# Calculating historical star maps from proper motion

I'm working on some software which needs to calculate the position of stars and galaxies visible to the naked eye at different periods of human history.

The Yale Bright Star Catalogue gives the position and proper motion of visible stars.

Is calculating the historic positions simply a matter of multiplying each stars proper motion by the number of years between the date in question and the epoch, then subtracting the result from the position?

If so how far back in history could one go with this method and still produce a map that resembles what a human would observe with the naked eye? Would this method alone be sufficient to go back as far as 5000 years or are the other factors in play here that would need to be accounted for to make this accurate?

My criteria for "accurate" here is that a human observer wouldn't see a noticeable difference between the map and the night sky with the naked eye. Smaller inaccuracies are tolerable.

• 61 Cyg A is the naked eye star with largest p.m. moving ~7.3deg in 5000 yrs; most will be much less. I think you might be better with the Hipparcos & Tycho for the proper motions as they should be more accurate than YBS. A general issue will be the error on the proper motion (which is mas/yr) is often a large fraction of the measured value so this will be a big effect if you extrapolate 5000 years. Also this is ~20% of the ~26,000 precessional cycle of the pole so you will likely want to include that Oct 15, 2019 at 16:40
• @astrosnapper That looks more like an answer than a comment... ;) Oct 15, 2019 at 20:14
• @astrosnapper: That is now outdated information, as already with Gaia data realease 2 (DR2) the astrometric precision is higher than what the TGAS stars had. Oct 15, 2019 at 21:03
• @AtmosphericPrisonEscape was going to mention Gaia as it's normally the "go-to" but the OP specifically mentioned bright, naked eye stars. From what I remember there were still some residual issues with the gated mode on Gaia fro very bright stars so Hipparcos may still be better... ? Oct 15, 2019 at 21:56
• @astrosnapper: I'll ask around about that issue tomorrow in the institute with the people working on Gaia, but we were recently chatting about this and the consensus was that the Tycho-Gaia astrometric solution is now superfluous. Oct 15, 2019 at 22:23