New relationships between the orbital period and some parameters of W Ursae Majoris (W UMa) type systems are presented in this study. To investigate the relationships, we calculated the absolute parameters of a sample of 118 systems. For this purpose, we used the parallax values obtained from the Gaia Early Data Release 3 (Gaia EDR3) star catalog for more precise calculations. The other required parameters, including the light curve solutions and the orbital period were derived from previous research. For some relationships, we added 86 systems from another study with an orbital period of less than 0.6 days to our sample, allowing us to increase the number of systems to 204. Therefore, the mass (M) values of each component along with all the other absolute parameters were recalculated for these contact systems. We used the Markov Chain Monte Carlo (MCMC) approach in order to gain the new orbital period-mass relations (P − M) per component, and added the temperature (T) to the process to acquire the new orbital period-temperature (P − T1) relation. We presented the orbital period behaviour in terms of log(g) by new relations for each component. We have also obtained a model between the orbital period, the mass of the primary component and temperature (P − M1 − T1) using the Artificial Neural Networks (ANN) method. Additionally, we present a model for the relationship between the orbital period and the mass ratio (P − q) by fitting a Multi-Layer Perceptron (MLP) regression model to a sample of the data collected from the literature.

The first multi-color CCD photometric study of 27 δ Scuti stars is presented, which was performed over the three observing years. We obtained the maximum times and magnitude changes in the observation period for each star. The ephemeris of our δ Scuti stars was calculated based on the Markov chain Monte Carlo (MCMC) method, using the observed times of maxima and the period of star oscillations. We used Gaia EDR3 parallax for calculating the absolute magnitude of δ Scuti stars. The precise fundamental physical parameters of all studied stars, such as mass, radius, luminosity, and temperature, were estimated. The pulsation modes of stars were investigated according to their Periodogram, indicating they are all in radial pulsation modes. Since the period changing of pulsating variable stars indicates the stellar evolution, the Period-Luminosity (𝑃 − 𝐿) relation was calculated and discussed. Moreover, we present new 𝑃 − 𝐿 relations for fundamental and overtone modes; Machine Learning Classification was used for this purpose.

WASP-43 b is one of the most important candidates for detecting an orbital decay. We investigate pieces of evidence for this expectation as variations in its transit timings, based on the ground and space observations. The data set includes the transit observations at the TÜBİTAK National Observatory of Turkey and Transiting Exoplanet Survey Satellite (TESS). We present a global model of the system, based on the most precise photometry from space, ground, and archival radial velocity data. Using the homogenized data set and modeled light curves, we measure the mid-transit times for WASP-43 b. Our analysis agrees with a linear ephemeris for which we refine the light elements for future observations of the system. However, there is a negative difference between the transit timings derived from TESS data in two sectors (9 and 35) and a hint of an orbital period decrease in the entire data set. Both findings are statistically insignificant due to the short baseline of observations, which prevents us from drawing firm conclusions about the orbital decay of this ultra-short-period planet. However, assuming the effect of this decrease of the period in the planet's orbit, we derive a lower limit for the reduced tidal quality factor as Q * ′ > ( 4.01 ± 1.15 ) × 10 5 from the best-fitting quadratic function. Finally, we calculate a probable rotational period for this system as 7.52 days from the out-of-transit flux variation in the TESS light curves due to spot modulation.

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We present the photometric analysis of six short-period systems (EI Oct, V336 TrA, NX Boo, V356 Boo, PS Boo, and V2282 Cyg). This is the first photometric analysis of these systems except for V336 TrA. Observations were conducted for 27 nights at three observatories in the northern and southern hemispheres. We calculated a new ephemeris for each of the systems using our minimum times and additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to determine the eclipse timing variation trends of the systems. We found a likely orbital growth for V336 TrA and PS Boo; four other systems show a linear trend in orbital period changes, which is most likely due to the accumulation of measurement errors in their linear ephemeris parameters. The light curve analysis was performed using the Physics of Eclipsing Binaries (PHOEBE) 2.3.59 version code with the MCMC approach. The absolute parameters of the systems were calculated by using the Gaia Early Data Release 3 (EDR3) parallax. The positions of the systems were also depicted on the Hertzsprung–Russell (H-R) and log J 0 – log M diagrams. According to a sample, we were able to present relations for the mass–radius (M–R) relationships of contact binary systems. There is also a strong relationship between the mass ratio and the radius ratio in the W UMa systems for which we also provided a new relation. We compared the M–R updated relationships in this study with seven systems in other studies obtained using the spectroscopic method. In addition, we estimated some of the absolute parameters for 1734 EW systems, based on the new relationships.