This is a series of novels probably written in the last 15-20 years. I read them about 8 years ago.
The future Earth has many problems but it is not a dystopia. A means of FTL is discovered. It is easy to run (most ships require only a single crew member) but expensive to operate - Earth only builds and finances a very small number of the ships. The explorer corps (not capitalized because I do not think this is its proper name) is a very small group. Over time, it has grown smaller as Earth becomes more self-interested and less interested in paying the steep cost of learning about "what's out there."
The protagonist is a woman (who I think was petite and pretty but not beautiful). She had feelings for her mentor pilot who died before the events of the novels in the series. The novels are about how she personally survives the many pitfalls of exploring the Universe essentially by herself during her missions.
Some of the novels included these events (a line item per novel):
- Rescue stranded science team, who was running out of air.
- Witnessing the collision of a terrestrial and Jovian planet as well as attempting to rescue a portion of the inhabitants they discover there while observing.
- Investigating a giant alien artifact discovered by the explorer corps.
- Investigate why stars are exploding for an unexplained reason and why that reason seems to be approaching the Earth (maybe in conjunction with #3).
I can almost visualize the name of the author and/or the book names but it is buried just a bit too far back in my mind.