In August 1982, the International Astronomical Union (IAU)
General Assembly adopted a value of *k* = 0.2725076 for the mean lunar
radius. This value is now 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. The adoption of one single value for *k*
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.
Using the IAU value for k, the Astronomical Almanac identified this
event as a total eclipse of 3 seconds duration when it was, in fact, a
beaded annular eclipse. Since a smaller value of *k* is more
representative of the deeper lunar valleys and hence the minimum
solid disk radius, it helps ensure the correct identification of an
eclipse's true nature.

Of primary interest to most observers are the times when
umbral eclipse begins and ends (second and third contacts,
respectively) and the duration of the umbral phase. When the IAU's
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* = 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 at total eclipses, we depart from standard
convention by adopting the smaller value of *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 value for *k*. Similarly, predictions using a smaller
*k* result in longer umbral durations and wider paths for annular
eclipses than do predictions using the IAU's *k*.

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