Beside Still Waters by Robert Sheckley — Read

Mark Rogers was a prospector, and he went to the asteroid belt looking for radioactives and rare metals. He searched for years, never finding much, hopping from fragment to fragment. After a time he settled on a slab of rock half a mile thick.

Rogers had been born old, and he didn't age much past a point. His face was white with the pallor of space, and his hands shook a little. He called his slab of rock Martha, after no girl he had ever known.