I compiled the source code and got the planets to work. They're pretty bland so far so have a few screenshots.
Small 8000m planet
Large 120,000m planet
Surface of large planet
I'm sure they won't at first. Part of developing planets is taking new things that their Medival Engineers team discovers, so I am guessing they will release Planets mostly as a large asteroid with gravity and possibly oxygen, and once water physics is figured out in Medieval Engineers they'll add it to SE.
Habital planets have oxygen and an atmosphere. The gravity gets gradually larger the closer you get. The smallest planets (8000m) has a gravity of 0.3 and the largest planet (120,000m) has a gravity of 1.2.
There's an option to limit jetpacks on planets. I was able to use mine on the smallest but on the largest I couldn't. Once you're on a planet with this on you're forgeted unless you have a ship with the muscle to push back up.
Oh and did I mention how long it would take to get to a bigger sized planet with a max speed of 104m/s? I had to use a mod to increase the max speed to even think about going to it.
EDIT: I uploaded a video.
https://www.youtube.com/watch?v=wbvdTGVccus