One problem you might have if you use the astrotracer mode with an ultrawide is that stars won't track at the edges. These lenses cover such a wide area that moving the imager can't keep all the stars in the same place. If you use an ultrawide on a tracking mount (equatorial), then the entire camera is moved to keep the star field stationary and stars will be sharp to the edges (assuming your lens is sharp to the edges). Just something to be aware of. Either of the lenses you mentioned will work well with the K-1 which has great sensitivity and should provide really good star photos. The faster f2.8 will allow some room for stopping down a bit which can sharpen star images though the Pentax 20mm should be reasonably sharp wide open. Of course, the 15mm will give you some gain on capturing larger expanses and f4 will still be plenty fast enough.
Note also that the latest firmware for the K-1 (1.4 &1.41) allows longer "bulb" exposures suitable to astro-photography so be sure to get the update for your K-1 if you haven't already.
Last edited by Bob 256; 05-04-2017 at 07:55 PM.