I'm not 100% familiar with the KM, but I have it's close relative the K-x. I don't know if the same on the KM, but the K-x has some weird time exposure issues going over 30 seconds. I had to use a script in the form of a file that was placed in the root directory of the memory card to turn off the dark frame subtract. Again, this might not be a problem with the KM, I'm not sure. The guys on the Pentax forum would know.
For star trails, or circular trails, you need to find the south celestial pole for your location. The SCP is due south and the elevation from the horizon is equal to your latitude. Mid to wide angle lenses work best.
To make trails, take a bunch of consecutive exposures one after the other without pauses for an hour or 3 with the camera set to 30 seconds or longer. Use Deep Sky Stacker (download it if you haven't already, it's free) to stack the files. In the stacking method, click the light tab and then choose "maximum". This will give you nicer trails from lots of short subs.
I've probably forgotten a few steps!
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