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solar eclipses

Astronomical Algorithms - second edition - Jean Meeus - Chapter 54

Eclipses

Solar 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 percentage decimal value smaller than or equal to 1
k (49.2) k value of k with decimals
Modified k (Page 379) modified k rounded k
 
JDE (49.1) JDE JDE
M (49.4) M degrees
MA (49.5) MA degrees
F (49.6) F degrees
How close is F to 0, 180 or 360? F rest degrees
omega (49.7) omega degrees
F1 (Page 380) F1 degrees
P (Page 381) P dimensionless
Q (Page 381) Q dimensionless
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
Radius of the penumbral cone in the fundamental plane (Page 381) radius penumbral cone Earth's equatorial radius
 
Is there a solar eclipse? (Page 380) solar eclipse text
 
Location? (Page 380) location text
Visibility visibility text
Solar type (is gamma between -0.9972 and 0.9972?) solar type text
Solar type (is abs(gamma) > 1.5433 + u?) solar type text
Solar type (is abs(gamma) between 0.9972 and 1.5433+u?) solar type text
Solar type (is abs(gamma) between 0.9972 and 1.0260?) solar type text
Solar type (is abs(gamma) between 0.9972 and 0.9972 + abs(u)?) solar type text
Central type (total, annular or annular-total) central type text
Magnitude eclipse (in case of partial eclipse) (54.2) magnitude eclipse unitless
 
Correction to be added to the JDE (54.1) correction JDE fraction
DeltaT for the given year deltaT dayfraction
Final JDE final JDE JDE
Gregorian date/time for the maximum of the eclipse final gregorian date/time weekday/date/time (UT)

Remarks:

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

For limit cases, determining the eclipse type needs a more accurate calculation.

For the solar eclipses of the years A.D. 1951 to 2050, the mean error is 22 seconds, and the greatest error 66 seconds for the time of the maximum of the eclipse.

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