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.

Table 8 directly tabulates the coordinates of the zones of grazing eclipse at each limit along all land based sections of the path. The coordinates are given every 7.5' in longitude and include the time of maximum eclipse in the northern and southern graze zones as well as on the center line. The Sun's center line position (altitude and azimuth) and the path's azimuth are also listed. The Elevation Factor is the factor by which the path must be shifted north perpendicular to itself for each unit of elevation (height) above sea level. In practice, a location's elevation in multiplied by the Elevation Factor to obtain the shift. Negative values (usually the case for eclipses in the Northern Hemisphere) indicate that the path must be shifted south for positive elevations. For instance, if one's elevation is 1000 meters above sea level and the Elevation Factor is -0.20, then the shift is 1000m x -0.20 = -200m. Thus, the observer must shift the path coordinates 200 meters in a direction perpendicular to the path and in a negative or southerly sense.

The final column of Table 8 lists the Scale Factor (km/arc-second). This parameter provides an indication of the width of the zone of grazing phenomena, due to the topocentric distance of the Moon and the projection geometry of the Moon's shadow on Earth's surface. For example, let us assume a value of 2 km/arc-seconds for the Scale Factor. Since the chromosphere has an apparent thickness of about 3 arc-seconds, it would then be visible continuously during totality for any observer in the path who is within 6 kilometers of each interior limit. The most dynamic beading phenomena occurs within 1.5 arc-seconds of the Moon's limb. Using the above Scale Factor, this projects to the first 3 kilometers inside the interior limits. However, observers should position themselves at least 1 kilometer inside the interior limits (south of the northern interior limit or north of the southern interior limit) to ensure that one is inside the path due to small uncertainties in Watts' limb datum and the actual path limits.

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