Oh, I don’t know if you should have deleted it...maybe added to it about the difference between solar and stellar days if possible.
For Earth’s stellar day rotation of 23h 56m 4.1s of 360deg, 15d offers up 1h 1m 1.5s regression for star culmination, which kind of means that for every day forward that one observes the sky at just 4.1s earlier than the appropriate hour, one would observe star culmination exactly 1h difference 15d hence. I reckon it would be too hard to observe 0.1s as something to time against in those ancient days but every 10d offers a whole second, and one would be able to table observations in such a way that very good time keeping could be had for astronomical observations. (Is this the basis for a 10d week? Might be.) Of course, using exact timing over longer periods of years and common number factors would define that every x-amount of years, an extra second would be implemented to have the perfect x-amount of years length.
The solar day is 24hrs where the Sun crosses a meridian in the same place every day when viewed from an Earthly location, albeit a slight difference in altitude. Could one move a staff the appropriate distance so the cast shadow is the same length as the previous day? Of course, but one would have to do so during the correct days or findings would be off. For our current tilt of 23.4392811o, the Sun ‘travels’ 5,209.752649km along Earth’s meridian during a ½ year but does so quite slowly on the solstices and quite evenly on the equinoxes, with the ‘equinox speed’ prevalent for much of the journey. I have yet to work out which length of days are the right ones to do such a thing on, and how far the Sun ‘travels’ in 1 day during that time. Overall, one would think the Sun ‘travels’ some 28 ½ km each day but it does not. It is around that figure but not that figure. Now you know why I mentioned the Faiyum Basin as a place to make such observations at...when it is full and empty so water-and-land surface measures can be identified. I hazard a guess there is an appropriate celebratory observation in the AE special days which indicates Sun-measures were made...probably Seshat, Thoth and Ra would be a triple identity on that day.
I like your quote from Renouf. It identifies most of the glorious and memorable tales we have, including the Book of the Dead, which have astronomy as the foundation from which translation of observation creates the tale. It only matters how well the tale is told and what characters are used in order to be popular. Care to have Horus, Rama or Jesus as the important ‘person’? Too easy for a religion...the Sun rejuvenated either each day or each winter. How about a fairy tale about a hare and tortoise? Why not...the fast and slow Suns throughout the year.
I’m reading Gerald Massey at the mo, Ancient Egypt volume 1. I’ll check what you link to after I’ve read Massey’s volume 2 and digested both.