The Orbital Elements of a Visual Binary Star

Abstract

Although astronomers regard the brighter component as fixed and map the motion of the fainter one around it, in reality, both stars in a binary system move in ellipses around the common centre of gravity. The size of the ellipse is inversely proportional to the mass of the star, so in the Sirius system, for instance, the primary has a mass of 2.1 sun, the white dwarf companion 0.98 sun and so the size of ellipses traced out on the sky are in the ratio 1:2.1 for the primary and secondary (Fig. 7.1). The ratio of the masses is inversely proportional to the size of the apparent orbits [see Eq. (1.1)] so this gives one relation between the two masses. To get the sum of the masses requires the determination of the true orbit from the apparent orbit and this is what this chapter will describe.