Is there any particular methods that help us calculate the position of a star at a certain point in time? This question is what I am trying to achieve, but for me, I do not want to use the data because the data that we can access to calculate the position is limited to only a few years. I want a method which uses the current position, speed, velocity of stars and calculate its position for many years back (like in 11000 BCE to 13000 BCE). I am trying to use astropy and I am really new to this, so I just need a push in the right direction; helpful resources will serve a great deal as well, thank you.
Edited: There are a few stars' positions that are recorded and mentioned in one of our history books. SO what I am trying to do is collect all the recorded stars' positions and try to map them in real-time at a particular year and see if the recorded data exists or not.
Now out of this data, the one that stands out as puzzling as is was the movements of Alcor and Mizar in the sky.
If we observe these 2 stars from earth, for a naked eye it would seem like Mizar is always in front and Alcor is always in following Mizar.
But in one of our history books, there is a recorded event where Mizar follows Alcor (it looks like it is following, I know they just revolve around each other), so what I am trying, is to see if there was any particular period where this would be possible.
This is the starting problem there are many observations like this so it would be really helpful if I could get any info on achieving this.