Limb Profile Effects on the Duration of Totality

As was previously discussed, the Moon's center of figure (i.e., the geometric center of the Watts' datum) is displaced from the Moon's center of mass. A case in point is the lunar limb geometry at 13:00 UT (Figure 8) where the center of figure is displaced -0.13 arc seconds in ecliptic latitude and +0.53 arc seconds in ecliptic longitude. This shift is fairly characteristic along much of the 2001 umbral path but varies considerably between eclipses due to different libration geometry's. Since most predictions appearing in this publication are calculated with respect to the Moon's center of mass, the center of figure offset has a small but significant consequence on the duration of totality. When compounded with the irregularities of the lunar limb profile, the overall result is to shift the maximum duration of totality north of the center line by 0-9 kilometers along the African path, and 10 kilometers north along the Madagascar path.

Figure 9 shows a series of calculations for the duration of totality within 60 kilometers of the center line and spaced at ten minute intervals along the path through Africa and Madagascar. For a given time, the duration of totality is calculated at 1 kilometer intervals perpendicular to the path within a 120 kilometer zone centered on the center line. Predictions using the Moon's center of mass and mean limb are represented by the dotted curves. Predictions using the actual limb profile to calculate corrected contact times and the resulting duration of totality are plotted as solid curves. What becomes immediately apparent upon inspection of Figure 9, is the asymmetry of the true limb duration curves and is a consequence of the complex Sun/Moon limb geometry which changes quickly with path position.

Observers wishing to witness the maximum possible duration of totality from a given section of the path can use Figure 9 to optimize their location with respect to the center line.

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