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For some reason I remembered the siderial day was 23 hours, 56 minutes and 3.9 seconds. I just Googled it and it says 23 hours, 56 minutes and 4.091 seconds. I can't believe that it has chnged almost 0.2 seconds in my lifetime but I remembered looking it up somewhere, about 50 years ago, and that is the value firmly planted in my head. I just looked at my 1937 American Ephemeris and Nautical Almanac at it has the "4.091" value so, wherever I got the "3.9" value, it was erroneous. 

I remember in my meteorology class, the professor was lecturing about the geostrophic wind equation and he said that "the earth turns 360 degrees a day" and I corrected him, that it turns 361 degrees in a day( in inertial space, relevant to the wind formula) and I got an eraser thrown at me.

gl

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So i've been off by 0.191 seconds per day while doing my computations for the last 50 years. Let's see, there are 86,400 seconds in a day (I hope I didn't get that wrong too.)  So, 0.191 / 86,400 = 0.0000022106 or 0.00022% so I guess that error isn't large enough to explain away the inaccuracies in all those thousands of celestial computations I have done. 

gl