Spherical trigonometry of the projected baseline angle

Abstract

The basic vector geometry of a stellar interferometer with two telescopes is defined by the right triangle of (i) the baseline vector between the telescopes, of (ii) the delay vector which points to the star, and of (iii) the projected baseline vector in the plane of the wave front of the stellar light. The plane of this triangle intersects the celestial sphere at the position of the star; the intersection is a circular line segment. The interferometric angular resolution is high (diffraction limited to the ratio of the wavelength over the projected baseline length) in the two directions along this line segment, and low (diffraction limited to the ratio of the wavelength over the telescope diameter) perpendicular to these. The position angle of these characteristic directions in the sky is calculated here, given either local horizontal coordinates, or celestial equatorial coordinates.