Mount RA/DEC slew math


I'm trying to correct my pier's N/S and E/W positions in my dome, so I stuck a camera in the middle of my scope's lens cap and ran a tape marker down the length of the dome shutter. I'm then trying to align one axis at a time.

I thought that if I slew from Alt:0 Az:90 to Alt:0, Az:270, the mount will only slew DEC without moving RA. So if the dome alignment is correct, I should be able to move the lock the RA axis and move the DEC axis manually bit by bit, mark a path on the dome (waiting for the dome to re-slew after each scope movement), then after Meridian flip follow that path down again and the up-and-down path markers should be in alignment. 

That's the theory... In practice what happens is that the RA axis also moves during this slew. Not a lot, but enough to make my doubt my hypothesis. I obviously can't move 2 axis's by hand.

Why is that? Isn't Alt:0 Az:90 and Alt:0, Az:270 on the same RA plane for every Lat?

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