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lunar eclipses

Astronomical Algorithms - second edition - Jean Meeus - Chapter 54

Eclipses

Lunar eclipses

Designation Result Units
Day number (Page 65) day number integer between 1 and total days in year
Days in the given year (Page 62) days in the given year 365 (no leap year) or 366 (leap year)
Day number / days in the given year decimal value decimal value smaller than or equal to 1
k (49.2) k value of k with decimals
Modified k (Page 379) rounded k truncated k - 0.5
 
JDE (49.1) JDE JDE
M (49.4) M degrees
MA (49.5) MA degrees
F (49.6) F degrees
Gamma = least distance from the axis of the moon's shadow to the center of the earth (Page 381) gamma Earth's equatorial radius
u = radius of the moon's umbral cone in the fundamental plane (the plane through the center of the earth and perpendicular to the axis of the moon's shadow)(Page 381) u Earth's equatorial radius
Radii at the distance of the moon for the penumbra ro penumbra Earth's equatorial radius
Radii at the distance of the moon for the umbra sigma umbra Earth's equatorial radius
 
Magnitude penumbral eclipse (54.3) magnitude penumbral eclipse unitless
Magnitude umbral eclipse (54.4) magnitude umbral eclipse unitless
Is there a lunar eclipse? (Page 383) lunar eclipse text
 
Location? location text
Visibility visibility text
 
p = p t = t h = h n = n
Semiduration of the partial_phase (Page 383) semiduration of the partial phase minutes
Semiduration of the total phase (Page 383) semiduration of the total phase minutes
Semiduration of penumbral phase (Page 383) semiduration of penumbral phase minutes
Delta T for the given year deltaT dayfraction
 
Correction to be added to the JDE (54.1) correction JDE fraction
Final JDE for the maximum of the eclipse final JDE for the maximum of the eclipse JDE
 
First contact with the penumbra first contact with the penumbra weekday/date/time (UT)
First contact with the umbra first contact with the umbra weekday/date/time (UT)
Beginning of total phase beginning of total phase weekday/date/time (UT)
Maximum of the eclipse (in case there is an eclipse) final gregorian date/time weekday/date/time (UT)
End of total phase end of total phase weekday/date/time (UT)
Last contact with the umbra last contact with the umbra weekday/date/time (UT)
Last contact with the penumbra last contact with the penumbra weekday/date/time (UT)

Remarks:

The algorithms in this chapter are not intended to give highly accurate results.

Still, for lunar eclipses the results will be precise enough for historical research, or when high accuracy is not needed.

DeltaT is based on the "Five Millenium Canon of Lunar Eclipses (Espenak and Meeus)"