In August 1982, the IAU General Assembly adopted a value of **k**=0.2725076
for the mean lunar radius. This value is currently used by the Nautical Almanac
Office for all solar eclipse predictions [Fiala and Lukac, 1983] and is
currently the best mean radius, averaging mountain peaks and low valleys along
the Moon's rugged limb. In general, the adoption of one single value for
**k** is commendable because it eliminates the discontinuity in the case of
annular-total eclipses and ends confusion arising from the use of two different
values. However, the use of even the best 'mean' value for the Moon's radius
introduces a problem in predicting the true character and duration of umbral
eclipses, particularly total eclipses. A total eclipse can be defined as an
eclipse in which the Sun's disk is completely occulted by the Moon. This
cannot occur so long as any photospheric rays are visible through deep valleys
along the Moon's limb [Meeus, Grosjean and Vanderleen, 1966]. But the use of
the IAU's mean **k** guarantees that some annular or annular-total eclipses
will be misidentified as total. A case in point is the eclipse of 3 October
1986. The *Astronomical Almanac* identified this event as a total eclipse
of 3 seconds duration when it was, in fact, a beaded annular eclipse. Clearly,
a smaller value of **k** is needed since it is more representative of the
deeper lunar valley floors, hence the minimum solid disk radius and helps
ensure that an eclipse is truly total.

Of primary interest to most observers are the times when central eclipse
begins and ends (second and third contacts, respectively) and the duration of
the central phase. When the IAU's mean value for **k** is used to calculate
these times, they must be corrected to accommodate low valleys (total) or high
mountains (annular) along the Moon's limb. The calculation of these corrections
is not trivial but must be performed, especially if one plans to observe near
the path limits [Herald, 1983]. For observers near the center line of a total
eclipse, the limb corrections can be more closely approximated by using a
smaller value of **k** which accounts for the valleys along the profile.

This publication uses the IAU's accepted value of **k**
(**k**=0.2725076) for all penumbral (exterior) contacts. In order to avoid
eclipse type misidentification and to predict central durations which are
closer to the actual durations for at total eclipses, we depart from convention
by adopting the smaller value for **k** (**k**=0.272281) for all umbral
(interior) contacts. This is consistent with predictions in *Fifty Year
Canon of Solar Eclipses: 1986 - 2035* [Espenak, 1987]. Consequently, the
smaller **k** produces shorter umbral durations and narrower paths for total
eclipses when compared with calculations using the IAU **k** value.
Similarly, the smaller **k** predicts longer umbral durations and wider
paths for annular eclipses than does the IAU **k**.

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