Despite the confusion I had over titles (wait, is this Murder on a Moon Trek or Fly Me To The Moon?), this was charming. 

I liked the fact that the action starts immediately and we get backstory as relevant. I liked the characters and their interactions. I liked that I didn't know immediately who'd done it and that there were several good options. I do think the main character made a few leaps of logic in some of her suppositions (there are only two options, and here they are, and it's very black and white and one of them is always that it is that person who did it), but sometimes you need to pack in some extra characters that could have committed the murder, so it is forgiven, especially in an early novel. 

I'll absolutely travel to whatever planet is next with Sylvia and the crew, though.