I am in the middle of "The Martian" by Andy Weir and remembered this thread. Sorry for resurrecting this, but it seemed better than a new thread.
This is a story of how an astronaut is marooned on Mars when an accident happens and how he tries to survive. The majority of the story is told through his journal entries, so not quite letters to someone, but similar. There are portions of 3rd person perspective when discussing situations on earth, but most of it is in the journal format.
So far this has been an excellent story and has been very engaging, I started reading last night and couldn't stop till 1 AM despite needing to be up at 6. Oops. The protagonist must overcome many problems using very limited resources and a hostile planet (MacGyver on Mars?) The story is fast paced and has a lot of humor (despite the situation) and most of the science is accurate and very believable. The science has a couple problems, but is overall very realistic and his solutions make sense.
It could use some editing and clean up, but that should be corrected in the nearish future (see below) and hasn't taken anything away from the story for me.
Now for the bad news, it is no longer available except in Audiobook. The author received a book deal after self-publishing and has withdrawn it until it is available from the new publisher. It will be re-released in February 2014 in electronic and hardcover formats.
http://www.amazon.com/dp/B00EMXBDMA