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 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 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,
a smaller *k* predicts longer umbral durations and wider
paths for annular eclipses than does the IAU's *k*.

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