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 11:00 UT (Figure 20) where the center of figure is displaced ­0.28 and +0.38 arc-seconds in ecliptic latitude and longitude, respectively. This shift is fairly characteristic along much of the 1999 umbral path but varies considerably between eclipses due to different libration geometries. 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 south of the center line by 2-6 kilometers along the European path, and 3-10 kilometers along the Middle Eastern path.

Furthermore, the true limb profile of the 1999 eclipse actually produces a longer duration of totality than the one calculated using a mean limb. This results in maximum durations lasting 1 to 3 seconds longer than the nominal center line durations along much of the path.

Figure 21 shows a series of calculations for the duration of totality within ±30 kilometers of the center line and spaced at ten minute intervals along the path through Europe (a) and the Middle East (b). For a given time, the duration of totality is calculated at 1 kilometer intervals perpendicular to the path within a 60 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 21, 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 21 to optimize their location with respect to the center line.

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