Re: Time Units

[Leigh Palmer <palmer@SFU.CA>]

First, Neugebauer is reputable, reliable authority on history.
Accept what he says uncritically or be prepared to translate some
rather inaccessible stuff in dead languages.

Practice today is to treat the hour as sixty minutes, the minute as
sixty seconds, and the second as being defined in terms of the well
known cesium hyperfine transition. When one does this the hour is
slightly shorter than 1/24 of a mean solar day because the length
of the day (LOD), measured in seconds, more or less steadily
increases with the passage of time. I say "more or less" because
there is a long term secular increase in LOD with smaller temporal
variations superimposed upon it. The dominant secular term is the
result of tidal retardation in Earth's rotation rate; the smaller
terms are attributable to things like the variation in rotational
inertia due to polar cap melting or freezing, nutation, etc. Since
the definition of the second was made to be as nearly as possible
1/86400 of the mean solar day at the epoch 1900.0, the Earth is
constantly falling behind. Even if the secular slowing were to
cease it would still be necessary to intercalate leap seconds into
civil time just about as frequently as they are intercalated now.

When I talk about this in my teaching I always use a transparency
taken from "Gravitation" by Meisner, Thorne & Wheeler. I don't have
it here at home, but it is about p. 25. It is an eclipse map for
the event of 484 AD, well observed around Athens, which shows where
that eclipse should have been seen had the Earth rotated at an
unvarying rate. I recommend this as a source of data for this
exercise:

By how much time does the present LOD exceed that of 1900.0 given
the eclipse map of 484, and assuming the angular deceleration of
the Earth has remained constant since then? How often do you expect
leap seconds to be intercalated into civil time?

Incidentally, this business of civil time running with occasional
hiccups would be a major annoyance to astronomers and celestial
mechanics if they used civil time. For that reason they use their
own continuously running time (one flavor of which is called
ephemeris time, ET) which is, regardless of what one might think to
be an improvement, still rendered in sexagesimal numeration using
the Gregorian Calendar. (There is also a flavor of ET using what is
called the Julian Day Number (JD) or the modified Julian Day Number
(MJD) which itself comes in two subflavors!)

Finally I will refer you to "Explanatory Supplement to the
Astronomical Ephemeris and the American Ephemeris and Nautical
Almanac", a new edition of which was published recently (in my
terms - I have an older copy) by University Science Books. The
sections on time and the calendar are most entertaining.

Leigh


> I am still interested in the definition of the hour and the minute and when
> they became a fixed/defined period.  The following from another
> list:  Comments? Corroboration?
>
> Jim Green
>
> =======================================
>
> From:  Eric's Treasure Trove of Astronomy
>  http://www.treasure-troves.com/astro/Hour.html
>
> Hour
>
> A unit of time of which 24 comprise a Solar Day. The Egyptians were the
> first to so divide the day, although the lengths of each of the hours in a
> day was not a fixed number to the Egyptians and changed with the seasons.
> In their investigation of theoretical astronomy, the Greeks used
> "equinoctial" hours of equal length, and divided these hours into 60
> Minutes (Neugebauer 1969).
>
> References
> Neugebauer, O. The Exact Sciences in Antiquity, 2nd ed. New York: Dover,
> pp. 81, 1969.
>
> Jim Green
> mailto:JMGreen@sisna.com
> http://users.sisna.com/jmgreen