Limb Corrections to the Path Limits: Graze Zones
The northern and southern umbral limits provided in this publication
were derived using the Moon's center of mass and a mean lunar
radius. They have not been corrected for the Moon's center of
figure or the effects of the lunar limb profile. In applications
where precise limits are required, Watts' limb data must be used
to correct the nominal or mean path. Unfortunately, a single correction
at each limit is not possible since the Moon's libration in longitude
and the contact points of the limits along the Moon's limb each
vary as a function of time and position along the umbral path.
This makes it necessary to calculate a unique correction to the
limits at each point along the path. Furthermore, the northern
and southern limits of the umbral path are actually paralleled
by a relatively narrow zone where the eclipse is neither penumbral
nor umbral. An observer positioned here will witness a slender
solar crescent that is fragmented into a series of bright beads
and short segments whose morphology changes quickly with the rapidly
varying geometry of the Moon with respect to the Sun. These beading
phenomena are caused by the appearance of photospheric rays that
alternately pass through deep lunar valleys and hide behind high
mountain peaks as the Moon's irregular limb grazes the edge of
the Sun's disk. The geometry is directly analogous to the case
of grazing occultations of stars by the Moon. The graze zone is
typically five to ten kilometers wide and its interior and exterior
boundaries can be predicted using the lunar limb profile. The
interior boundaries define the actual limits of the umbral eclipse
(both total and annular) while the exterior boundaries set the
outer limits of the grazing eclipse zone.
Table 6 provides topocentric
data and corrections to the path
limits due to the true lunar limb profile. At five minute intervals,
the table lists the Moon's topocentric horizontal parallax, semi-diameter,
relative angular velocity of the Moon with respect to the Sun
and lunar libration in longitude. The Sun's center line altitude
and azimuth is given, followed by the azimuth of the umbral path.
The position angle of the point on the Moon's limb which defines
the northern limit of the path is measured counter-clockwise (i.e.
- eastward) from the north point on the limb. The path corrections
to the northern and southern limits are listed as interior and
exterior components in order to define the graze zone. Positive
corrections are in the northern sense while negative shifts are
in the southern sense. These corrections (minutes of arc in latitude)
may be added directly to the path coordinates listed in
Table 3. Corrections to the
center line umbral durations due to the
lunar limb profile are also included and they are all negative.
Thus, when added to the central durations given in Tables
3,
4,
5 and
7, a slightly shorter central
total phase is predicted.
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