The diopters of Tycho

– and their accuracy.
Erling Poulsen  
skyggekant1The normal arrangement of pinnules or diopters at the time of Tycho Brahe were two plates with holes and you had to see the same star through both holes to aim the sight. It was not practical because you’d have to cover the part of the sky where the star was and therefore you could not be sure that your aim was right.

Tycho preferred a different method as can be seen on the picture. He writes that to be sure that your aim is right, the brightness of the star must be equal in both slits, that means the star often look different in the two slits and therefore must have a small angular size. Tycho (as everybody else) believed that light travelled in straight lines and he could then measure their angular diameter.




To understand what he saw, we have to look on light passing a straight edge, light is waves so what you see is a diffactionpattern. From the graph you see that it is impossible to be more exact than ½’-1′ (1 arcminut=1/60°). When you want to measure the angular size of a star, the easiest method has been to aim a little to the right of the star and then measure the time (by counting) from when you just can see it in the right slit until it disappears in the left slit (in 4 sec. a star near equator moves 1′). A bright star will be visible shortly before a fainter star in the right slit and you can see it a little longer in the left slit and in that way you will measure a greater angular diameter of the bright star.

He could not measure a stellar parallax (it must be smaller than 1′) so if the Earth moved around the Sun then the stars must be in a very great distance, and he could measure their angular diameter (he believed) then he could calculate the physical size of the stars and the result were stellar diameters greater than the size of the orbit of the Earth (Tychonis Brahe Dani Opera Omnia VI, page 197, København 1913-1929). The result was impossible and the Earth must be in the center of the Universe.