Lunar eclipses

Bill J. Gray Jun 22, 2000

Hi folks,

As Jan Manek indicated, I'd added 2% to the earth's radius when
computing those tables of lunar eclipses. I hadn't realized that
Jean Meeus favors a different rule, but sure enough, page 353 of
_Astronomical Algorithms_ states:

"...instead of the traditional rule consisting of increasing by
1/50 the theoretical radii, we have preferred the method used since
1951 by the _Connaissance des Temps_... As compared to the results of
the 'French rule', the magnitude of a lunar eclipse calculated by
using the traditional rule is too large by .005 for umbral eclipses,
by about .026 for penumbral eclipses."

The tables of lunar eclipses are computed with the 2% rule. The
shadow calculations, though, did _not_ include that added 2%.
Including it has brought Guide's shadow drawing into much better
agreement with the predicted times of lunar eclipse contacts.

As Paul stated, the actual times of these events varies a bit
due to weather and volcanic eruptions (if I recall correctly, all
the volcanic ash in the atmosphere after Pinatubo erupted caused
eclipses in the early 1990s to have larger, darker shadows, for
example.)

-- Bill