# Total Solar Eclipse Local Circumstances

## Fred Espenak

The local circumstances tables present the eclipse contact times and the instant of maximum eclipse for many cities and locations around the world. The coordinates are listed along with the location's elevation (meters) above sea-level, if known. Otherwise, the local circumstances are calculated for sea-level. The Universal Time of each contact is given to a tenth of a second, along with position angles P and V and the altitude of the Sun. The position angles identify the point along the Sun's disk where each contact occurs and are measured counter-clockwise (i.e., eastward) from the north and zenith points, respectively. Locations outside the umbral path miss the total eclipse and only witness first and fourth contacts of a partial eclipse. The Universal Time of maximum eclipse (either partial or total) is listed. Next, the position angles P and V of the Moon's disk with respect to the Sun are given, followed by the altitude and azimuth of the Sun at maximum eclipse. Finally, the corresponding eclipse magnitude and obscuration are listed. For total eclipses, the eclipse magnitude is replaced by the topocentric ratio of the apparent diameters of the Moon to the Sun.

Two additional columns are included if the location lies within the path of the Moon's umbral shadow. The umbral depth is a relative measure of a location's position with respect to the central line and path limits. It is a unitless parameter which is defined as:

u = 1 - abs(x/R)      [1]

where:

 u = umbral depth x = perpendicular distance from the shadow axis (kilometers) R = radius of the umbral shadow as it intersects Earth's surface (kilometers)

The umbral depth for a location varies from 0.0 to 1.0. A position at the path limits corresponds to a value of 0.0 while a position on the central line has a value of 1.0. The parameter can be used to quickly determine the corresponding center line duration. Thus, it is a useful tool for evaluating the trade-off in duration of a location's position relative to the central line. Using the location's duration and umbral depth, the center line duration is calculated as:

D = d/(1 - (1 - u)2)1/2 seconds      [2]

where:

 D = duration of totality on the central line (seconds) d = duration of totality at location (seconds) u = umbral depth

The final column gives the duration of totality. The effects of refraction have not been included in these calculations, nor have there been any corrections for center of figure or the lunar limb profile.

Locations were chosen based on general geographic distribution, population, and proximity to the path. The primary source for geographic coordinates is The New International Atlas (Rand McNally, 1991). Elevations for major cities were taken from Climates of the World (U. S. Dept. of Commerce, 1972). The city names and spellings presented here are for location purposes only and are not meant to be authoritative. They do not imply recognition of status of any location by the United States Government.

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