What is the difference between UT0, UT1 and GMT time?

Every reference I find says that they are "essentially" the same, which we all know really means that they are not the same, but different only by a some small amount that someone else other than me decides is negligible.

They also like to say that UT1 and UTC are the same, but if you look into it you find that they differ by as much as 0.9 seconds. This is, admittedly, insignificant to me. But the practicality of it is not my concern here. The technical reality of it is.

I want specifics and exactness where applicable here.

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Have you tried to read the basic definitions of these quantities? See en.wikipedia.org/wiki/Universal_Time#Versions –  Luboš Motl Dec 14 '12 at 8:46
@Cog: If you feel a comment is inappropriate, flag it. I feel your comments may not motivate the answer you desire. –  RedGrittyBrick Dec 14 '12 at 9:44
Dear Cogito, it's a very thankless task to be writing an extension of the - already long - description in Wikipedia, especially if it is absolutely not clear from your question what you actually find unsatisfactory or inexact about the Wikipedia's definitions. I am not worshiper of Wikipedia's infallibility - it's not infallible - but I would bet that the Wikipedia definition is complete, right, accurate, and well-defined. And answers on this server aren't infallible, either. You may disagree but 'cause it's unclear why you disagree and what you want to be clarified, it's very hard to help you –  Luboš Motl Dec 14 '12 at 10:22
Without speaking for anyone who may have cast downvotes I'd like to suggest some things that Cognito could do to prevent the kind of reception that this question has received. (1) Two very similar questions in one hour can make readers (especially if no familiar with the topic) think that you are not taking the resource here seriously; (2) name or link to the resources that you are familiar with this will both indicate to potential answers your level of preparation, prevent comments of the "Have you read..." variety and spare users the effort of paraphrasing things you already know; (cont.) –  dmckee Dec 14 '12 at 16:06
(3) Don't take "Have looked at [basic resource]..." comments personally if you haven't indicated that you have, we get questions from users at all levels of preparation here elementary school to active professionals and know your level is crucial to providing a good answer, (4) even if you violate #3 don't lash out at potential answers: it just isn't going to help. –  dmckee Dec 14 '12 at 16:08

UT1 is a specific "flavor" of Universal Time, which is a measure of Earth's rotation relative to the mean sun, a fictitious "prime mover" upon which all our clocks are based. UT1 is related to sidereal time (Earth's rotation relative to the fixed background stars) by a rather long mathematical expression usually expressed as a polynomial function of mean solar time. Earth's rotation is not uniform though; it varies. UTC (Coordinated Universal Time) is a specific "flavor" of Universal Time intended to smooth out these variations by staying within 0.9 s of UT1. The difference between the two is called $\Delta UT1$ and is adjusted as necessary, but can only be adjusted after observation. Larger adjustments come in the form of leap seconds. The current approximate value of $\Delta UT$ is called $DUT1$ and is encoded in the standard time signals broadcast by stations such as WWV (in America) and CHU (in Canada). Listen for doubling of pips at the beginning of each minute.

UT0 is an observational approximation to UT1 based on meridian observations of standard stars. UT0 must be corrected for polar motion, which varies from observatory to observatory.

Both UT1 and UTC are generically referred to as Universal Time and the distinction between them is important only if the that maximum discrepancy of 0.9 s is important for your application.

There is another "flavor" of Universal Time called UT1R, which is intended to account for tidal variations in Earth's rotation.

There is another "flavor" of Universal Time called UT2, which is intended to account for seasonal variations in Earth's rotation. UT2 isn't used any more.

GMT, Greenwich Mean Time, is a sometimes deprecated historic term equivalent to UT, but is no longer used in astronomical applications. It used still used in many civil applications though (and remains the legal time standard (outside the period of daylight-saving summer time) in the UK).

By far your best reference on this topic is the latest edition of The Explanatory Supplement to the Astronomical Almanac, edited by Sean Urban and Kenneth Seidelmann. The third edition was just published in November by University Science Books. My own book, Fundamental Ephemeris Computations (Willmann-Bell, 2000) also discusses this topic and includes computer code.

Be aware that since FEC was published, certain astronomical terminology has changed and now the term "Earth rotation angle" is now used to mean roughly what sidereal time previously meant. The new terminology is reflected in the new Explanatory Supplement referenced above.

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I have a big problem with students deciding what is and is not correct around here. –  user11266 Feb 23 '13 at 18:00
Whoever suggested the most recent edit is not familiar with time. GMT, which is now fully deprecated for astronomical use, was indeed used at one time to mean the same thing that UTC is now used to mean. That GMT (obviously) had no connection with atomic time is irrelevant. –  user11266 Feb 23 '13 at 18:03
The description of utc here is wrong. Utc is always an integral number of seconds different to tai. –  Julian Dec 5 '13 at 19:35