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I stopped trying to use my K-1 for astrophotography a long time ago because of the limitations of the batteries when attempting multiple and/or longer exposure times. Usually I would not be near electrical outlets so I was wondering if anyone has figured out a way to provide power to the K-1 from a 12 vdc car battery?

You could use a DC to AC inverter. I have one that plugs into the cigar lighter socket, works great for many AC power needs, laptop, charging camera batteries, etc.

Is the K-1 really that much of a power hog? On a typical night my K-3II last several hours on its battery. I switch it out to another fresh one to avoid running the original battery down too much. The two batteries last all night, from sundown to sunup (which I have done a couple of times). I am doing Astrotracer the entire time and previewing images as I take them on the LCD, so it's not like I am conserving battery power. Note that I am using the Pentax brand batteries, not substitutions.

I get a few hours of shots on fresh batteries for mine, then if it runs down I stick another one in it. I use the crap out of mine.

I also am usually fine with just exchanging batteries once every few hours. The only exception being very long single exposures, for example if you want to do star trails in a single shot. In that case the battery often runs out somewhere between 1 and 2 hours, and if it runs out it does not save the shot. Of course this can be remedied by instead using the star trails feature or just setting up an intervalometer.

Its not enough of a problem for me to consider trying to connect it to a battery. If I had an equatorial setup that I could leave unattended for entire nights, I might attempt to connect the camera to the same battery used for the mount.

I did a quick google on this, and found that people have discussed DIY solutions on these very forums.

I have bought a dc coupler and an 8.000mAh LiPo battery (2 cell) for my K-70, it works just fine.
I also use an adjustable power supply I can connect directly to the power supply use for my eq mount.

my plan was to get the AC adapter for the camera and use an inverter once I get an equatorial and then run it all off of a deep cycle battery