Kepler's Constant and WDS Orbit

TL;DR

This paper estimates Kepler's constant using polynomial regression on observational data of binary stars, then derives their orbital elements and stellar properties, demonstrating a method for analyzing binary star systems.

Contribution

It introduces a novel approach combining polynomial regression with Thiele-Innes method to determine orbital elements and stellar parameters from observational data.

Findings

Kepler's constant estimated for two binary systems.

Derived orbital elements and stellar properties including masses and magnitudes.

Confirmed main-sequence classification and estimated stellar lifetimes.

Abstract

The aim of this work are to find a Kepler's constant by using polynomial regression of the angular separation \rho = \rho(t) and the position angle \theta = \theta(t). The Kepler's constant obtained is used to derive the element of orbit. As a case study the angular separation and the position angle of the WDS 00063 +5826 and the WDS 04403-5857 were investigated. For calculating the element of orbit the Thiele-Innes van den Bos method is used. The rough data of the angular separation \rho(t) and the position angle \theta(t) are taken from the US Naval Observatory, Washington. This work also presents the masses and absolute bolometric magnitudes of each star.These stars include into the main-sequence stars with the spectral class G5V for WDS04403-5857and the type of spectrum G3V for WDS 00063+5826. The life time of the primary star and the secondary star of WDS 04403-5857 nearly equal to 20 Gyr. The life time of the primary star and the secondary star of WDS 00063+5826 are 20 Gyr and 19 Gyr, respectively.