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I read a sci-fi short story sometime before 1983 I think. In this story there were two characters who were deadly enemies. For some reason I can no longer remember they met on a large asteroid which was an artifact of some alien civilization. They knew it was an artifact because a gigantic concave mirror was embedded in its surface. The two characters approached the mirror from different directions and both became disoriented from seeing a perfect reflection of the sky at their feet. The two spacesuited men fell onto the mirror and began sliding around in slow arcs on the nearly frictionless surface. They spoke about their situation on their suit radios and figured out a way to attach a tether between them and use it to sling themselves off the mirror.

I've been wanting to reread this story for years, but I can no longer remember who wrote it. I'm pretty sure I read it in a book anthology rather than in a magazine. Can someone identify this story?

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It's most likely Ross Rocklynne's "The Men and the Mirror", a classic problem story. One reviewer says

Colbie and Deverel land on a planet whose entire top has been scooped out and polished into a mirror, hundreds of miles across, and somehow fall into it.... The problem here is how to get out again, given that they are on an almost frictionless concave surface.

(longer summary here).

If the book was a hardcover, you read it in Isaac Asimov's Before the Golden Age (US, UK). If it was a paperback, probably Before the Golden Age, book 3 (UK: volume 4 at first, volume 3 in later printings ). Or in Rocklynne's collection, The Men and the Mirror. Do these covers look familiar?

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  • The covers don't look familiar but the link to Asimov is a good fit because I was huge Asimov fan and would read pretty much anything with his name on it, anthologies, non-fiction, whatever. Plus the summary perfectly matches what I remember about the story.
    – Kyle Jones
    Commented Oct 28, 2012 at 19:00
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You might be thinking of the Fredric Brown novel Rogue in Space. According to the Fredric Brown bibliography, two short stories were incorporated into the novel.

I'm only mostly sure that is the book but I am completely sure that it was a Fredric Brown book.

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  • It's been a long, long time since I last read Rogue in Space, and I remember the sentient asteroid, but I don't remember a giant mirror.
    – sjl
    Commented Oct 29, 2012 at 5:24
  • All of my books are still packed away or I'd look. I do remember that the two people on the mirror were enemies (a criminal and cop, I think), also mentioned by the OP.
    – seth.miller
    Commented Oct 29, 2012 at 23:50
  • I know how that frustration feels. Mine are boxed up, too.
    – sjl
    Commented Oct 30, 2012 at 0:56

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