These are all from my own experiences, so if you have seen it happen on your own planet any other way feel free to correct me.

Small Moon +10% planet space - Analyze Event Only

Planetary Rings - +20% to all production - Analyze Event Only

Large Moon - +20% planet space - Analyze Event Only

Advanced Civilization Ruins - +20% artifact production - Analyze Event Only

From what i have seen the above 4 are the only analyze effects you can get.

Stealth Screen +30% cloak - This is a random planetary event(it is not a colonize or analyze event). You will get a message like this appear - Reothy-Jose reports that a Stealth Screen has been discovered around the planet! Cloaking has increased by 30%

My advice is to make a 22x+ planet and rift it. I was over level 1k before I got my first dyson and I had to buy that. It isn't much better than a 22x rifted at that.

If you are really ambitious, you can make a 18x/22x/23x irradiated planet and then rift it. Personally, I think worrying about that 1 extra mining x isn't worth it or using data cubes on it, isn't worth it.

I personally have gotten Advanced Civilization Ruins on a Vl vr desert as a random event.