Concepts of Space by Jammer Max;

Author:Jammer, Max;
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2013-08-14T16:00:00+00:00

Fig. 3.

is defined to be the angle AFS subtended by the radius r of the earths orbit. For a direct measurement of the parallax AFS the transit circle can be employed. On the assumption of Euclidean geometry the parallax is then given by the angle ½π—SAF. A second method of measuring the parallax consists in comparing the position of F with that of another star G whose distance is taken to be very much greater than that of F. By measuring the angle GAF, the parallax, on the basis of Euclidean geometry, is found immediately, since it is equal to GAF. However, if space is assumed to be of hyperbolic structure, the two methods explained will yield different results, since the sum of the two angles GAF and FAS is different from ½π. In fact, this sum is just the angle of parallelism Π(r), corresponding to the radius r of the earth’s orbit. Let δ be defined by the equation 2δ = ½π — Π(r). Then according to a fundamental theorem of hyperbolic geometry we have

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.