Shadow Diameters and Lunar Eclipses

Fred Espenak

To compensate for Earth's atmosphere when calculating the circumstances for lunar eclipses, Chauvenet [1891] introduced an empirical enlargement of 1/50 to the diameters of the umbral and penumbral shadows. This rule has been employed by many of the national institutes in their official eclipse predictions. However, Danjon [1951] pointed out a flaw in this method because it applies the same relative correction to the umbra and penumbra instead of using the same absolute correction. From eclipse observations, Danjon proposed to enlarge Earth's diameter by 1/85 to compensate for the atmosphere. The umbral and penumbral shadow diameters are then calculated based on this modified geometry. The French almanac Connaissance des Temps has used the Danjon rule in its eclipse predictions since 1951. The resulting umbral and penumbral eclipse magnitudes are smaller by approximately 0.005 and 0.026, respectively, as compared to predictions using the traditional 1/50 rule.

The Danjon rule is adopted on this website in the calculation of lunar eclipse circumstances and magnitudes.

See Enlargement of Earth's Shadows for a more detailed discussion on how it effects predictions of lunar eclipses.