If you mark the ground or cave where specific shadows or sunbeam hits, those markings move and change through the year very very predictably to the inch. Each year specific points are marked and future validated. They also saw same star constellations and moon paths in same place through year, each year repeating
Oldest lunar calendar https://sservi.nasa.gov/articles/oldest-lunar-calendars/
They watched the sun. They knew about solstices (high point, low point of sun in sky). They tracked how many days between the solstices. They were interested in this because it correlated with growing seasons.
None of this happened overnight. There is always a large amount of trial and error involved in the development of ancient calendars. The idea of a leap year was a ‘fix’ to a calendar that wasn’t quite right. It seems like it happened instantly but if you look back, the trial-and-error time was often quite lengthy.
Throughout the year the sun appears to move to the North and South because the planet is tilted. In the middle of Winter and the middle of summer it reaches the furthest point and changes direction, and these points are called the solstices.
The length of time between the solstices tells you the length of time of a year. And by the time people figured out the whole concept of leap years, they had been keeping track of the solstices for hundreds of years. So eventually they were able to figure out that the 365 days that they had used as an approximate length of the year was not quite accurate because every 4 years the Solstice moved by a day.
For the calendar – The best indicator is that once you realize the days and the nights shift around in length you keep track and find the equinoxes and the solstices. Equinoxes are the days in fall and spring where night and day are the same length. The winter solstice has the longest night and the summer solstice has the longest day. So you start counting these and realize year after year they’re about the same number of days apart. After many years you realize that they are 365 or 366 days apart and with the right record keeping and math you pinpoint that once every four years is good.
Then a religion comes along which decided that certain days of the year should be holy days and they align with a fixed date on the calendar and also on a flexible date depending on the alignment of days of the week with phases of the moon. After several centuries you realize that these days are slowly migrating. So you look at the calendar again and look at all the records over the centuries and realize that the extra day out of four years is just a tad too much. So you remove the extra day every few centuries to get back on track.
If you lived in a world without light pollution the stars would be much more prominent in the sky. And if you live in a world without constant entertainment, you’d be a little bored. I’m sure that after a cycles of cold time warm time you’d start to notice patterns in the days from one warm time to another.
Without modern technology and our busy, regimented lifestyle, you have a lot of time to notice the changing of the day length, the seasons, the night sky, etc. There were detailed calendars well before 45 B.C. That said, they believed that the sun orbited the Earth, but the ancient Greeks had already even calculated the size of the Earth by around 200 B.C.
Ancient peoples were as intelligent as we are and had lots of tools. For example, they could count the days of the year, and could measure the height of the sun in the sky using things like the length of the shadow cast by a pole or tower, so they could see it was about 360+ days from when the shadow was longest, until the next time it got that long and they could see that it was always summer when the shadow was shortest and winter when it was longest, so clearly the seasons were linked to how high the sun was in the sky, and to how many days had passed since the previous winter. And this was very useful information as it helped them figure out when to plant, or when to hunt migrating herds or seasonal wild food plants and so on.
So over many years of observation and record keeping they would have figured out that the length of the year was 365 days, but you had to add a day now and then to keep it working.
Most ancient civilizations did not know the earth orbited around the sun. However some ancient thinkers might have suspected it. We don’t know who first came up with the idea, but Copernicus pretty much proved it, so he gets the main credit. As well we don’t know who first suspected the earth was a sphere but it’s possible it was thought of by some ancient thinkers long before the ones we credit. The clues were there, for example ships or mountains seeming to drop below the horizon, the farther away they were.
And all this would have happened long before 45 BC – maybe thousands of years earlier. Stonehenge might have been started around 3000 BC and it contains a fair amount of advanced astronomical features, that would have been based on knowledge people might have been developing from even much earlier.
Edit: Okay people, Galileo, Newton and probably others provided proof of Copernicus’s model.
The Sumerians figured out the length of the year a lot earlier than 45BC. The first observation you might make if you were to do this yourself is that seasons follow a regular pattern and that pattern coincides with celestial observations. In the northern hemisphere, the sun rises and sets farther to the south in the winter than it does in the summer. Also, certain stars and constellations are only visible during certain times of the year.
Something you might try to do is count the number of days between the most southerly sunrises. All you need to do that is three sticks, some way of tallying numbers (a jar and a bunch of pebbles will do), and a whole lot of patience. You don’t know what day it is because calendars don’t exist, but you know it’s autumn because it’s getting colder and the leaves are changing, from that you know the sunrise should be moving south. You find a spot that has a good, unobstructed view, maybe a hill top overlooking the sea and you drive one of your sticks into the ground. The next morning, you get up at dawn and see where the sun rises. You take your second stick and drive it into the ground so that the two sticks and the sun form a straight line. The next day you do the same thing, drive the third stick into the ground and note that it is to the right of the second. Keep doing that every morning, leapfrogging the second and third stick over one another until you get to a morning where the latest observation is to the left of the last. That is your reference for the start if the year, toss a pebble into the jar. Keep doing that every day and you’ll notice that some time during the summer, the sticks will change course again and you’ll have something like 180-200 pebbles in the jar. Keep going and once the sticks get back to where you started counting (you’ll know because they change direction again) you can count count the pebbles and there should be about 365 of them. Do that a couple more times and you can be sure of your results.
Another way you can check your work is by following a particular star, let’s use Sirius because it’s the brightest and close to an easily recognized constellation. Conveniently, the first night you would be able to see Sirius after the sun sets is close to the winter solstice. If you start putting pebbles in your jar each day after that and keep going until it becomes visible the next winter, you should also wind up with about 365 pebbles in your jar
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