How should I understand this 59 degree mentioned below, what does it mean? I could not get it. The photo is a diagram from an article dedicated to the invention of the ecliptic. The photo is from my tablet (the title could be seen)
This is almost too short to be answer. Using the "rise" formula at Need Simple equation for Rise, Transit, and Set time and plugging in 32.54 degrees for Babylon's latitude, we get:
When an object's declination is +23.5 degrees (the Sun at summer solstice), it rises 61.77 degrees east of north.
When an object's declination is -23.5 degrees (the Sun at winter solstice), it rises 118.23 degrees east of north, which is more conveniently expressed as 61.77 degrees east of south (note the expected symmetry here)
The azimuth degree difference between these positions is 56.46 degrees, close to the 59 degrees in the diagram.
The calculations for the Sun setting are very similar.
Why the difference?
If the Sun were a point and there were no refraction, the numbers above would be more accurate. Because the Sun is a disk and because of refraction, the sun actually rises when the geometric position of the center of its disk is 50 minutes below the horizon.
Minor: I'm using +-23.5 degrees as an approximation of the Sun's declination at the solstices: the actual number is a little different.
To be fair, even after applying some corrections, I couldn't quite get 59 degrees or even anything about 58.5 degrees, but I'm sure this is what they're talking about.
TODO: I invite someone to create a graph showing how the "59 degrees" varies with latitude.
The Earth's equator is at an approximate 23.4 degree angle to the plain of its orbit around the Sun. That means that to an Earth-bound observer the Sun appears to move north and south of the celestial equator (which is merely the projection of the Earth's equator on to the sky) during the course of the year.
In fact this is what gives us the seasons - so in the the Sun is at maximum northern declination (the equivalent of latitude when projected on to the sky) at the time of the Summer Solstice (around 21 June - hence summer in the northern hemisphere) and at maximum southern declination at the time of the winter solstice (around 21 December - hence northern winter).
But this movement also means different rising and setting points - in the Northern hemisphere the Sun's rise is between north and ast in the summer and between south and east in the winter (unless, that is, you are within the Artic circle in which case it will not set/rise at all for at least some period in the summer and winter).
There are a variety of online tools that show you this effect - this one: https://www.timeanddate.com/sun/iraq/baghdad?month=12&year=2017 - shows that in Baghdad the sun rises - in 2017 - at 61 degrees East on 21 June and at 118 degrees East on 21 December - a difference of 58 degrees.