Explanation of Lunar Eclipse Data Tables

by Fred Espenak

The following tables contain brief explanations for the various parameters used in the prediction of lunar eclipses.

Eclipse Characteristics
Parameter Description
Penumbral Eclipse Magnitude the fraction of the Moon’s diameter occulted by Earth’s penumbral shadow at the instant of Greatest Eclipse; the Penumbral Eclipse Magnitude is less that 1.0 for partial penumbral eclipses (and equal to or greater than 1.0 for total penumbral eclipses); the Penumbral Eclipse Magnitude is equal to or greater than 1.0 for most partial eclipses and for all total eclipses
Umbral Eclipse Magnitude the fraction of the Moon’s diameter occulted by Earth’s umbral shadow at the instant of Greatest Eclipse; the Umbral Eclipse Magnitude is less that 1.0 for partial eclipses (and less than 0.0 for penumbral eclipses); the Umbral Eclipse Magnitude is equal to or greater than 1.0 for total eclipses
Gammathe distance (in units of equatorial Earth radii) of the center of the Moon’s disk from the center of Earth’s umbral shadow at the instant of Greatest Eclipse; since this is the instant when the Moon passes closest to the axis of Earth’s umbral shadow, Gamma is, by definition, the minimum distance of the shadow axis from center of the Moon
Epsilonthe apparent geocentric angular distance (in degrees) of the center of the Moon’s disk from the center of Earth’s umbral shadow at the instant of Greatest Eclipse; Epsilon is, by definition, the minimum angular distance of the Moon from the shadow axis during a lunar eclipse


Conjunction Times
Parameter Description
Greatest Eclipsethe instant when the Moon’s disk passes closest to the center of Earth’s shadow
(by convention the date of an eclipse is fixed to this instant)
Ecliptic Oppositionthe instant when the Sun and Moon have ecliptic longitudes differing by 180° this defines the instant of the Full Moon phase
Equatorial Oppositionthe instant when the Sun and Moon have celestial longitudes differing by 180° in the equatorial coordinate system; this is the instant when the Sun and Moon Right Ascensions differing by 12 hours

Geocentric Coordinates of Sun and Moon
Parameter Description
Right Ascensionthe longitudinal position (in the equatorial coordinate system) of the Sun and the Moon at the instant of greatest eclipse
Declinationthe latitudinal position (in the equatorial coordinate system) of the Sun and the Moon at the instant of greatest eclipse
Semi-Diameterthe apparent geocentric angular radius of the disk of the Sun or Moon at the instant of greatest eclipse
Eq. Hor. ParallaxEquatorial Horizontal Parallax, the angle subtended by the radius of Earth at the distance of the Sun or Moon at the instant of greatest eclipse

Geocentric Libration of Moon
Parameter Description
lthe Moon’s geocentric libration in longitude at greatest eclipse
bthe Moon’s geocentric libration in latitude at greatest eclipse
cthe Moon’s geocentric libration in position angle of lunar rotation axis with respect to celestial north

Earth’s Shadows
Parameter Value
Penumbral Radiusthe apparent geocentric angular radius (in degrees) of Earth’s penumbral shadow at the distance of the Moon at the instant of Greatest Eclipse
Umbral Radiusthe apparent geocentric angular radius (in degrees) of Earth’s penumbral shadow at the distance of the Moon at the instant of Greatest Eclipse

Prediction Parameters
Parameter Description
Ephemeridesidentifies the ephemerides used to calculate the postions of the Moon and Sun
ΔTthe value of ΔT used in the eclipse predictions
Shadow Rulethe computational method used for enlarging Earth's radius to compensate for the effects of the atmosphere on eclipse contact times; see Earth’s Shadow for more information
Shadow Enlargementthe fractional enlargement of Earth's penumbral and umbral shadows used in the eclipse predictions; see Earth’s Shadow for more information
Saros Seriesthe Saros series number followed by the sequence number and total number of eclipses in the series