On the Distances Between Sun, Moon, and Earth: According to Ptolemy, Copernicus and Reinhold

by J.A. Henderson

The Prutenic Tables of Erasmus Reinhold, published in 1551, were the first set of astronomical tables to use the Copernican model of the solar system. Reinhold left a detailed account of his derivation of the parameters used in these tables in his "Commentarius in opus Revolutionum Copernici". The present work is based on an analysis of this unpublished manuscript, which was rediscovered early in this century.
In particular, this work analyses the geocentric distances of the sun and moon as found in Ptolemy's Almagest , in both the manuscript version and the Nuremberg edition of Copernicus' De Revolutionibus , in Reinhold's commentary on the Almagest , and in Reinhold's commentary on this section of De Revolutionibus . Chapter one contains a detailed analysis of the lunar distance, and chapter two concerns the apparent diameters of the sun, moon and shadow. The Ptolemaic method, which is the model for Copernicus and Reinhold, requires the determination of these quantities as a preliminary to the calculation of the solar distance, which is treated in chapter three. The fourth chapter is a brief analysis of the relative magnitudes of the sun, moon and earth, which Ptolemy, Copernicus and Reinhold discuss after they have reached values of the lunar and solar distances. The final chapter concerns an application of the distances - the solar and lunar parallaxes and diameters.

236 pages, Hardcover

First published April 1, 1991

Reviews

[Justin Boden · Rating 5 out of 5]

This is an excellent thesis, but I would not recommend it for anyone who doesn't have an academic interest in this topic. In the book, Henderson carefully recreates the mathematical calculations that Nicolas Copernicus and Erasmus Reinhold (and, to a lesser extent, Ptolemy) performed in order to calculate the relative distances between the earth and moon, the earth and sun, and the moon and sun. In doing so, she manages to uncover a few interesting observations – namely, that Reinhold was a very careful mathematician, that Copernicus was not, and that both men held Ptolemy in such high regard that they sometimes adjusted their findings to agree with The Almagest even when their own calculations brought them to different results. Such that even though Copernicus was attempting to correct the unwieldy moon that we find in Ptolemy's system, he still deferred to his predecessor quite a lot more often than not.

If you're interested in the heliocentric theory of Copernicus, look elsewhere. Henderson is not concerned with it, and in terms of the calculations being discussed here it did not concern Copernicus or Reinhold either. But if you want a quick overview of the painstaking calculations that were part and parcel of ancient and early modern astronomy, then this isn't the worst place to start. Just be sure you bone up on your trigonometry first! There's a whole mess of angles and equations in this book.