On a side note, is it just me or does it seem like defending a planet is damn near impossible. From your screen shot, how does the attacker win so easily in that scenario?
It's got a much lower "power" rating and much lower population. WTF?!
Check out the invasion mechanics on the WIKI (now linked on the GC3 main screen in the bottom left corner). Basically, planet population is divided amoungst the active tiles on the planet, and the invading force moves from one tile to the next. Its not a typical "we'll meet you all on the battlefield" scenario. Hence, the best way to defend a planet is through planetary defense, which kills troops before they even land.
However, getting 100% planetary defense can be very difficult to do without Elurium Defense shields. Its easier once you get Planetary Defense Dome and other related buffs at the similar age of ascension tech levels (actually, a lot easier due to a bug where you can build ANOTHER planetary defense system after building planetary defense dome - bug reported, ticket closed, devs know about it, no idea if fixed, I'm guessing not). Even at 90% Planetary Defense, all you need to do is amass enough troops to give yourself an extremely high chance of winning, and if you win, no consequences.
Example: Planet 30 pop. Class 20 world. 1.5 pop per tile. Planetary Defense 90%. To defeat 1.5 troops with decisely and take very few losses, and have enough to win on 19 more tiles, I'm just guessing that it would take 5B troops. But 90% were 'killed' by planetary defenses. So, amass 50B troops (which is A LOT). Let's say only 5B defenders survive. Well, you only lose say 3B invaders of your 5B that reached the surface. You SHOULD lose 45B+3B=48B of your original troops. 2B left out of 50B, plus you are 'rewarded' with 5B enemy survivors/converts. 50B-2B-5B=43B. 43B is a decent sacrifice to take over a planet with 30B, especially when it has such high defenses, utilizing several tiles just for planetary defense. But, the sacrifice was only 2B.
This is why a human player can steamroll the AI, once the ZOC of a planet is cleared. Once you have taken over the planet, just put the new conquered planet on birthing subsidies, and your losses will be recovered in less than 6-7 turns, which is plenty of time to clear the next planet's ZOC.