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Josh,

I've been following this with great interest and have attached my contribution.  To understand if Kochab was below or above the pole I drew the simple diagram at the bottom of the attached pro-formas and with your relatively low altitude (Hs), the first pro-forma (IMG_0249) showed Kochab to be left of the vertical.  Hs and Zd are marked at your latitude and when slid down to the centre of the Earth it shows Kochab is the far side of north and illustrates your latitude will be 180^o - (Decⁿ + Zd).

To work out the meridian passage time I used  GHA(Aries) = LHA(star) – SHA(star) +(DR) W Long and subtracted 180 degrees (for below the pole situation) giving a GHA (aries) = 165^o 14'.5  (see the maths top left) and reverse engineered this to get the time. 01hr gave GHA (aries) of 152^o 10'.4 with a remainder of 13^o 04'.1 and from the increments and corrections this equated to 52 minutes and 8 sec giving a mer pass time of 01:52:08 UT at your position (which I took as 47^o 48'.3N, 122^o 34'.2W).

Applying your sight and equating Lat = 180^o - (Decⁿ + Zd) I came up with your Lat of 47^o 30'.1N.

Because Kochab circles the Pole star, I figured that there would be a second mer pass opportunity roughly 12 hours later and those workings are shown in the second pro-forma.  Again, starting with the diagram and the much greater Hs, Kochab is clearly above the pole this time.

Putting the mer pass time calculated to be 13:50:18 UT @ DR and your DR position into Stellarium I got an Hs of 63^o 46'.3 (when it crossed the meridian at 13:50:20 UT@DR) and latitude of 47^o48'.2N.

Hope this makes sense !

Cheers

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