I did small experiments with this, but not extensively. I am fairly certain it depends on: (a) The galaxy size and (

The distance the planet is from the star. In the galaxy I created, I made the size 10,000; at about 2 units from the sun (sun radius of 2.5 units), the planets got "freaky". As far as the importance of the star's radius, I am fairly uncertain of its purpose in-game.