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UT1, UTC, TAI, TDB, or what?

I need to determine the time difference between a given observation and the epoch from which certain constants apply. I typically work with the J2000.0 epoch. This is to determine how much time has passed and how far motions have propagated.

I recently learned that when making planetary observations, I should convert the observation time into TDB time for improved accuracy (Jean Meeus). But I also found out that we use Earth-based time for sidereal time computations, so the rule doesnt apply for sidereal time... but unfortunately which Earth-based time scale to use was not specified in my research.

There are a half dozen or so. UT1, UTC, TAI to name just a few. They differ from as much as 0.00017 seconds to as much as 1 minute 6 seconds. Now, when I compute sidereal time, I am consistently in error by anywhere from 20 to 35 seconds, depending on the resource I compare to. And I cannot seem to resolve this inconsistency, no matter how complicated or detailed my math gets; I find I am getting more and more out of synch with the quoted, expected value with each new variable I factor in (exactly opposite Id expect).

I LOVE exactness. This is an exercise in conceptual understanding of the variables at play and in the technicality of it all; practicality is not an issue here, Im just trying to figure it all out with as much precision as possible.

Any help at finding as precise a value as possible for sidereal time would be appreciated.

I have been using my local clock time and date (local civil time). Factoring out daylight savings if applicable, converting to GMT (time zone offset). I assume that my result is the time in UT or UTC (I may be wrong). While my resource (Astronomical Algorithms, Jean Meeus) assumes that UT and UTC are identical to one another, so I dont concern myself with any more details. Then I use the equations in chapter 12 and (?)22, on sidereal time and nutation.

In doing this I get results that differ by as much as 35 seconds, max, from that which Im quoted on sites like WolframAlpha, other EDU and GOV (time keeping) sites, as well as iPod Touch apps that purport to display sidereal time.

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1 Answer 1

By definition, sidereal time is computed as a function of mean solar time and UT1 is the best approximation to the latter. Remember that apparent sidereal time accounts for nutation. Again, I suggest you consult the Explanatory Supplement for all the details. It's pretty much the definitive source. Regarding exactness, in science there is no such thing. Time is ultimately defined by astronomical observation (that may very well change in the near future if atomic clocks are adopted as the standard) so the best we can do is compare any mathematical theory with Nature, or to compare one mathematical theory with another mathematical theory. Feel free to contact me privately if you have further questions. I don't know if I'm "allowed" to give my email address here so I'll put it in my profile.

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