When is the Sun due East or West, at what angle does it rise and set?
by Shayk Idris
the Book of Shadows
Al-Biruni,(973-1048) a polymath who lived in Afghanistan, came up with these simple methods of determining direction by the sun:
The Amplitude, or the skew from east that the sun rises on a given day at a given latitude; and the shadow length of a stick, when the sun is at east or west for that day & place.
Method, mark latitude angle from vertical, declination angle from horizontal, axis. Extend Dec to Lat, then extend arcs to horizontal & vertical axes. From the vertical extend horizontally to determine angle of amplitude. This is the skew of sunrise & sunset towards the pole.
From the arc to the Horizontal, extend vertically until the Lat, thence horizontally, to determine the angle of the Sun's altitude when it is due east or due west. Take (a) as the hight of the gnomon, or stick; take (b) as the length of the shadow for that moment. To use, describe an arc around your stick, when the Shadow touches that arc, the shadow shoes us due east in the p.m. or west in the a.m. data for Sun's declination for the period needed, can be easily got, latitude likewise.
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