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* is 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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