I use Burnham’s Celestial Handbook, which gives objects’ celestial coordinates for equinox 1950.0. How do I convert these to 2000.0, the current standard?
First off, the difference isn’t great. Fifty years of precession change an object’s right ascension and declination by a total of 0.7° at most (if it’s near the ecliptic; less elsewhere). That’s a little less than the width of the view in a typical 50× eyepiece.
To get within 0.2° of the correct 2000.0 coordinates in most parts of the sky, just add 2.5 minutes to the 1950.0 right ascension in your head. The result is better than the pointing accuracy of many Go To telescopes.
For higher accuracy, get out your calculator and use the formulas
Δα = 2.56m + 1.11m sin α tan δ,
Δδ = 16.7' cos α,
where α is right ascension, δ is declination, Δα is the rightascension change in minutes of time over 50 years, and Δδ is the declination change in arcminutes.
To express a right ascension in degrees to input into your calculator, convert it to hours and decimals of an hour, then multiply by 15. The precessed position is good to better than 1' unless you are within 3° of the north or south celestial pole, where special formulas are needed.
— Alan MacRobert