 and KIC 5480114, are newly discovered. They both pass more detailed aperture photometry and bright star contamination checks. The results of the time-frequency analysis demonstrate that the companions are stellar objects with orbital periods of approximately 265 days and 445 days, respectively. The orbital parameters of the two systems and the lower mass limits of the companions are obtained. The primary stars of both systems are slightly evolved intermediate-mass stars. The detection of intermediate-mass binary stars is helpful to understand the formation and evolution mechanism of binary stars in this mass region.

Evidence from the analysis of eclipsing binary systems revealed that late-type stars are larger and cooler than predicted by models, and that this is probably caused by stellar magnetic activity. In this work, we revisit this problem taking into account the advancements in the last decade. We provide and updated a list of 32 eclipsing binary or multiple systems, including at least one star with a mass ≲0.7 M⊙ and with mass and radius measured to an accuracy better than 3%. The comparison with stellar structure and evolution theoretical models reveals an overall discrepancy of about 7% and −4% for the radius and effective temperature, respectively, and that it may be larger than previously found below the full convection boundary. Furthermore, the hypothesis of stellar activity is reinforced by the comparison of different systems with similar components. Further eclipsing binaries with accurately determined masses and radii, and with estimated activity levels, as well as the implementation of magnetic activity in theoretical models will help to improve our knowledge of low-mass stars, which are prime targets for exoplanet surveys.

We present a method for deriving the stellar fundamental parameters. It is based on a regularized sliced inverse regression (RSIR).We first tested it on noisy synthetic spectra of A, F, G, and K-type stars, and inverted simultaneously their atmospheric fundamental parameters: Teff., log g, [M/H] and v sin i. Different learning databases were calculated using a range of sampling in Teff., log g, v sin i, and [M/H]. Combined with a principal component analysis (PCA) nearest neighbors (NN) search, the size of the learning database is reduced. A Tikhonov regularization is applied, given the ill-conditioning of SIR. For all spectral types, decreasing the size of the learning database allowed us to reach internal accuracies better than PCA-based NN-search using larger learning databases. For each analyzed parameter, we have reached internal errors that are smaller than the sampling step of the parameter. We have also applied the technique to a sample of observed FGK and A stars. For a selection of well-studied stars, the inverted parameters are in agreement with the ones derived in previous studies. The RSIR inversion technique, complemented with PCA pre-processing proves to be efficient in estimating stellar parameters of A, F, G, and K-type stars.

HW Vir systems are rare eclipsing binary systems including a subdwarf B star (sdB) with a faint companion, mostly M-dwarfs. Up to now, 19 HW Vir systems have been published, three of them with substellar companions. We report the spectroscopic as well as photometric observation of the eclipsing sdB binary PTF1 J011339.09+225739.1 (PTF1 J0113) in a close (a=0.722 ± 0.023 R⊙), short period (P = 0.0933731(3)d) orbit. A quantitative spectral analysis of the sdB yields Te.=29280 ± 720 K, log(g)=5.77 ± 0.09 dex, and log(y)=−2.32 ± 0.12. The circular orbital velocity of the sdB of K1=74.2 ± 1.7 km s−1 is derived from the radial velocity curve. Except for the strong reflection effect, no other light contribution of the companion could be detected. The light curves - recorded with ULTRACAM - were analyzed using the Wilson-Devinney code. We find an inclination angle of i=79.88 ± 0.18∘. Because our first attempts to determine q failed, we calculated large grids of synthetic lightcurves for several mass ratios. Because of degeneracy, good solutions for different mass ratios were found - the one at q = 0.24 is consistent with the sdB’s canonical mass (MsdB = 0.47 M⊙). Accordingly, the mass of the companion is M2=0.112 ± 0.003 M⊙. The radii of the two components were also derived: RsdB=0.178 ± 0.006 R⊙ and R2 = 0.158 ± 0.009 R⊙. Thus, the results for the secondary are consistent with an M-dwarf as secondary

We present photometric observations in Sloan filters g’, i’ of the short-period eclipsing stars KR Lyn, CSS J110212+244412, NSVS 4917488 and NSVS 7336024. The light curve solutions revealed that all targets are overcontact binaries whose components are G and K stars. Their temperature differences do not exceed 300 K but they differ considerably in size and mass. NSVS 4917488 and NSVS 7336024 reveal total eclipses and their parameters can be considered as well-determined. We found that KR Lyn, NSVS 4917488 and NSVS 7336024 are of W-subtype while CSS J110212+244412 is A-subtype W UMa-type star.

Decades ago, 3He isotope enrichment in helium-weak B-type main-sequence, in blue horizontal branch and in hot subdwarf B (sdB) stars, i.e., helium-core burning stars of the extreme horizontal branch, were discovered. Diffusion processes in the atmosphere of these stars lead to the observed abundance anomalies. Quantitative spectral analyses of high-resolution spectra to derive photospheric isotopic helium abundance ratios for known 3He sdBs have not been performed yet. We present preliminary results of high-resolution and high S/N spectra to determine the 3He and 4He abundances of nine known 3He sdBs. We used a hybrid local/non-local thermodynamic equilibrium (LTE/NLTE) approach for B-type stars investigating multiple He i lines, including λ4922 Å and λ6678 Å, which show the strongest isotopic shifts in the optical spectral range.We also report the discovery of four new 3He sdBs from the ESO Supernova Progenitor survey. Most of the 3He sdBs cluster in a narrow temperature strip between ∼ 26000 K and ∼ 30000 K and have almost no atmospheric 4He at all. Interestingly, three 3He sdBs show evidence for vertical helium stratification.

Binary stars are crucial laboratories for stellar physics, so have been photometric targets for space missions beginning with the very first orbiting telescope (OAO-2) launched in 1968. This review traces the binary stars observed and the scientific results obtained from the early days of ultraviolet missions (OAO-2, Voyager, ANS, IUE), through a period of diversification (Hipparcos, WIRE, MOST, BRITE), to the current era of large planetary transit surveys (CoRoT, Kepler, TESS). In this time observations have been obtained of detached, semi-detached and contact binaries containing dwarfs, sub-giants, giants, supergiants, white dwarfs, planets, neutron stars and accretion discs. Recent missions have found a huge variety of objects such as pulsating stars in eclipsing binaries, multi-eclipsers, heartbeat stars and binaries hosting transiting planets. Particular attention is paid to eclipsing binaries, because they are staggeringly useful, and to the NASA Transiting Exoplanet Survey Satellite (TESS) because its huge sky coverage enables a wide range of scientific investigations with unprecedented ease. These results are placed into context, future missions are discussed, and a list of important science goals is presented.

A significant part of the project is already implemented. Actually, high-resolution spectra of more than 100 early B stars were obtained. A number of basic parameters was determined including the effective temperatures Teff , surface gravities log g, masses M, ages t etc. A detailed non-LTE analysis of HeI lines was effected to find the helium abundance He/H, microturbulent parameter Vt and rotational velocity v sin i . Relations between He/H and Vt , from the one hand, and M, t/tms and v sin i , from the other hand, were constructed. It was confirmed that there is the helium enrichment during the MS phase, which correlates with the masses M and rotational velocities v sin i . It is necessary to note that from the outset we tried to get a highest accuracy on each stage of this work. At present we are implementing a last stage of the project, i.e. an analysis of CII, NII and OII lines on the basis of non-LTE computations. Our goal is an accurate determination of the C, N and O abundances and a search for correlations with M, t/tms and v sin i.

We carried out light curve solutions of four detached binaries observed by Kepler. As a result, their orbital inclinations, temperatures and relative stellar radii were determined. KIC 10031409 and KIC 11228612 reveal partial eclipses while the components of KIC 11403216 and KIC 11913071 undergo total eclipses. The secondary component of KIC 11403216 is probably a very late M dwarf or brown dwarf. The out-of-eclipse brightness of KIC 10031409, KIC 11228612 and KIC 11913071 vary with the orbital period and might be explained by spots on synchronously-rotating star(s). The out-of-eclipse variability of KIC 11403216 is with a period that is a third of its orbital period and may be due to spot on asynchronous rotating component. The resonance 1:3 needs future study of KIC 11403216.

Developing methods for analyzing and extracting information from modern sky surveys is a challenging task in astrophysical studies. We study possibilities of parameterizing stars and interstellar medium from multicolor photometry performed in three modern photometric surveys: GALEX, SDSS, and 2MASS. For this purpose, we have developed a method to estimate stellar radius from effective temperature and gravity with the help of evolutionary tracks and model stellar atmospheres. In accordance with the evolution rate at every point of the evolutionary track, star formation rate, and initial mass function, a weight is assigned to the resulting value of radius that allows us to estimate the radius more accurately. The method is verified for the most populated areas of the Hertzsprung-Russell diagram: main-sequence stars and red giants, and it was found to be rather precise (for main-sequence stars, the average relative error of radius and its standard deviation are 0.03% and 3.87%, respectively).

The paper presents light curve solutions of our observations of four new ultrashort-period eclipsing binaries with MS components. Two of them have periods almost at the upper limit (0.22 days) of the ultrashort-period binaries, while the periods of around 0.18 days of CSS J171508.5+350658 and CSS J214633.8+120016 are amongst the shortest known orbital periods. CSS J171410.0+ 445850, CSS J214633.8+120016 and CSS J224326.0+154532 are over contact binaries with fill out factors around 0.25 while CSS J171508.5+350658 is a semidetached system. The two targets with shortest periods consist of M dwarfs.

We present follow-up photometric observations in Sloan filters g', i' of the newly discovered eclipsing stars USNO-B1.0 1395-0370184 and USNO-B1.0 1395-0370731. Our data revealed that their orbital periods are considerably bigger than the previous values. This result changed the classification of USNO-B1.0 1395-0370184 from ultrashort-period binary (P=0.197 d) to short-period system (P=0.251 d). The light curve solutions of our observations revealed that USNOB1.0 1395-0370184 and USNO-B1.0 1395-0370731 are overcontact binaries in which components are K dwarfs, close in masses and radii. The light curve distortions were reproduced by cool spots with angular radius of around 20°.

Modern spectrophotometric atlases are burdened with significant systematic errors. In particular, the problems of spectrum calibration in the ultraviolet region are not solved; different parts of the spectrum are not thoroughly fit to each other; spectra of (even bright) stars, obtained by different authors, display large discrepancies. Here we discuss a possibility to construct a new atlas of spectral energy distributions (SEDs) for a large set of stars by comparison of empirical stellar spectra in dozens of modern spectrophotometric atlases, as well as the comparison of synthetic and observed color indices in different multicolor photometric systems. In this way we suppose to exclude most of systematic errors and construct a new three-dimensional (spectral class, luminosity class, metallicity) atlas of empirical stellar spectra for several thousand stars. After exclusion of interstellar reddenings, a semi-empirical atlas of average SEDs can be constructed for about 150–200 spectral subtypes. This would allow us to make calibrations of spectrophotometric and photometric parameters in terms of spectral types and physical parameters (Teff, log g, [m/H]) and to verify the accuracy of model stellar atmospheres.

We present the simultaneous light and radial velocity curve analysis of two contact binaries in Pegasus using the Wilson-Devinney code. The following absolute astrophysical parameters are determined: masses, radii and effective temperatures. BB Peg is a W-subtype W UMa-type binary, components of which are main sequence stars with 0.50 M⊙ and 1.40 M⊙. The radii of its components are R1 = 0.81 R⊙ and R2 = 1.28 R⊙. V407 Peg is an A-subtype contact binary composed of two subgiant components with masses 1.70 M⊙ and 0.43 M⊙, and radii R1 = 2.17 R⊙ and R2 = 1.25 R⊙. Comparisons with the theoretical models for solar composition by Girardi et al. (2000) confirms our classification and supports the results.

Since the discovery of λ Bootis stars, a permanent confusion about their classification can be found in literature. This group of non-magnetic, Population I, metal-poor A to F-type stars, has often been used as some sort of trash can for "exotic" and spectroscopically dubious objects. Some attempts have been made to establish a homogeneous group of stars which share the same common properties. Unfortunately, the flood of "new" information (e.g. UV and IR data) led again to a whole zoo of objects classified as λ Bootis stars, which, however, are apparent non-members. To overcome this unsatisfying situation, a spectral atlas of well established λ Bootis stars for the classical optical domain was compiled. It includes intermediate dispersion (40 and 120Å mm-1) spectra of three λ Bootis, as well as appropriate MK standard stars. Furthermore, "suspicious" objects, such as shell and Field Horizontal Branch stars, have been considered in order to provide to classifiers a homogeneous reference. As a further step, a high resolution (8Å mm-1) spectrum of one "classical" λ Bootis star in the same wavelength region (3800-4600Å) is presented. In total, 55 lines can be used for this particular star to derive detailed abundances for nine heavy elements (Mg, Ca, Sc, Ti, Cr, Mn, Fe, Sr and Ba).

We present a new calibration of the seven-color Vilnius system in terms of [Fe/H], applicable to F–M stars in the metallicity range −2.8 ≤[Fe/H]≤ +0.5. We employ a purely empirical approach, based on ~1000 calibrating stars with high-resolution spectroscopic abundance determinations. It is shown that the color index P–Y is the best choice for a most accurate and sensitive abundance indicator for both dwarf and giant stars. Using it, [Fe/H] values can be determined with an accuracy of ±0.12 dex for stars of solar and mildly subsolar metallicity and ±0.17 dex for stars with [Fe/H] < −1. The new calibration is a significant improvement over the previous one used to date.

The main features of the temperature correction methods, suggested and used in modeling of plane-parallel stellar atmospheres, are discussed. The main features of the new method are described. Derivation of the formulae for a version of the Unsöld-Lucy method, used by us in the SMART (Stellar Model Atmospheres and Radiative Transport) software for modeling stellar atmospheres, is presented. The method is based on a correction of the model temperature distribution based on minimizing differences of flux from its accepted constant value and on the requirement of the lack of its gradient, meaning that local source and sink terms of radiation must be equal. The final relative flux constancy obtainable by the method with the SMART code turned out to have the precision of the order of 0.5 %. Some of the rapidly converging iteration steps can be useful before starting the high-precision model correction. The corrections of both the flux value and of its gradient, like in Unsöld-Lucy method, are unavoidably needed to obtain high-precision flux constancy. A new temperature correction method to obtain high-precision flux constancy for plane-parallel LTE model stellar atmospheres is proposed and studied. The non-linear optimization is carried out by the least squares, in which the Levenberg-Marquardt correction method and thereafter additional correction by the Broyden iteration loop were applied. Small finite differences of temperature (δT/T = 10−3) are used in the computations. A single Jacobian step appears to be mostly sufficient to get flux constancy of the order 10−2 %. The dual numbers and their generalization – the dual complex numbers (the duplex numbers) – enable automatically to get the derivatives in the nilpotent part of the dual numbers. A version of the SMART software is in the stage of refactorization to dual and duplex numbers, what enables to get rid of the finite differences, as an additional source of lowering precision of the computed results.

In the present study we had three main aims. First to study the possibility of reducing the initial model atmosphere data to short analytical polynomials. The second was to use as the depth variable the logarithm of the local gas pressure instead the Rosseland mean. The third aim was to check the applicability of the derived formulae and proposed computation methods to obtain high precision self-consistent results in modeling hot plane-parallel stellar atmospheres. Introducing the dimensionless (reduced) local quantities θ = T/Teff and β = P/P(Teff) it has been shown that for hot convection-free stellar atmospheres the curves log θ versus log β reduce an initial grid of models to simple polynomials and bring forth some general features of the model stellar atmospheres. Even for stellar atmospheres having the convective zones in the deeper atmospheric layers, the outer part of the atmosphere (up to T = Teff and for Teff > 5000 K) can be described in the same manner by curves log θ versus log β as for the hotter stars. Iterative modeling of any hot stellar atmosphere can be started from these formulae (obtained for solar abundances), using rational polynomial ratios for P(Teff), obtaining from these data the needed T versus P dependence. To check suitability of the formulae, the iterative correction of the model stellar atmospheres has been carried out by the traditional Unsöld-Lucy method and by the novel least squares optimization based on Levenberg-Marquardt method, followed by Broyden correction loop. It has been shown that the flux constancy obtained by it is almost 2 dex higher than obtained by the Unsöld-Lucy method. The precision estimators as criteria of the modeling algorithms self-consistency and of the computational precision level have been proposed and used.

The paper presents an analysis of photometric observations of the eclipsing binary QW Gem. The orbital and physical parameters of the system are derived using the modeling code by G. Djurašević. Photometric observations are obtained from the SuperWASP public archive and the spectroscopic elements are adopted from a recently published radial velocity study. The results suggest that QW Gem is a binary in overcontact configuration, consisting of two stars of similar surface brightness but in different evolutionary stages.

In the Sixth Catalog of Orbits of Visual Binary Stars we found those belonging to the Main Sequence to form a sample containing 432 visual binaries. Their total masses were obtained dynamically, i.e. they were calculated using the orbital elements and the new Hipparcos parallaxes. For the same pairs the total mass was also found astrophysically - by applying the mass-luminosity relation. The apparent magnitudes of the components were found in two different ways: by deriving them from total magnitudes and magnitude differences, and by taking their values directly from a catalogue. The results for these two approaches show no essential discrepancy. The values of total masses obtained dynamically have a large dispersion involving even completely unrealistic values. This is a clear indication that the input data are not sufficiently reliable. Nevertheless, in a large number of cases the agreement between total masses obtained by usin two different ways is quite satisfactory indicating that i) for many visual binaries, as a rule not too distant and with high-quality orbital elements, the dynamical total masses can be reliable; ii) the mass-luminosity relation yields quite satisfactory estimates for the component masses when they belong to the Main Sequence and iii) a correlation between the relative parallax error and orbit grade exists.

In the Sixth Catalog of Orbits of Visual Binary Stars we found those belonging to the Main Sequence to form a sample containing 432 visual binaries. Their total masses were obtained dynamically, i.e. they were calculated using the orbital elements and the new Hipparcos parallaxes. For the same pairs the total mass was also found astrophysically - by applying the mass-luminosity relation. The apparent magnitudes of the components were found in two different ways: by deriving them from total magnitudes and magnitude differences, and by taking their values directly from a catalogue. The results for these two approaches show no essential discrepancy. The values of total masses obtained dynamically have a large dispersion involving even completely unrealistic values. This is a clear indication that the input data are not sufficiently reliable. Nevertheless, in a large number of cases the agreement between total masses obtained by us in two different ways is quite satisfactory indicating that i) for many visual binaries, as a rule not too distant and with high-quality orbital elements, the dynamical total masses can be reliable; ii) the mass-luminosity relation yields quite satisfactory estimates for the component masses when they belong to the Main Sequence and iii) a correlation between the relative parallax error and orbit grade exists.

The publication of new tables of calibration of some fundamental parameters of Galactic B0-B5 supergiants in the two classes $I_mathrm{a}$ and $I_mathrm{b} $ allows to particularize the eight parameters conjecture that model five fundamental parameters. The numerical expressions for visual magnitude, radius, mass, luminosity and surface gravity are derived for supergiants in the range of temperature between 29700 K and 15200 K. The availability of accurate tables of calibration allows us to estimate the efficiency of the derived formulas in reproducing the observed values. The average efficiency of the new formulas, expressed in percent, is 94 for the visual magnitude, 81 for the mass, 96 for the radius, 99 for the logarithm of the luminosity and 97 for the logarithm of the surface gravity.

The publication of new tables of calibration of some fundamental parameters of Galactic B0-B5 supergiants in the two classes Ia and Ib allows to particularize the eight parameters conjecture that model five fundamental parameters. The numerical expressions for visual magnitude, radius, mass, luminosity and surface gravity are derived for supergiants in the range of temperature between 29700 K and 15200 K. The availability of accurate tables of calibration allows us to estimate the efficiency of the derived formulas in reproducing the observed values. The average efficiency of the new formulas, expressed in percent, is 94 for the visual magnitude, 81 for the mass, 96 for the radius, 99 for the logarithm of the luminosity and 97 for the logarithm of the surface gravity.

The absolute visual magnitude as function of the observed color (B-V), also named Hertzsprung-Russell diagram, can be described through five equations; that when calibrated stars are available means eight constants. The developed framework allows to deduce the remaining physical parameters, mass, radius and luminosity. This new technique is applied to the first 10 pc, the first 50 pc, the Hyades and to the determination of the distance of a cluster. The case of the white dwarfs is analyzed assuming the absence of calibrated data: our equation produces a smaller $chi^2$ with respect to the standard color-magnitude calibration when applied to the Villanova Catalog of Spectroscopically Identified White Dwarfs. The theoretical basis of the formulas for the colors and the bolometric correction of the stars is clarified by a Taylor expansion in the temperature of the Planck distribution.

In this paper orbits for 13 binaries are recalculated and presented. The reason is that recent observations show higher residuals than the corresponding ephemerides calculated by using the orbital elements given in the Sixth Catalog of Orbits of Visual Binary Stars. The binaries studied were: WDS 00182+7257 = A 803, WDS 00335+4006 = HO 3, WDS 00583+2124 = BU 302, WDS 01011+6022 = A 926, WDS 01014+1155 = BU 867, WDS 01112+4113 = A 655, WDS 01361−2954 + HJ 3447, WDS 02333+5219 = STT 42 AB,WDS 04362+0814 = A 1840 AB,WDS 08017−0836 = A 1580, WDS 08277−0425 = A 550, WDS 17471+1742 = STF 2215 and WDS 18025+4414 = BU 1127 Aa-B. In addition, for three binaries - WDS 01532+1526 = BU 260, WDS 02563+7253 = STF 312 AB and WDS 05003+3924 = STT 92 AB - the orbital elements are calculated for the first time. In this paper the authors present not only the orbital elements, but the masses dynamical parallaxes, absolute magnitudes and ephemerides for the next five years, as well.