Floating mirror horizon. Theory and design

Geodetical Observatory Pecný, Ondřejov 244, Czech Republic

Received: 26 November 1997
Accepted: 10 March 1998

Abstract

A "floating mirror horizon" could substitute for the plate with mercury now used with astronomical instruments. It would have a greater and more stable reflectivity (by about 25%) than the present surface of just mercury, and have a distinctly better definition of images. With astrolabe instruments both images of a star would have practically the same brightness. There would be no need to clean the surface of the mercury, so the particular instrument would be permanently ready for use. Theory and design of the new device are presented in this paper, along with tests from an experimental model. Regarding conditions of the mirror's flotation, it is shown that its optimum shape is that of a cylindrical plate of minimum (necessary) thickness. For some typical dimensions (with a diameter, say, of 10 or 20 cm, and the metacentric height of the mirrors being between 20-40 cm), its conditions of stability are comparable to those of transoceanic ships. The whole appliance has to consist of three basic parts: a basin with mercury; a floating mirror; and a centring device. The latter, while enabling the mirror its free floating, maintains with adequate accuracy its centring in relation to the centre of the mercury basin. This reduces to negligible (say, ) the amount of concentric deformation by capillary forces of the surface of the mercury. It also enables preservation of proper orientation of the mirror — of its sloping line — with respect to the axis of observation and rotation of the particular instrument (of an astrolabe, PZT, etc.); and it also effectively dampens vibrations of the mirror when the instrument is rotated and set to a particular object a star, for example. In general, the surface of a floating mirror is inclined at an angle to a horizontal surface. This effect can be eliminated by simultaneous rotation of the mirror and the instrument (of an astrolabe, e.g.), or by the mirror's rotation through (with a PZT or meridian circle). The autocollimation method of observing a small experimental model of the floating mirror horizon showed that it possessed the expected properties.