Time period in which a planet rotates I notice that Wikipedia give two contradictory terms for the time period in which a planet rotates in relation to an infinitely-distant object. In one place this is called a "sidereal day" and in another "stellar day". Which of these are correct? For that point, is this an IAU definition? I cannot find the definitions on the IAU website.

From the Sidereal Day page:


  A sidereal day is the length of time it takes a planet to rotate from the perspective of a distant star.


From the Day page:


  
  stellar day - an entire rotation of a planet with respect to the distant stars
  sidereal day - a single rotation of a planet with respect to the vernal equinox
Since etymologically sidereal references the stars (Latin sidus), one might expect a sidereal day to correspond to the rotation of the Earth with respect to distant "fixed" stars. But this does not seem to be the case, and because the the difference is not significant, the two definitions are sometimes used interchangeably.

I don't know of an explicit IAU definition of sidereal day. However, since sidereal time is defined as the hour angle vernal equinox (which is a local definition, although Greenwich is conventional), defining the (mean) sidereal day in terms in reference to the equinox is practically the only sensible choice.

Effective 1985, UT1 is now computed using very long baseline interferometry of distant quasars, and so can be taken to be authoritative regarding the "fixed stars". The coordinated universal time (UTC) time approximates UT1 with atomic clocks. Anyway, UT1 derived the rotational period of the Earth as $p = 86164.09890369732\,\mathrm{s}$ of UT1 time and the mean sidereal day (in 2000) would be $86164.090530833\,\mathrm{s}$ of UT1 time, following the explanation:


  The length of one sidereal day is defined by two successive transits of the mean equinox; while the Earth is rotating eastward, the mean equinox is moving westward due to precession. Therefore, one sidereal day is shorter than the Earth's rotational period by about $0.008\,\mathrm{s}$, the amount of precession in the right ascension in one day.


See: Aoki, S., et al., The new definition of universal time, Astron. Astrophys. 105, 359-361 (1982).