numbers in English

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sun moves through the sky relative to fixed stars at about 1degree each day.

I know you don't mean that exactly but let's run with that for a bit. Defining velocity (direction/speed) requires a point of reference. To describe the actual velocity of the sun requires that reference point. #1. Using the local neighborhood stars the sun is moving toward the star Vega at 70,000 km/hr. #2. Relative to the center of the Milky Way the sun's orbital velocity is 828,000 km/hr for a Galactic year of 225 million years. #3. Relative to the CBR (Cosmic Backround Rdiation) the Milky Way galaxy and its neighboring galaxies are moving towards the Great Attractor (vicinity of Leo/Virgo) at 2.1 million km/hr.

Now I suspect you mean the sun's apparent motion along the ecliptic. #1. Each fixed star is really in the same direction from us all day and all the year. The stars seem to us to change their direction only because we live on the moving earth. #2. The sun is nearly, but not exactly, in the same direction from us all day, from its rising to its setting. But this direction changes during the year in consequence of the earth revolving round it.
So we're back to the the Earth's motion. Since the Earth orbits once each year the Sun appears to move across the "fixed" stars (Celestial Sphere) in the same period of time. The ancient astronomers described a "belt" of star patterns (8 degrees above and below the ecliptic) named the zodiac. Good old duodecimal system gives us 12 patterns (constellations) each covering 30 degrees of sky which the sun enters about the 21st of each month. When people tell you their SIGN it is their Sun sign. When I was born the sun was in the constellation Aquarius.

Now we're back to those fixed reference points. Since the Earth axis is inclined 23.5 degrees to the solar equator the ecliptic is also inclined by the same amount. Thus the sun's path along the ecliptic crosses the celestial equator twice a year, the Vernal and Autumnal Equinoxes. The time it takes the sun to return to the same equinox is a Solar Year: 365 d - 5 hr - 48 min - 46 sec. Since the ecliptic is a circle were back to 360 degrees.
Howsomeever, we can also measure against the "fixed" stars, i.e., the time it takes the sun to pass the same star, the SIDEREAL Year: 365 d. - 6 hr. - 9 min - 9 sec. A difference of 20 min and 23 sec. As a consequence the position of the equinoxes against the fixed stars is PRECESSING about a degree every 70 years. Thus when the Vernal Equinox is in the constellation Aquarius we will be in the AGE OF AQUARIUS for the next 2,160 years. When is hard to say as astrologers can't agree on the boundaries though they should be 30 degrees apart.
I know you don't mean that exactly .

I didn't mean that exactly which is why I posted "about" 365 is about 360 when using the equipment and knowledge available to the Babylonians 3500 years ago. My post was entirely concerned with the origin of the system for time, as per my original post, which was only to show another type of logic anyway.

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