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.

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.

New CCD photometric observations and their investigation of the W UMa-type binary, V870 Ara, are presented. Light curves of the system taken in filters from Congarinni Observatory in Australia. The new ephemeris is calculated based on seven new determined minima times together with the TESS data and others compiled from the literature. Photometric solutions determined with the Wilson-Devinney (W-D) code combined the Monte Carlo simulation to determine the adjustable parameters' uncertainties. These solutions suggest that V870 Ara is a contact binary system with a mass ratio of 0.244±0.019, a fillout factor of 69±4%, and an inclination of 67.53±0.35 degrees. Absolute parameters of V870 Ara were determined by combining the Gaia EDR3 parallax and photometric elements.