I was rereading George R R Martin and thought this was by him, but didn't see it. I probably read it between 5 and 15 years ago. The man is one of the crew. He killed various other crewmembers in different ways. I think he killed one or two of the others by flooding the ship with something poisonous while he wore a suit and clung to the outside. The ship is in an orbit around the earth where every year or so he talks to home base. I can't remember if they just ignore him, or are polite and noncommital for some reason. The story ends with him rationalizing/hoping that one year they'll let him come home.
I might be mixing up this part, but I kind of think they are polite, and it's because the crew had just done something heroic. And they didn't have life support enough for everyone to get home, or something like that. So that's why he killed them.
I'm almost thinking their heroic action took hundreds of years on Earth, while they might've gone FTL or something. Otr maybe he's just out of gas. Either way, they no longer have a way for him to land. And they were going to build something, or send a rescue ship, but then they found out he was a murderer. So they are polite like "We won't kill you, but you aren't worth saving either."