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Angular distance between Sirius and the North Pole of the ecliptic

As it is not affected by the precession, a polar distance can often be considered as immutable when it is seen in historical times. Yet, the star Sirius is an exception : between 4000 BC and 2000 AD, its important proper motion has increased by 1.4 the distance between it and the North Pole of the ecliptic.
The graph shows, in blue, the variation of polar distance and, in red, the supplement of 51.8 (180 - 51.8 = 128.2).
Let's remember the angle phi (51.8) belongs to a "triangle phi" whose proportions are ruled by the golden ratio.

As we can see, the angular distance between Sirius and the North Pole of the ecliptic (vertical axis) equalled the supplement of the angle phi in 4000 BC. In other words, the angular distance between Sirius and the South Pole of the ecliptic equalled, in 4000 BC, the angle phi (51.8). Two thousands years later, at the time of Sesostris I, a difference of 0.5 was noticed between this "ideal" value and the existing angular distance. It's most likely that this difference was not seen as meaningful by the Egyptians. Moreover, the astronomers of the time may not have been able to determine the polar distance by 0.5 .

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