Thursday, April 7, 2011

Measuring the Altitude of the Sun

Ptolemy claims to have used a meridian circle and a quadrant to measure the Inclination of the Sun on the Ecliptic but the shadows produced by a small nail at a distance of 60 cm are rather fuzzy due to the angular width of the Sun. Ptolemy discribes a instrument called a triquetrum (see p. 244 of the Toomer's Almagest), designed to measure the parallax of the Moon, which might be adapted to measure the altitude of the Sun. Replacing the large aperature which was used to sight the Moon with a pinhole and using a screen instead of a small sighting aperature at the other end one can use the triquetrum is reverse. Placing a small lens with a long focal length helps improve the quality of the projected image of the Sun.

It occurred to me that small telescope without an eyepiece could be used as one side of the triquetrum. Using one with a 50mm objective lens with a focal length of 625mm I tested the idea this afternoon. The image produced was quite bright and hot and so I "stopped" the lens down by drawing a circle on an index card slightly larger than the aperature of the telescope at the ojective end and poking a small hole in the card at the center of the circle with the point of the compass. The card was then pressed to fit into the telescope aperature.

With this arrangement one does not have to wear sunglasses to view the image of the Sun which was focused on a white card and was a little smaller than 1/4 of an inch. As can be seen in the image above two sides of the triquetrum would be equal and form an isosceles triangle. Both the telescope and the measuring rod would pivot on the vertical post. The length of the measuring rod at the bottom between the pivot and the image of the Sun is proportional to the chord of the angle at the top of the triangle.

It would be interesting to see if one could get measurements with this device which are as good as Ptolemy's for the Ecliptic.

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