The squint Moon and the witch ball

Abstract

A witch ball is a reflecting sphere of glass. Looking into the disk that it subtends, the whole sky can be seen at one glance. This feature can be exploited to see and photograph the squint Moon illusion, in which the direction normal to the illuminated face of the Moon—its ‘attitude vector’—does not appear to point towards the Sun. The images of the Sun and Moon in the disk, the geodesic connecting them, the Moon’s attitude, and the squint angle (distinct from the tilt), can be calculated and simulated, for all celestial configurations and viewing inclinations. The Moon direction antipodal to the Sun, corresponding to full Moon, is a singularity of the attitude vector field, with index +1. The main features of the witch ball images also occur in other ways of imaging the squint Moon.

Keywords

• geometrical optics
• projections
• imaging
• illusions
• 42.15.Dp
• 42.30.Va