This is a really interesting concept and I appreciate the sandbox feel to it. The main issue seemed to me that once you've fully evolved a planet, there's nothing to do but wait (possibly a while) for things to go nova. The other issue that I thought undermined the experience was how quickly life could be evolved. I think the fun in this sort of game comes from slowly accumulating your progress. Drawing a couple +3 cards essentially ends the game.
I hope this is something you keep developing as it's clear there's a lot of good astronomical knowledge and passion going into it and you created a really cool atmosphere.
In terms of specific suggestions, I would get rid of the +3 evolution cards and maybe add something like a "Coronal Mass Ejection" card that devolves life one level. I also think it would be cool if the distances could be clarified with labels on the gridlines. It would be more immersive (illustrating the different distances the Goldilocks zones are for different star types) and helpful in planning your Push and Pull cards. It might also be nice to have a counter on how many planets your system has.
Overall, this was intriguing enough for me to play it a couple times and your medals all work, so that is itself a moderate success.

There must be a method for getting the medals.

I can't seem to see whatever my planet's life status is, but it's a pretty fun game trying to keep the clock running as long as possible!

Edit: The issue with it going to far away planets was exactly what was happening! Thanks!