Each satellite has it's own special ability. There are some that can increase your population, others increase your production rate, reduce food requirements, and more. For a more detailed description of satellite abilities, please see: Where can I find satellites, and how can I use them?
When the Enhance Ability icon is lit in the lower right side of your satellite, and you see a smiley face in the upper right side of the planet, this means the planet and the satellite are an ideal match! In this case, the satellite will be able to start using its special ability with this planet (as seen in the image below).
As far as which specific satellites match best with which planets, we suggest you try different combinations for yourself!
You can also check out the forums below to see what other captains have tried:
1. https://www.reddit.com/r/walkr/