Key to Catalog of Lunar Eclipses

Fred Espenak

Catalogs of lunar eclipse circumstances include the following data. The date and Universal Time [1] of the instant of greatest eclipse[2] are found in the first two columns. The eclipse type is given (T=Total, P=Partial, or N=Penumbral) along with the Saros series. Gamma is the distance of the Moon's center from the shadow axis of Earth at greatest eclipse (in Earth radii). The penumbral and umbral magnitudes of the eclipse are defined as the fractions of the Moon's diameter obscured by each shadow at greatest eclipse. The semi-durations of the partial and total phases of the eclipse are given to the nearest minute. Finally, the Greenwich Sidereal Time at 00:00 U.T., along with the Moon's Geocentric Right Ascension and Declination at greatest eclipse complete each record. A more detailed key is listed below.

[1] For most practical purposes, Universal Time (UT) is equivalent to Greenwich Mean Time (GMT).

[2] Greatest eclipse is defined as the instant when the Moon passes closest to the axis of Earth's shadows. This marks the instant when the Moon is deepest in Earth's shadow(s).

Calculating Eclipse Contact Times

The start and end times, respectively, of the partial phases of any eclipse can be calculated by subtracting or adding the partial semi-duration (S.D. Par) to the instant of greatest eclipse. Similarly, the start and end times, of the total phase of an eclipse can be calculated by subtracting and adding the total semi-duration (S.D. Tot) to the instant of greatest eclipse.

For example, the catalog lists the following record for the total lunar eclipse of 2000 Jan 21:

               U.T.
            Greatest    Saros          Pen.   Umb. S.D. S.D.  GST    Moon  Moon
     Date    Eclipse Type #    Gamma   Mag.   Mag. Par  Tot  (0 UT)   RA    Dec
                                                                h     h      °
  2000 Jan 21  04:43  T  124  -0.296  2.331  1.330 102m  39m   8.0   8.17  19.8

Thus, we have:

             Time of Greatest Eclipse:        tm = 04:43 UT
     Semi-Duration of Partial Eclipse:   S.D.Par = 102 minutes = 1h 42m
       Semi-Duration of Total Eclipse:   S.D.Tot =  39 minutes = 0h 39m

Times of the eclipse phases can then be calculated as:

      Partial Eclipse Begins:  tm - S.D.Par  =  04:43 - 1h 42m  =  03:01 UT
        Total Eclipse Begins:  tm - S.D.Tot  =  04:43 - 0h 39m  =  04:04 UT
          Total Eclipse Ends:  tm + S.D.Tot  =  04:43 + 0h 39m  =  05:22 UT
        Partial Eclipse Ends:  tm + S.D.Par  =  04:43 + 1h 42m  =  06:25 UT

Calculating the Moon's Altitude and Azimuth

To determine whether an eclipse is visible from a specific geographic location, it is simply a matter of calculating the Moon's altitude and azimuth during each phase of the eclipse. The calculations can be performed on any pocket calculator having trig functions (SIN, COS, TAN). Armed with the latitude and longitude of the location, the lunar eclipse catalog provides all the additional information needed to make the calculations. (For those wishing to avoid the tedium performing of these calculations, several Microsoft Excel spread sheets are available to automate the calculations for any geographic location and for all lunar eclipses from 1951 to 2050. See: Local Visibility of Lunar Eclipses.)

The altitude 'a' and azimuth 'A' of the Moon during any phase of an eclipse depends on the time and the observer's geographic coordinates. Neglecting the effects of atmospheric refraction and lunar parallax, 'a' and 'A' are calculated as follows:

             h  = 15 * (GST0 + t - ra ) + l
             a  =  ArcSin  [ Sin d Sin f + Cos d Cos h Cos f ]
             A  =  ArcTan  [ - (Cos d Sin h) / (Sin d Cos f -  Cos d Cos h Sin f) ]

     where:
             h  =  Hour Angle of the Moon (in degrees)
             a  =  Altitude (in degrees)
             A  =  Azimuth (in degrees)
          GST0  =  Greenwich Sidereal Time at 00:00 UT
             t  =  Universal Time
            ra  =  Right Ascension of the Moon (in hours)
             d  =  Declination of the Moon (in degrees)
             l  =  Observer's Longitude (East +, West -)
             f  =  Observer's Latitude (North +, South -)

For example, determine whether the Moon will be above the horizon at greatest eclipse during the total lunar eclipse of 2000 Jan 21 (catalog record from previous example) as seen from Washington DC. The geographic coordinates of Washington DC are:

                  Latitude:   f =  38°53´N  =   +38.9°
                 Longitude:   l = 077°02´W  =  -077.0°

From the catalog record, we have:

             Time of Greatest Eclipse:     t =  04:43 = 4.72
  Greenwich Sidereal Time at 00:00 UT:  GST0 =   8.0
          Right Ascension of the Moon:    ra =   8.17 
              Declination of the Moon:     d =  19.8

Thus:

    Hour Angle of the Moon:  h  = 15 * (GST0 + t - ra ) + l
                                = 15 * (8.0 + 4.72 - 8.17) + -077.0
                                = 15 * (4.55) -077.0
                             h  = -9°

    Altitude of Moon:   a = ArcSin [Sin d Sin f + Cos d Cos h Cos f]
                          = ArcSin [Sin(19.8) Sin(38.9) + Cos(19.8) Cos(-9) Cos(38.9)]
                          = ArcSin [0.339 * 0.628 + 0.941 * 0.988 * 0.778]
                          = ArcSin [0.213 + 0.723]
                          = ArcSin [0.936]
                          = 69°

With an altitude of 69°, the Moon will indeed be visible at greatest eclipse during the total lunar eclipse of 2000 Jan 21 as seen from Washington DC.

The expression for the Moon's azimuth contains the trigonometric function ArcTan. The ArcTan function results in an angle between -90° and +90°, with an ambiguity of + or - 180°. If the desired calculation has the form A = ArcTan [ x / y], then the ambiguity can be resolved using a simple test: if the denominator y is negative, then add 180° to the final answer.

In our current example the azimuth of the Moon is then:

 
   Azimuth of Moon:  A = ArcTan [-(Cos d Sin h)/(Sin d Cos f - Cos d Cos h Sin f)]
                       = ArcTan [-(Cos(19.8) Sin(-9))/(Sin(19.8) Cos(38.9) - Cos(19.8) Cos(-9) Sin(38.9))]
                       = ArcTan [-(0.941 * -0.156) / ((0.339 * 0.778) - (0.941 * 0.988 * 0.628))]
                       = ArcTan [-(-0.147) / ((0.264) - (0.584))]
                       = ArcTan [ +0.147 / (-0.320)]
                       = ArcTan [ -0.459 ]
                       = -24.7°

Since the denominator in ArcTan [ +0.147 / (-0.320)] is negative, we must add 180° to the final answer:

                     A = -24.7° + 180°
                     A = 155.3°

This places the Moon in the southeast at greatest eclipse during the total lunar eclipse of 2000 Jan 21 as seen from Washington DC.

Calendar Dates

The Julian calendar is used for all dates up to 1582 Oct 04. After that date, the Gregorian calendar is used. Due to the Gregorian Calendar reform, the day after 1582 Oct 04 (Julian calendar) is 1582 Oct 15 (Gregorian calendar). Note that Great Britian did not adopt the Gregorian calendar until 1752. For more information, see Calendars.

The Julian calendar does not include the year 0, so the year 1 BCE is followed by the year 1 CE. This is awkward for arithmetic calculations. In this catalog, dates are counted using the astronomical numbering system which recognizes the year 0. Historians should note the numerical difference of one year between astronomical dates and BCE dates. Thus, the year 0 corresponds to 1 BCE, and year -100 corresponds to 101 BCE, etc.. (See: Year Dating Conventions )

There is some historical uncertainty as to which years from 43 BCE to 8 CE were counted as leap years. For the purposes of this catalog, we will assume that all Julian years divisible by 4 will be counted as leap years.

Lunar Eclipse Predictions

Eclipse predictions presented here are based on j=2 ephemerides for the Sun (Newcomb, 1895) and Moon (Brown, 1919, and Eckert, Jones and Clark, 1954). A revised value used for the Moon's secular acceleration is n-dot = -26 arc-sec/cy*cy, as deduced by Morrison and Ward (1975) from 250 years of Mercury transit observations. The diameter of the umbral shadow was enlarged by 2% to compensate for Earth's atmosphere and the effects of oblateness have been included.

The largest uncertainty in the time of eclipse predictions in the distant past or future is caused by fluctuations in Earth's rotation due primarily to tidal friction of the Moon. The resultant drift in apparent clock time is expressed as delta-T. The value for delta-T was determined as follows:

pre-1600: delta T was calculated from empirical fits to historical records derived by Stephenson (1997)
1600-present: delta T was obtained from published observations
future: delta-T was extrapolated from current values and a model of tidal effects

Acknowledgments

All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy. Some of the information presented in these tables is based on data originally published in Fifty Year Canon of Lunar Eclipses: 1986 - 2035.

Permission is freely granted to reproduce this data when accompanied by an acknowledgment:

"Eclipse Predictions by Fred Espenak, NASA/GSFC"