Arcetri Technical Reports 5/1998

Le Proiezioni Stereografica, Pseudostereografica
e Polare Equidistante  nella costruzione
dell'Astrolabio di Arcetri

R. Andreoni, G. Forti, P. Ranfagni

Osservatorio Astrofisico di Arcetri

Abstract

At the end of 1984 we needed, for didactic purposes, a good and cheap Astrolabe.  We wrote in FORTRAN a general program to draw it on a plotter. The result was the design of a cheap, precise, easy to reproduce Astrolabe. The program has several features: the possibility to select the limiting magnitude of the stars, the epoch of their coordinates, the Astrolabe size and many others.

To satisfy the frequently asked questions of teachers, friends and colleagues we collected our old hand written notes about the astrolabe and decided to publish them as an Arcetri technical report.

We have arranged our notes to describe first the two geometrical projections traditionally used to design an astrolabe, the stereographic and the pseudostereographic equatorial projections. Then we examine the equidistant polar projection which we choose for the design of Arcetri Astrolabe in order to optimize the typographical space and to reduce distorsions. In this report we explain all the geometrical and the astronomical details of all three projections, we compare their advantages and their defects and we give all the necessary equations to draw them.