This sounds very like ‘The Seventh Voyage of Ijon Tichy’ by Stanisław Lem, collected in The Star Diaries. The collection was first published in Polish as Dzienniki Gwiazdowe in 1957; the English translation by Michael Kandel appeared in 1976. This story has all the features you remembered:
Ijon Tichy is travelling alone in a spaceship:
It was on a Monday,...
Another Possibility - but not as close - might be "The Man Who Folded Himself". He ends up having relationships (and relations) with himself, though, and you said there was no sex in your original post.