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John Cowan writes:
 > Roger Mills scripsit:
 >
 > > I recall a SF novel (and a ST(NG? episode) that dealt with a
 > > planet orbiting its primary so quickly that in earth/ship time of
 > > one hour or so, life on the planet went from stone to bronze age;
 > > after another hour they were developing rockets.
 >
 > Robert Forward, _Dragon's Egg_.  The ST:V episode was called "Blink
 > of an Eye".
 >

It wasn't a planet, though, in _Dragon's Egg_.  It was a neutron star.
IIRC, time wasn't actually "going faster" on the surface, it's just
that time-perception was different for the Cheela because the
"chemical" reactions in impure neutronium are so much more
rapid... it's a long time since I read it though, there may have been
a relativistic element.  Certainly "earth/ship time of one hour or so,
life on the planet went from stone to bronze age; after another hour
they were developing rockets" describes the story.

(Ever read _The Flight of the Dragonfly_, by the same author?  That
was my favourite book, at one time.  Hard to say why, now - the aliens
and the spacecraft are interesting, and described in detail (there's a
diagram of the ship in the back) but I don't recall much of the plot
or characters.  Probably worth rereading, when I have time.)

Oh, and if we're just listing all ST episodes with any kind of
relative time difference, there's an original series episode called
"Wink of an Eye" with (humanoid) aliens who move about so quickly that
they can't be detected by normal instruments.