Spectroscopic Binaries

Abstract

Two bodies which are moving under a force which varies as r⁻², where r is the distance separating the bodies, will move along a conic section. Periodic motion is along an ellipse, with the centre of gravity at one focus. The motion of each star relative to the other is along a similar ellipse with the centre of gravity at one focus of the ellipsein which the star is moving. The geometry of the situation is illustrated in Figure 32. The XY plane is the plane of the sky and it is perpendicular to the line of sight which lies in the Z direction. The plane containing the orbit cuts the plane of the sky along the line of nodes. The ascending node, Ω, is the point A in the diagram. At the ascending node the star moves through the line of nodes with a positive radial velocity. The descending node, ℧, is at B. Here the radial velocity is negative. The orbit is inclined at an angle i to the plane of the sky. This angle is measured as positive when at the ascending node the companion is moving away from the other star. (In the diagram i is negative since the companion is approaching periastron.) The angle from the line of nodes (ascending node) to periastron measured in the direction of motion is called the longitude of periastron and it is denoted by ω. The true anomaly, υ, is the angle measured in the plane of the orbit in the direction of motion from periastron to the star. The distance of the star behind or in front of the plane of the sky is denoted by +z or −z respectively. The component of radial velocity of the star due to orbital motion is dz/dt.