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Duffett-Smith, in 'Practical Astronomy With Your Calculator', says of converting a given Greenwich mean sidereal time into the corresponding universal time.

The problem is complicated, however, by the fact that the sidereal day is slightly shorter than the solar day so that on any given date a small range of sidereal times occurs twice. This range is about 4 minutes long, the sidereal times corresponding to UT Oh to Oh 4m occurring again from UT 23h 56m to midnight (see Figure 3). The method given here correctly converts sidereal times in the former interval, but not in the latter.

What is a solution for arriving at the correct UT from GST for both cases?

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    $\begingroup$ Does this answer your question? Sidereal times occuring twice a day question If not, what's the difference? $\endgroup$
    – Mike G
    Commented Feb 1 at 11:54
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    $\begingroup$ You would solve normally for the first case, then subtract one sidereal day to get the second case. But the problem is further complicated by the fact that Earth's rotation varies, so only an approximate solution is possible. For the most accurate result, you will need to incorporate the UT1-UTC value from the IERS: iers.org/IERS/EN/Publications/Bulletins/bulletins.html $\endgroup$ Commented Feb 1 at 13:28
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    $\begingroup$ MIke G. The link you provided is to a page I already looked at. The 'difference' is that the answer it gives does not address how to convert from GST to UT. $\endgroup$ Commented Feb 1 at 22:05
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    $\begingroup$ Greg, how would I conclude that I needed to subtract a sidereal day to be correct? I would need to know somehow that the first answer was incorrect. (I can be a slow learner betimes. ) $\endgroup$ Commented Feb 1 at 22:14
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    $\begingroup$ @Andalusional How do you want to deal with the ambiguity? A mean solar day is ~4m longer than a sidereal day. So if the Duffett-Smith method gives a UT time in the first 4 minutes of the day there's a 2nd solution 23h56m (UT) later. $\endgroup$
    – PM 2Ring
    Commented Feb 8 at 0:28

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If you have a correct UT (including date) for a given GMST, adding a sidereal day yields another correct UT. So, if you have the earliest correct UT for a given date, just add a sidereal day to it. If it's the same date, it's the second solution for that date.

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