# Local Circumstances Tables

Local circumstances for approximately 400 cities, metropolitan areas and places in Africa, Australia, etc. are presented in Tables 11 through 18. These tables give the local circumstances at each contact and at maximum eclipse for every location. The coordinates are listed along with the location's elevation (meters) above sea-level, if known. If the elevation is unknown (i.e., not in the data base), then the local circumstances for that location are calculated at sea-level. In any case, the elevation does not play a significant role in the predictions unless the location is near the umbral path limits and the Sun's altitude is relatively small (<10°). 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 umbral eclipse and only witness first and fourth contacts. The Universal Time of maximum eclipse (either partial or total) is listed to a tenth of a second. 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 umbral eclipses (both annular and total), the eclipse magnitude is identical to the topocentric ratio of the Moon's and Sun's apparent diameters.

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 center 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 center 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 center 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 center 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). In this rapidly changing political world, it is often difficult to ascertain the correct name or spelling for a given location. Therefore, the information presented here is for location purposes only and is not meant to be authoritative. Furthermore, it does not imply recognition of status of any location by the United States Government. We hereby solicit corrections to names, spellings, coordinates and elevations in order to update the geographic data base for future eclipse predictions.

For countries in the path of totality, expanded versions of the local circumstances tables listing many more locations are available via a special web site of supplemental material for the total solar eclipse of 2002 December 4.

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