ELEMENTS, SHADOW CONTACTS AND ECLIPSE PATH TABLES

The geocentric ephemeris for the Moon and Sun, various parameters and constants used in the predictions, the besselian elements (polynomial form) are given in Table 1. The eclipse predictions and elements were derived from solar and lunar data contained in the DE200 and LE200 ephemerides developed jointly by the Jet Propulsion Laboratory and the U. S. Naval Observatory for use in the Astronomical Almanac for 1984 and after. Unless otherwise stated, all predictions are based on center of mass positions for the Sun and Moon with no corrections made for center of figure, center of motion, lunar limb profile or atmospheric refraction. Furthermore, these predictions depart from IAU convention by using a smaller constant for the mean lunar radius k for all umbral contacts (see: LUNAR LIMB PROFILE). Times are expressed in either Terrestrial Dynamical Time (TDT) or in Universal Time (UT), where the best value of [[Delta]]T available at the time of preparation is used.

Table 2 lists all external and internal contacts of penumbral and umbral shadows with Earth. They include TDT times and geodetic coordinates both with and without corrections for [[Delta]]T. These contacts are defined as follows:

P1 - Instant of first external tangency of penumbral shadow cone with Earth's limb.

(partial eclipse begins)

P2 - Instant of first internal tangency of penumbral shadow cone with Earth's limb.

P2 - Instant of last internal tangency of penumbral shadow cone with Earth's limb.

P4 - Instant of last external tangency of penumbral shadow cone with Earth's limb.

(partial eclipse ends)

U1 - Instant of first external tangency of umbral shadow cone with Earth's limb.

(umbral eclipse begins)

U2 - Instant of first internal tangency of umbral shadow cone with Earth's limb.

U2 - Instant of last internal tangency of umbral shadow cone with Earth's limb.

U4 - Instant of last external tangency of umbral shadow cone with Earth's limb.

(umbral eclipse ends)

Similarly, the northern and southern extremes of the penumbral and umbral paths, and extreme limits of the umbral center line are given. The IAU longitude convention is used throughout this publication (i.e. - eastern longitudes are positive; western longitudes are negative; negative latitudes are south of the Equator).

The path of the umbral shadow is delineated at five minute intervals in Universal Time in Table 3. Coordinates of the northern limit, the southern limit and the center line are listed to the nearest tenth of an arc-minute (~185 m at the Equator). The path azimuth, path width and umbral duration are calculated for the center line position. The path azimuth is the direction of the umbral shadow's motion projected onto the surface of the Earth. Table 4 presents a physical ephemeris for the umbral shadow at five minute intervals in UT. The center line coordinates are followed by the topocentric ratio of the apparent diameters of the Moon and Sun, the eclipse obscuration[1], and the Sun's altitude and azimuth at that instant. The central path width, the umbral shadow's major and minor axes and its instantaneous velocity with respect to Earth's surface are included. Finally, the center line duration of the umbral phase is given.

Local circumstances for each center line position listed in Tables 3 and 4 are presented in Table 5. The first three columns give the Universal Time of maximum eclipse, the center line duration of totality and the altitude of the Sun at that instant. The following columns list each of the four eclipse contact times followed by their related contact position angles and the corresponding altitude of the Sun. The four contacts[2] identify significant stages in the progress of the eclipse. The position angles P and V identify the point along the Sun's disk where each contact occurs[3]. The altitude of the Sun at second and third contact is omitted since it is always within 1deg. of the altitude at maximum eclipse (column 3).

Table 6 presents topocentric values at maximum eclipse for the Moon's horizontal parallax, semi-diameter, relative angular velocity with respect to the Sun, and libration in longitude. The altitude and azimuth of the Sun are given along with the azimuth of the umbral path. The northern limit position angle identifies the point on the lunar disk defining the umbral path's northern limit. It is measured counter-clockwise from the north point of the lunar disk. In addition, corrections to the path limits due to the lunar limb profile are listed. The irregular profile of the Moon results in a zone of 'grazing eclipse' at each limit which is delineated by interior and exterior contacts of lunar features with the Sun's limb. The section LIMB CORRECTIONS TO THE PATH LIMITS: GRAZE ZONES describes this geometry in greater detail. Corrections to the center line durations due to the lunar limb profile are also included. When added to the durations in Tables 3, 4, 5, and 7, a slightly shorter central total phase is predicted.

To aid and assist in the plotting of the umbral path on large scale maps, the path coordinates are also tabulated at 1deg. intervals in longitude in Table 7. The latitude of the northern limit, southern limit and center line for each longitude is tabulated along with the Universal Time of maximum eclipse at each position. Finally, local circumstances on the center line at maximum eclipse are listed and include the Sun's altitude and azimuth, the umbral path width and the central duration of totality.


[1] Eclipse obscuration is defined as the fraction of the Sun's surface area occulted by the Moon.

[2] First contact is defined as the instant of external tangency between the Sun and Moon; it marks the beginning of the partial eclipse.

Second and third contacts define the two instants of internal tangency between the Sun and Moon; they signify the commencement and termination of the umbral (total or annular) phase.

Fourth contact is the instant of last external contact and it marks the end of the partial eclipse.

[3] P is defined as the contact angle measured counter-clockwise from the north point of the Sun's disk.

V is defined as the contact angle measured counter-clockwise from the zenith point of the Sun's disk.


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