Five Millennium Canon of Lunar Eclipses:

–1999 to +3000 (2000 BCE to 3000 CE)

NASA/TP–2009–214172

January 2009

Fred Espenak and Jean Meeus
 

COVER CAPTION:

Basic lunar eclipse geometry is illustrated in this figure from “New Astronomy” by David Todd (1906).

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NASA/TP–2009–214172

Five Millennium Canon of Lunar Eclipses:

–1999 to +3000 (2000 BCE to 3000 CE)

January 2009

Fred Espenak

NASA Goddard Space Flight Center, Greenbelt, Maryland

Jean Meeus (Retired)

Kortenberg, Belgium

National Aeronautics and 

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771
Available from:

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TABLE OF CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Section 1: Figures and Predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Section 2: Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Section 3: Lunar Eclipse Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Section 4: Eclipses and the Moon’s Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Section 5: Lunar Eclipse Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Acronyms and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) iii

TABLE OF CONTENTS

PREFACE

PREFACE

Theodor von Oppolzer’s 1887 Canon der Finsternisse (Canon of Eclipses) stands as one of the greatest accomplishments 

in computational astronomy of the nineteenth century. It contains the elements of all 8000 solar eclipses and 5200 lunar 

eclipses occurring between the years –1207 and +2161, together with maps showing the approximate positions of the 

central lines of total, annular and hybrid solar eclipses.

To make this remarkable achievement possible, a number of approximations were used in the calculations and maps. Furthermore, the 19th century ephemerides for the Sun and Moon, which are critical to eclipse predictions, cannot compare to 

the accuracy and precision of modern ephemerides. Finally, the 1887 canon did not take into account the shifts in latitude 

and timing of ancient eclipses due to Earth’s variable rotation rate and the secular acceleration of the Moon.

Nevertheless, von Oppolzer’s canon remained the seminal reference on predictions of eclipses until well into the 20th 

century. With the arrival of the electronic computer, the time was ripe to produce updated solar

a and lunar eclipse canons. In 1979, Meeus and Mucke published Canon of Lunar Eclipses: –2002 to +2526 containing the Besselian elements 

of 10,936 lunar eclipses. It was intended mainly for historical research and served as the modern day successor of von 

Oppolzer’s great canon.

The Meeus-Mucke work also contains data on penumbral eclipses that are not included in von Oppolzer’s canon. Neither 

of these publications offers diagrams or maps to illustrate the geometry or visibility of each eclipse. Espenak’s Fifty Year 

Canon of Lunar Eclipses (1989) includes individual Moon-shadow geometry diagrams and eclipse visibility maps of all 

lunar eclipses, but it covers a relatively short period from +1986 to +2035.

Both of these recent lunar eclipse canons are based on Newcomb’s Tables of the Sun (1895) and Brown’s lunar theory 

(1905), subject to later modifications in the Improved Lunar Ephemeris (1954). These were the best ephemerides of their

day but they have since been superseded.

The Canon of Lunar Eclipses 1500 B.C.–A.D. 3000 (Liu and Fiala, 1992) uses modern theories of the Sun and the Moon

prepared by the Bureau des Longitudes of Paris. However, it does not contain individual eclipse geometry diagrams or 

maps. Instead, it offers a series of map templates to approximate the geographic regions of eclipse visibility, and an optional computer program do generate these figures for any eclipse in the Canon.

The present publication is the first to offer eclipse geometry diagrams and visibility maps for every lunar eclipse (12,064 

eclipses) over a period covering five thousand years from –1999 to +3000. The following points highlight the features and 

characteristics of this work.

• based on modern theories of the Sun and the Moon constructed at the Bureau des Longitudes of Paris rather than 

the older Newcomb and Brown ephemerides

• ephemerides and eclipse predictions performed in Terrestrial Dynamical Time

• covers historical period of eclipses as well as one millennium into the future

• diagrams for each eclipse depict the Moon’s path through Earth’s penumbral and umbral shadows 

a. Several new solar eclipse canons were published in the second half of the 20th century. Meeus, Grosjean, and Vanderleen 

published Canon of Solar Eclipses(1966) containing the Besselian elements of allsolar eclipsesfrom +1898 to +2510, together 

with central line tables and maps. The aim of this work was principally to provide data on future eclipses. The Mucke and 

Meeus work Canon of Solar Eclipses: –2003 to +2526 (1983) was intended mainly for historical research and served as a 

modern day successor of von Oppolzer’s great canon. Espenak’s Fifty Year Canon of Solar Eclipses (1987) includesindividual 

detailed maps and central path data for all solar eclipses from +1986 to +2035. Finally, the Espenak and Meeus work Five 

Millennium Canon of Solar Eclipses: –1999 to +3000 (2006) contains individual maps of every solar eclipse and uses modern 

ephemerides of the Sun and Moon.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) v

PREFACE
• world maps identify geographic regions of visibility for each phase of every eclipse

• visibility maps are based of the most current determination of the historical values of ∆T

• estimates of eclipse visibility map accuracy based on the uncertainty in the value of ∆T (i.e., standard error in ∆T)

A primary goal of this work is to assist historians and archeologists in the identification and dating of eclipses found in 

references and recordsfrom antiquity. For example, an ancient mechanical calculator known asthe Antikythera mechanism

was apparently designed to calculate eclipses and other astronomical phenomena (Freeth, et. al., 2008). The decoding of 

this device was possible in part by comparing its combination of wheel positions with the dates of lunar eclipses.

Correlating historical records with specific eclipses is no easy task since there are usually several possible candidates. Accurate visibility maps using the best available values of ∆T coupled with estimates in the standard error of ∆T are critical 

in discriminating among potential eclipses candidates. Ultimately, historical eclipse identification can lead to improved 

chronologies in the time line of a particular culture.

The maps can also be used to quickly estimate the approximate circumstances for any geographic location during each 

eclipse without any calculations. The position of the moonrise and moonset curves for each eclipse contact show which 

eclipse phases can be seen from any location.

The Canon will also be of value to educators, planetariums, and anyone interested in knowing when and where past and 

future eclipses occur. The general public is fascinated by eclipses—with each major eclipse, the question always arises 

as to when a particular location experienced its last and next eclipses. The maps presented here are ideally suited to addressing such queries.

—Fred Espenak and Jean Meeus

2009 January

 vi FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

PREFACE
SECTION 1: FIGURES AND PREDICTIONS

1.1 Introduction

Earth will experience 12,064 eclipses of the Moon during the 5000-year period from –1999 to +3000 (2000 BCE to 

3000 CEa ). An individual diagram and visibility map for every lunar eclipse over the five-millennium interval is presented 

in the Appendix. The Moon’s path through Earth’s penumbral and umbral shadows illustrates the eclipse geometry, and 

the accompanying equidistant cylindrical projectionb map shows the geographic region of visibility during every phase 

of each eclipse.

1.2 Explanation of Lunar Eclipse Figures

The figure for each eclipse consists of two diagrams. The top one depicts the Moon’s path through Earth’s penumbral and 

umbral shadows with Celestial North directed up. The Moon’s orbital motion is from west to east (right to left)

c with respect to the shadows. Each phase of the eclipse is defined by the instant when the Moon’s limb is externally or internally 

tangent to the penumbra or umbra as follows.

Penumbral lunar eclipses have two primary contacts. Neither of these events is observable.

P1—Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)

P4—Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)

Partial lunar eclipses have two additional contacts as the Moon’s limb enters and exits the umbral shadow (U1 and U4, 

respectively). At these two instants, the partial phase of the eclipse begins and ends.

P1—Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)

U1—Instant of first exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Begins)

U4—Instant of last exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Ends)

P4—Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)

Total lunar eclipses have two additional umbral contacts at the instants when the Moon’s entire disk is first and last internally

tangent to the umbra (U2 and U3, respectively). These are the times when the total phase of the eclipse begins and ends.

P1—Instant of first exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Begins)

U1— Instant of first exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Begins)

U2—Instant of first interior tangency of the Moon with the Umbra. (Total Umbral Eclipse Begins)

U3—Instant of last interior tangency of the Moon with the Umbra. (Total Umbral Eclipse Ends)

U4—Instant of last exterior tangency of the Moon with the Umbra. (Partial Umbral Eclipse Ends)

P4— Instant of last exterior tangency of the Moon with the Penumbra. (Penumbral Eclipse Ends)

The instant when the Moon passes closest to the shadow axis is known as the instant of greatest eclipse. This corresponds 

to the maximum phase of the eclipse, and the Moon’s position at this instant is also shown in the eclipse path diagrams.

a. The terms BCE and CE are abbreviations for “Before the Common Era” and “Common Era,” respectively. They are the 

secular equivalents to the BC and AD dating conventions. A major advantage of the BCE/CE convention is that both terms 

are suffixes, whereas BC and AD are used as a suffix and prefix, respectively. 

b. The equidistant cylindrical projection (also known asthe equirectangular projection) is a simple x-y Cartesian map projection

where lines of latitude and longitude are represented by straight, equally spaced horizontal and vertical lines.

c. By convention, maps are plotted north up, west to the left, and east to the right. This orientation assumes the viewer is looking down on Earth. But if the viewer turns around and looks up at the sky, the directions are reversed with east to the left 

and west to the right.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 1

FIGURES AND PREDICTIONS
The bottom diagram in each figure is an equidistant cylindrical projection map of Earth showing the geographic region of 

visibility at each phase of the eclipse. This is accomplished using a series of curves showing where Moonrise and Moonset 

occur at each eclipse contact. The map is also shaded to indicate eclipse visibility. The entire eclipse is visible from the 

zone with no shading. Conversely, none of the eclipse can be seen from the zone with the darkest shading.

At the instant of greatest eclipse, the Moon is deepest in Earth’s shadow. A vertical line running through the middle of the 

clear zone (complete eclipse visibility) of a map indicates the meridian, or line of longitude, that the Moon is then crossing.

An observer positioned somewhere on this line would then see the Moon at its highest point in the sky either due south 

or due north, depending on the observer’s latitude and the Moon’s declination. The geographic location where the Moon 

appears in the zenith at greatest eclipse is shown by a black dot on the meridian of greatest eclipse. All salient features of 

the eclipse figures are identified in Figure 1-1, which serves as the key to the figures in the Appendix.

Total 2008 Feb 21

Saros 133 03:27 TD 

Par. = 205m

Tot. = 50m

P.Mag. = 2.1451 

U.Mag. = 1.1062 

Gam. = -0.3992 

Figure 1-1. Key to Eclipse Figures

Type of Eclipse

(Penumbral, Partial, or Total)

Saros Series 

Calendar Date

Gregorian Calendar 

(Julian Calendar before 1582 Oct 14)

Greatest Eclipse

(Terrestrial Dynamical Time)

Umbral Eclipse Magnitude

(for Partial and Total Eclipses)

Gamma

P - Penumbral Eclipse Begins

U - Partial (umbral) Eclipse Begins

U - Total (umbral) Eclipse Begins

Penumbral Shadow

Moon in Zenith at Greatest Eclipse

Duration of Total Phase 

Duration of Partial Phase 

Penumbral Eclipse Magnitude

U - Total (umbral) Eclipse Ends

U - Partial (umbral) Eclipse Ends

P - Penumbral Eclipse Ends

G - Greatest Eclipse

P - Penumbral Eclipse Begins

U - Partial (umbral) Eclipse Begins

U - Total (umbral) Eclipse Begins

U - Total (umbral) Eclipse Ends

U - Partial (umbral) Eclipse Ends

P - Penumbral Eclipse Ends

Eclipse Phase During Moon Set

P - Penumbral Eclipse Begins

U - Partial (umbral) Eclipse Begins

U - Total (umbral) Eclipse Begins

U - Total (umbral) Eclipse Ends

U - Partial (umbral) Eclipse Ends

P - Penumbral Eclipse Ends

Eclipse Phase During Moon Rise

Moon on Mereidian at Greatest Eclipse

Umbral Shadow

Ecliptic

Celestial North

1

1

2

3

4

4

1

1

2

3

4

4

1

1

2

3

4

4

Data relevant to a lunar eclipse appear in the corners of each figure. To the top left, are the eclipse type (penumbral, partial, 

or total) and the Saros series of the eclipse. To the top right are the Gregorian calendar date (Julian calendar dates are used 

prior to 1582 Oct 14) and the time of greatest eclipse (Terrestrial Dynamical Time). The lower left corner lists the duration of the major phases of the eclipse in minutes. Depending on the eclipse type, the duration of the penumbral (P4 – P1),

partial (U4 – U1), or total (U3 – U2) phases are given. Beneath the eclipse durations is the quantity gamma—the minimum 

distance of the Moon’s center from the axis of Earth’s penumbral and umbral shadow cones (in Earth equatorial radii) at 

the instant of greatest eclipse. The umbral and penumbral eclipse magnitudes

a

 are given to the lower right.

A detailed explanation of the data in the lunar eclipse figures appears in the following sections.

a. The eclipse magnitude is defined as the fraction of the Moon’s diameter immersed in either Earth’s penumbral or umbral 

shadows. It is a unit less parameter given at the instant of greatest eclipse.

 2 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
1.2.1 Lunar Eclipse Type

There are three basic types of lunar eclipses: 

1) Penumbral—Moon traverses through Earth’s penumbral shadow (Moon is partly or completely within the 

penumbra)

2) Partial—Part of the Moon traverses through Earth’s umbral shadow (Moon is partly within the umbra)

3) Total—Entire Moon traverses through Earth’s umbral shadow (Moon is completely within the umbra)

It is also possible for a penumbral eclipse to occur in which the Moon’s entire disk is enveloped within the penumbra. Such 

events are called total penumbral eclipses. They are indicated by “(T)” after the penumbral eclipse type [i.e., Penumbral

(T)].

With regard to total (umbral) lunar eclipses, most are non-central in that the Moon’s disk misses the central axis of the 

umbral shadow cone. If a total eclipse is central, it is indicated by a “+” or “–” after the eclipse type, depending on whether 

the Moon’s center passes north or south of the shadow axis (e.g., Total +).

1.2.2 Saros Series Number

Each lunar eclipse belongs to a Saros series (Sect. 5.3) using a numbering system first introduced by van den Bergh (1955). 

This system has been expanded to include negative values from the past, as well as additional series in the future. The 

eclipses with an odd Saros number take place at the descending node of the Moon’s orbit, while those with an even Saros 

number take place at the ascending node.

The Saros is a period of 223 synodic months (~18 years, 11 days, and 8 hours). Eclipses separated by this interval belong 

to the same Saros series and share similar geometry and characteristics.

1.2.3 Calendar Date

All eclipse dates from 1582 Oct 15 onwards use the modern Gregorian calendar currently found throughout most of the 

world. The older Julian calendar is used for eclipse dates prior to 1582 Oct 04. Because of the Gregorian Calendar Reform, 

the day following 1582 Oct 04 (Julian calendar) is 1582 Oct 15 (Gregorian calendar).

Pope Gregory XIII decreed the use of the Gregorian calendar in 1582 in order to correct a problem in a drift of the seasons.

It adopts the convention of a year containing 365 days. Every fourth year is a leap year of 366 days if it is divisible by 4 

(e.g., 2004, 2008, etc.). However, whole century years (e.g., 1700, 1800, 1900) are excluded from the leap year rule unless 

they are also divisible by 400 (e.g., 2000). This dating scheme was designed to keep the vernal equinox on, or within a 

day of, March 21.

Prior to the Gregorian Calendar Reform of 1582, the Julian calendar was in wide use. It was less complicated than the 

Gregorian calendar in that all years divisible by 4 were counted as 366-day leap years, but this simplicity came at a cost.

After more than 16 centuries of use, the Julian calendar date of the vernal equinox had drifted 11 days from March 21. It

was this failure in the Julian calendar that prompted the Gregorian Calendar Reform.

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 dating calculations. In this publication, 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 astronomical year 0 corresponds to 1 BCE, and the astronomical year –100 corresponds to 101 BCE, etc.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 3

FIGURES AND PREDICTIONS
There are a number of ways to write the calendar date through variations in the order of day, month, and year. The International Organization for Standardization’s (ISO) 8601 advises a numeric date representation, which organizes the 

elements from the largest to the smallest. The exact format is YYYY-MM-DD where YYYY is the calendar year, MM is 

the month of the year between 01 (January) and 12 (December), and DD is the day of the month between 01 and 31. For 

example, the 27th day of April in the year 1943 would then be expressed as 1943-04-27. The authors of this report support 

the ISO convention, but have replaced the month number with the three-letter English abbreviation of the month name for 

additional clarity. From the previous example, the date is expressed as 1943 Apr 27.

1.2.4 Greatest Eclipse

The instant of greatest eclipse occurs when the distance between the center of the Moon and the axis or Earth’s umbral 

shadow cone reaches a minimum. Because of Earth’s flattening, the instant of greatest eclipse differs slightly from the 

instant of greatest magnitude. In practice, Earth’s atmosphere diffuses the edges of the penumbral and umbral shadows 

such that the difference between greatest eclipse and greatest magnitude cannot be distinguished observationally.

Lunar eclipses occur when the Moon is near one of the nodes of its orbit and, therefore, moving at an angle of about 5° to 

the ecliptic. Hence, unless the eclipse is perfectly central, the instant of greatest eclipse does not coincide with that of apparent ecliptic conjunction with Earth’s shadow (i.e., Full Moon), nor with the time of conjunction in Right Ascension.

Greatest eclipse is given in Terrestrial Dynamical Time or TD (Sect. 2.3), which is a time system based on International

Atomic Time. As such, TD is the atomic time equivalent to its predecessor Ephemeris Time (Sect. 2.2) and is used in the 

theories of motion for bodies in the solar system. To determine the geographic visibility of an eclipse, TD is converted to

Universal Time (Sect. 2.4) using the parameter ∆T (Sects. 2.6 and 2.7). 

1.2.5 Duration of Eclipse Phases

The duration of a penumbral eclipse “Pen.” is the time between first and last external tangencies of the Moon with the 

penumbral shadow (i.e., P4 – P1). Similarly, the duration of a partial eclipse “Par.” is the time between first and last external 

tangencies of the Moon with the umbral shadow (i.e., U4 – U1). Finally, the duration of a total eclipse “Tot.” is the time 

between first and last internal tangencies of the Moon with the umbral shadow (i.e., U3 – U2).

The duration given for each eclipse phase is rounded to the nearest minute.

1.2.6 Gamma

The quantity gamma is the minimum distance from the center of the Moon to the axis of Earth’s umbral shadow cone, in 

units of Earth’s equatorial radius. This distance is positive or negative, depending on whether the Moon passes north or 

south of the shadow cone axis.

The change in the value of gamma after one Saros period is larger when Earth is near aphelion (June–July) than when it is 

near perihelion (December–January). Table 1-1 illustrates this point using eclipses from Saros series 129 (near aphelion—

table on left) and Saros series 134 (near perihelion—table on right).

 4 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
Table 1-1. Variation in Gamma at Aphelion vs. Perihelion

Date Gamma ∆ Gamma Date Gamma ∆ Gamma

1928 Jun 03 –0.3175 1928 Nov 27 0.3952

1946 Jun 14 –0.2324 0.0851 1946 Dec 08 0.3864 –0.0088

1964 Jun 25 –0.1461 0.0863 1964 Dec 19 0.3801 –0.0063

1982 Jul 06 –0.0579 0.0882 1982 Dec 30 0.3758 –0.0043

2000 Jul 16 0.0302 0.0881 2001 Jan 09 0.3720 –0.0038

2018 Jul 27 0.1168 0.0866 2019 Jan 21 0.3684 –0.0036

2036 Aug 07 0.2004 0.0836 2037 Jan 31 0.3619 –0.0065

2054 Aug 18 0.2806 0.0802 2055 Feb 11 0.3526 –0.0093

A similar situation exists in the case of solar eclipses. The explanation can be found in van den Bergh (1955).

1.2.7 Eclipse Magnitude

The eclipse magnitude is defined as the fraction of the Moon’s diameter immersed in Earth’s shadows. Because there 

are two shadows—penumbral and umbral—there are two corresponding eclipse magnitudes. The eclipse magnitudes 

appearing in the figures are given at the instant of greatest eclipse when the Moon passes closest to the axis of the two 

shadow cones.

The penumbral eclipse magnitude of penumbral eclipses in this Canon of Lunar Eclipses (hereafter referred to as the 

Canon) ranges from 0.0004 to 1.0858 (Sect. 3.5). For most penumbral eclipses, the penumbral magnitude is less than 1 

meaning only a fraction of the Moon’s disk enters the penumbra. When the penumbral magnitude is greater than or equal 

to 1.0, the Moon’s entire disk is immersed in the penumbra and the event is termed a total penumbral eclipse (Sect. 3.11).

It should be noted that penumbral eclipses are subtle events (Sect. 1.7.1). In fact, they cannot be detected visually—with 

or without optical aid—unless the eclipse magnitude is greater than ~0.6. The umbral eclipse magnitude of a penumbral 

eclipse is always negative. It is a measure of the distance of the Moon’s limb to the edge of the umbral shadow in units of 

the Moon’s diameter.

During a partial lunar eclipse, some fraction of the Moon’s disk enters the umbral shadow. The umbral magnitude for 

partial eclipses in the Canon ranges from 0.0001 to 0.9998 (Sect. 3.6). The Moon also passes through the penumbra during 

a partial eclipse so the penumbral magnitude is usually greater than 1.

In the case of a total lunar eclipse, the Moon’s entire disk passes through Earth’s umbral shadow. During totality, the Moon 

can take on a range of colors from bright orange, to deep red, dark brown, or even very dark grey (Sect. 1.7.2). The only 

light reaching the Moon at this time is heavily filtered and attenuated by Earth’s atmosphere. The umbral magnitude for 

total eclipses in the Canon ranges from 1.0001 to 1.8821 (Sect. 3.7).

1.2.8 Additional Elements

Two additional parameters are listed at the bottom of each page of the Appendix. The first element is ∆T (Sect. 2.6). It is 

the arithmetic difference between TD (Sect. 2.3) and Universal Time (Sect. 2.4). The value given is specific to the first 

eclipse on the page. To the right of ∆T is its corresponding standard error. This is the estimated uncertainty in ∆T (Sect. 

2.8) and is given both in seconds, and in the equivalent shift in longitude east or west.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 5

FIGURES AND PREDICTIONS
1.3 Solar and Lunar Coordinates

The coordinates of the Moon used in the eclipse predictions have been calculated on the basis of the VSOP87 theory constructed by Bretagnon and Francou (1988) at the Bureau des Longitudes, Paris. This theory gives the ecliptic longitude and 

latitude of each planet, and its radius vector, as sums of periodic terms. In the calculations presented here, the complete 

set of periodic terms of version Da of VSOP87 were used.

For the Moon, use has been made of the theory ELP-2000/82 of Chapront-Touzé and Chapront (1983), again of the Bureau 

des Longitudes. This theory contains a total of 37,862 periodic terms, namely 20,560 for the Moon’s longitude, 7,684 for 

the latitude, and 9,618 for the distance to Earth. However, many of these terms are very small: some have an amplitude of 

only 0.00001 arcsec for the longitude or the latitude, and of just 2 cm for the distance. In the computer program used for 

the Canon, all periodic terms were neglected with coefficients smaller than 0.0005 arcsec in longitude and latitude, and

smaller than 1 m in distance. Because of neglecting the very small periodic terms, the Moon’s positions calculated in the 

program have a mean error (as compared to the full ELP theory) of about 0.0006 s of time in right ascension, and about 

0.006 arcsec in declination. The corresponding error in the calculated times of the contacts of a lunar eclipse is of the order 

of 1/40 s, which is much smaller than the uncertainties in predicted values of ∆T, and several orders of magnitude smaller 

than the uncertainty due to the diffuse edge of Earth’s shadows caused by the terrestrial atmosphere.

Improved expressionsfor the mean arguments L ́, D, M, M ́, and F were taken from Chapront, Chapront-Touzé, and Francou

(2002). A major consequence of this work is to bring the secular acceleration of the Moon’s longitude (–25.858 arcsec/cy2, 

where arcsec/cy2 is arc seconds per Julian century squaredb) into good agreement with Lunar Laser Ranging (LLR) observations from 1972 to 2001 (Sect. 1.4).

A fundamental parameter used in eclipse predictions is the Moon’s radius k expressed in units of Earth’s equatorial radius. The Moon’s actual radius varies as a function of position angle and libration because of irregularities in the surface

topography of the Moon and the projection of these features along the line of sight onto the lunar limb profile. The current 

work uses a value for the lunar radius of k=0.2724880 representing a mean over the Moon’s topographic features. This is 

the same value used for partial solar eclipses in the Five Millennium Canon of Solar Eclipses: –1999 to +3000 (Espenak

and Meeus, 2006).

The center of figure of the Moon does not coincide exactly with its center of mass. The magnitude of this difference is 

~0.5 arcsec and is much smaller than the uncertainty in the edges of the penumbral and umbral shadows because of diffusion by Earth’s atmosphere (Sect. 1.5). Thus, the difference between center-of-figure and center-of-mass positions has 

no practical impact on the present work.

1.4 Secular Acceleration of the Moon

Ocean tides are caused by the gravitational pull of the Moon (and, to a lesser extent, the Sun). The resulting tidal bulge in 

Earth’s oceans is pulled ahead of the Moon in its orbit because of the daily rotation of Earth. As a consequence, the ocean 

mass offset from the Earth–Moon line exerts a pull on the Moon and accelerates it in its orbit. Conversely, the Moon’s 

gravitational tug on this mass exerts a torque that decelerates the rotation of Earth. The length of the day gradually increases as energy is transferred from Earth to the Moon, causing the lunar orbit and period of revolution about Earth to 

increase.

This secular acceleration of the Moon is small, but it has a cumulative effect on the lunar position when extrapolated over 

many centuries. Direct measurements of the acceleration have only been possible since 1969 using the Apollo retro-reflectors

left on the Moon. The results from LLR show that the Moon’s mean distance from Earth is increasing by 3.8 cm per year 

(Dickey, et al., 1994). The corresponding acceleration in the Moon’s ecliptic longitude is –25.858 arcsec/cy2 (Chapront, 

Chapront-Touzé, and Francou, 2002). This is the value adopted here in the lunar ephemeris calculations.

a. Version D of VSOP87 gives solar (and planetary) positions referred to the mean equinox of the date.

b. This unit, arcsec/cy2, is used in discussing secular changes in the Moon’s longitude over long time intervals.

 6 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
There is a close correlation between the Moon’s secular acceleration and changes in the length of the day. The relationship, 

however, is not exact because the lunar orbit is inclined anywhere from about 18.5° to 28.5° to Earth’s equator. The parameter ∆T (Sects. 2.6 and 2.7) is a measure of the accumulated difference in time between an ideal clock and one based on 

Earth’s rotation as it gradually slows down. Published determinations of ∆T from historical eclipse records have assumed 

a secular acceleration of –26 arcsec/cy2 (Morrison and Stephenson, 2004). Because a slightly different value for the secular 

acceleration has been adopted, a small correction “c” has to be made to the published values of ∆T as follows:

c = –0.91072 (–25.858 + 26.0 ) u2, (1–1)

where u = (year –1955)/100.

Then

 ∆T (corrected) = ∆T + c. (1–2)

Evaluation of the correction at 1,000-year intervals over the period of the Canon is found in Table 1–2.

Table 1-2. Corrections to ∆T Caused by Secular Acceleration

Year Correction (Seconds)

–2000 –202

–1000 –113

0 –49

1000 –12

2000 0

3000 –14

The correction is only important for negative years, although it is significantly smaller than the actual uncertainty in ∆T 

itself (Sect. 2.8).

The secular acceleration of the Moon is poorly known and may not be constant. Careful records for its derivation only go 

back about a century. Before then, spurious and often incomplete eclipse and occultation observations from medieval and 

ancient manuscripts comprise the database. In any case, the current value implies an increase in the length of day (LOD) 

of about 2.3 milliseconds per century. Such a small amount may seem insignificant, but it has very measurable cumulative 

effects. At this rate, time—as measured through Earth’s rotation—is losing about 84 seconds per century squared when 

compared to atomic time.

1.5 Enlargement of Earth’s Shadows

In the early 1700s, Philippe de La Hire made a curious observation about Earth’s umbra. The predicted radius of the 

shadow needed to be enlarged by about 1/41 in order to fit timings made during a lunar eclipse (La Hire 1707). Additional 

observations over the next two centuries revealed that the shadow enlargement was somewhat variable from one eclipse 

to the next. According to Chauvenet (1891):

“This fractional increase of the breath of the shadow was given by Lambert as 1/40, and by Mayer as 1/60. Beer and 

Maedler found 1/50 from a number of observations of eclipses of lunar spots in the very favorable eclipse of December 

26, 1833.”

Chauvenet adopted a value of 1/50, which has become the standard enlargement factor for lunar eclipse predictions published by many national institutes worldwide. The enlargement enters into the definitions of the penumbral and umbral 

shadow radii as follows.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 7

FIGURES AND PREDICTIONS
penumbral radius: Rp = 1.02 * (0.998340 * Pm + Ss + Ps) (1–3)

umbral radius: Ru = 1.02 * (0.998340 * Pm - Ss + Ps) (1–4)

where: Pm = Equatorial horizontal parallax of the Moon,

Ss = Geocentric semi-diameter of the Sun, and

Ps = Equatorial horizontal parallax of the Sun.

The factor 1.02 is the enlargement of the shadows by 1/50. Earth’s true figure approximates that of an oblate ellipsoid with 

a flattening of ~1/300. Furthermore, the axial tilt of the planet towards or away from the Sun throughout the year means the 

shape of the penumbral and umbral shadows vary although the effect is small. It is sufficient to use a mean radius of Earth 

at latitude 45° to approximate the departure from perfectly circular shadows. The Astronomical Almanaca uses a factor of

0.998340 to scale the Moon’s equatorial horizontal parallax to account for this (i.e., 0.998340 ~ 1 – 0.5 * 1/300).

In an analysis of 57 eclipses covering a period of 150 years, Link (1969) found a mean shadow enlargement of 2.3%.

Furthermore, timings of crater entrances and exits through the umbra during four lunar eclipses from 1972 to 1982 (Table 

1-3) closely support the Chauvenet value of 2%. From a physical point of view, there is no abrupt boundary between the 

umbra and penumbra. The shadow density actually varies continuously as a function of radial distance from the central 

axis out to the extreme edge of the penumbra. However, the density variation is most rapid near the theoretical edge of the 

umbra. Kuhl's (1928) contrast theory demonstrates that the edge of the umbra is perceived at the point of inflexion in the

shadow density. This point appears to be equivalent to a layer in Earth's atmosphere at an altitude of about 120 to 150 km.

The net enlargement of Earth's radius of 1.9% to 2.4% corresponds to an umbral shadow enlargement of 1.5% to 1.9%, in 

reasonably good agreement with the conventional value.

Table 1-3. Umbral Shadow Enlargement from Craters Timings

Lunar Eclipse 

Date

Crater Entrances

% Enlargement

Crater Exits

% Enlargement

Sky & Telescope

Reference

1972 Jan 30 1.69 [420] 1.68 [295] Oct 1972, p.264

1975 May 24 1.79 [332] 1.61 [232] Oct 1975, p.219

1982 Jul 05 2.02 [538] 2.24 [159] Dec 1982, p.618

1982 Dec 30 1.74 [298] 1.74 [ 90] Apr 1983, p.387

Note: Values in “[ ]” are the number of observations included in each shadow enlargement measurement.

Some authorities dispute Chauvenet’s shadow enlargement convention. Danjon (1951) notes that the only reasonable way 

of accounting for a layer of opaque air surrounding Earth is to increase the planet's radius by the altitude of the layer.

This can be accomplished by proportionally increasing the parallax of the Moon. The radii of the umbral and penumbral 

shadows are then subject to the same absolute correction and not the same relative correction employed in the traditional 

Chauvenet 1/50 convention. Danjon estimates the thickness of the occulting layer to be 75 km and this results in an enlargement of Earth's radius and the Moon's parallax of about 1/85.

Since 1951, the French almanac Connaissance des Temps has adopted Danjon's method for the enlargement Earth'sshadows

in their eclipse predictions as shown below.

penumbral radius: Rp = 1.01 * Pm + Ss + Ps (1–5)

umbral radius: Ru = 1.01 * Pm - Ss + Ps (1–6)

a. The Astronomical Almanac is published annually by the Almanac Office of the U.S. Naval Observatory.

 8 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
 where: Pm = Equatorial horizontal parallax of the Moon,

Ss = Geocentric semi-diameter of the Sun,

Ps = Equatorial horizontal parallax of the Sun, and

1.01 ≈ 1 + 1/85 – 1/594.

The factor 1.01 combines the 1/85 shadow enlargement term with a 1/594 terma to correct for Earth’s oblateness at a 

latitude of 45°.

Danjon’s method correctly modelsthe geometric relationship between an enlargement of Earth’sradius and the corresponding increase in the size of its shadows. Meeus and Mucke (1979) and Espenak (2006) both use Danjon's method. However, 

the resulting umbral and penumbral eclipse magnitudes are smaller by approximately 0.006 and 0.026, respectively, as 

compared to predictions using the traditional Chauvenet convention of 1/50.

For instance, the umbral magnitude of the partial lunar eclipse of 2008 Aug 16 was 0.813 according to the Astronomical Almanac (2008) using Chauvenet’s method, but only 0.806 according to Meeus and Mucke (1979) using Danjon's method.

Of course, the small magnitude difference between the two methods is difficult to observe because the edge of the umbral 

shadow is poorly defined. The choice of shadow enlargement method has the largest effect in certain limiting cases where 

a small change in magnitude can shift an eclipse from one type to another. For example, an eclipse that is barely total 

according to Chauvenet’s method will be a large magnitude partial eclipse if calculated using Danjon's method. Table 

1–4 shows five such instances where a shallow total eclipse calculated with Chauvenet’s method becomes a deep partial 

eclipse with Danjon’s.

Table 1-4. Total (Chauvenet) vs. Partial (Danjon) Lunar Eclipses: 1501–3000

Calendar Date Umbral Magnitude 

(Chauvenet)

Umbral Magnitude 

(Danjon)

Magnitude 

Difference

1540 Sep 16 1.0007 0.9947 0.0060

1856 Oct 13 1.0017 0.9960 0.0057

2196 Jul 10 1.0007 0.9960 0.0047

2413 Nov 08 1.0042 0.9993 0.0049

2669 Feb 08 1.0016 0.9951 0.0065

Similarly, small umbral magnitude partial eclipses using Chauvenet’s method must be reclassified as penumbral eclipses 

of large penumbral magnitude when calculated with Danjon’s method. A recent example was the eclipse of 1988 Mar 

03, which was partial with an umbral magnitude of 0.0028 according to Chauvenet’s method, but was penumbral with 

an umbral magnitude –0.0017b by Danjon’s method. A similar case will occur on 2042 Sep 29. For a list of all such cases 

from 1501 through 3000, see Table 1-5.

a. Connaissance des Temps uses a value of 1/297 for Earth’s flattening. At latitude 45°: 1/594 = 0.5 * 1/297.

b. A negative umbral magnitude means that the Moon lies completely outside the umbral shadow and is, therefore, a penumbral 

eclipse

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 9

FIGURES AND PREDICTIONS
Table 1-5. Partial (Chauvenet) vs. Penumbral (Danjon) Lunar Eclipses: 1501–3000

Calendar 

Date

Umbral Magnitude 

(Chauvenet)

Umbral 

Magnitude 

(Danjon)

Magnitude 

Difference

1513 Sep 15 0.0036 –0.0003 0.0039

1900 Jun 13 0.0012 –0.0040 0.0052

1988 Mar 03 0.0028 –0.0017 0.0045

2042 Sep 29 0.0027 –0.0031 0.0058

2429 Dec 11 0.0020 –0.0033 0.0053

2581 Oct 13 0.0017 –0.0054 0.0071

2678 Aug 24 0.0007 –0.0036 0.0043

2733 Aug 17 0.0037 –0.0040 0.0077

Finally, in some cases, the shadow enlargement convention can make the difference between a shallow penumbral eclipse 

(Chauvenet) or no eclipse at all (Danjon). Table 1–6 lists nine small magnitude penumbral eclipses over a 500-year interval 

as determined using Chauvenet’s method (Liu and Fiala, 1992). When the eclipse predictions are repeated using Danjon’s 

method, no lunar eclipses are found on these dates.

Table 1-6. Penumbral Lunar Eclipses (Chauvenet): 1801–2300

Calendar Date

Penumbral 

Magnitude 

(Chauvenet)

1864 Apr 22 0.0237

1872 Jun 21 0.0008

1882 Oct 26 0.0059

1951 Feb 21 0.0068

2016 Aug 18 0.0165

2042 Oct 28 0.0077

2194 Mar 07 0.0085

2219 Apr 30 0.0008

2288 Feb 18 0.0204

Practically speaking, the faint and indistinct edge of the penumbral shadow makes the penumbral eclipse contacts (P1

and P4) completely unobservable. So the small magnitude differences discussed here are only of academic interest. Still, 

it is important to note which shadow enlargement convention is used because it is critical in comparing predictions from 

different sources.

In the Canon, Earth’s penumbral and umbral shadow sizes have been calculated by using Danjon’s enlargement method.

Other sources using Danjon’s method include Meeus and Mucke (1979), Espenak (2006) and Connaissance des Temps.

Several sources using Chauvenet’s method are Espenak (1989), Liu and Fiala (1992), and Astronomical Almanac.

1.6 Map Accuracy

The accuracy of the eclipse maps depends principally on two factors. The first is the rigorousness of the solar and lunar 

ephemerides used in the calculations (Sect. 1.3). The Moon’s close proximity to Earth coupled with its relatively low mass, 

results in orbital perturbations that make the Moon’s position far more difficult to predict compared to the Sun’s position. 

 10 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
Nevertheless, the lunar ephemeris is accurate to better than an arc second within several centuries of the present. Even 

for eclipses occurring in the year –1999 (2000 BCE), the Moon’s position is correct to within a small fraction of a degree.

Such positional discrepancies correspond to errors in predicted eclipse paths that are below the resolution threshold of 

the figures presented in the Canon.

A far greater source of error in the geographic zones of eclipse visibility is due to the uncertainty in ∆T (Sect. 2.6). This 

parameter is the arithmetic difference between TD (Sect. 2.3) and Universal Time or UT (Sect. 2.4). TD can be thought 

of as time measured with an idealized or perfect clock. In contrast, UT is based on Earth’s rotation, which is gradually 

slowing down. TD is used to calculate solar system ephemerides and eclipse predictions, but UT is used for defining world 

time and longitudes.

Earth was rotating faster in the past so eclipse predictions generated in TD must first be converted to UT (via ∆T) before 

the geographic zones of eclipse visibility can be determined. In other words, the physical impact of ∆T on eclipse predictions is to shift the visibility zones east relative to the position calculated from TD. Because 1° in longitude corresponds 

to 4 min of time, a ∆T value of 240 s would shift the visibility zones 1° east of their TD positions. The maps in the Canon 

already include the ∆T translation of visibility zones from TD to UT; thus, they depict the actual geographic regions of 

visibility of each eclipse.

The problem with ∆T is that it is an observationally determined quantity. In the distant past or future, the value of ∆T 

must be estimated from historical trends. The further removed such evaluations are from actual measurements, the greater 

the uncertainty in the extrapolated value of ∆T. Small deviations can quickly propagate into large uncertainties over the 

course of 1,000 years.

At the bottom of each appendix page is the value of ∆T and its corresponding standard error. This is an estimate of the 

uncertainty in the longitude determination of each map. For years in which the standard error is greater than 480 s (2.0° 

in longitude), the maps include an uncertainty zone to graphically depict the longitudinal range of solutions within the 

standard error. The years prior to –630 and after +2428 have standard errors of this magnitude or greater.

The meridian representing the nominal value of ∆T is plotted as a line of longitude running vertically through each map 

in the center of the zone of visibility. The uncertainty zones then take the form of two dashed meridians of longitude east 

and west of the nominal ∆T meridian. They indicate the range of uncertainty in the position of the nominal ∆T meridian, 

given the standard error (S) in ∆T (i.e., ∆T ± S). This means that the entire map beneath the eclipse visibility zones can be 

shifted east or west by this amount to produce an acceptable solution that falls within the standard error of the estimated 

value of ∆T.

Figure 1-2a identifies the components of the uncertainty zone for the partial lunar eclipse of –1987 Apr 16 (1988 BCE). 

The instant of greatest eclipse is 12:21 TD (upper right corner) and the estimated value of ∆T (bottom) is 46,150 s or 12 h 

49min. The time expressed in UT is then:

UT = TD – ∆T = 12:21 – 12:49 = 23:32 UT. (1–7)

In this case, the conversion to UT shifts the instant of greatest eclipse into the previous day (–1987 Apr 15). The time 

in UT is needed to determine the shift of the geographic zone of eclipse visibility relative to its TD position. The result 

shows the geographic region of eclipse visibility (Fig. 1-2a), taking into account the fact that Earth rotated faster 4,000 

years ago. In Fig. 1-2a, the nominal ∆T meridian is identified as “∆T”, while the eastern and western uncertainty zone 

longitudes are labeled “∆T1” (= ∆T + S) and “∆T2” (= ∆T – S), respectively. These lines of longitude are located ±15.3° 

(S= ±3,676 s) with respect to the nominal ∆T meridian and show the range that the underlying map can be rotated to give 

a solution, given the uncertainty in ∆T.

The map in Figure 1-2b shows the solution when ∆T1 (= ∆T + S) is used to calculate UT. In this case, ∆T1 is equal to ∆T 

plus the standard error:

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 11

FIGURES AND PREDICTIONS
∆T1 = ∆T + S = 46,150 s + 3,676 s = 49,826 s = 13h 50m. (1–8)

The corresponding time in UT is then

UT = TD – ∆T1 = 12:21 – 13:50 = 22:31 UT. (1–9)

Once again, the conversion to UT shifts the instant of greatest eclipse into the previous day (–1987 Apr 15). The global 

map shows that entire eclipse visibility zone is shifted 15.3° east of the nominal solution for ∆T = 46,150 s.

Finally, the map in Fig. 1-2c shows the solution when ∆T2 (= ∆T – S) is used to calculate UT. In this case, ∆T2 is equal to 

∆T minus the standard error:

∆T2 = ∆T – S = 46,150 s – 3,676 s = 42,474 s = 11h 48m. (1–10)

The corresponding time in UT (–1987 Apr 16) is then

UT = TD – ∆T2 = 12:21 – 11:48 = 00:33 UT. (1–11)

The global map shows that the entire visibility zone is now shifted 15.3° west of the nominal solution for ∆T = 46,150 s.

The uncertainty zones plotted on eclipse maps prior to the year –630 and after the year +2428 can be used to estimate the 

range of uncertainty in the geographic visibility of an eclipse given the standard error in the corresponding value of ∆T.

Partial -1987 Apr 16

Saros -10 12:21 TD 

Par. = 164m

P.Mag. = 1.6347 

U.Mag. = 0.6897 

Gam. = -0.6515 

Partial -1987 Apr 16

Saros -10 12:21 TD 

Par. = 164m

P.Mag. = 1.6347 

U.Mag. = 0.6897 

Gam. = -0.6515 

Partial -1987 Apr 16

Saros -10 12:21 TD 

Par. = 164m

P.Mag. = 1.6347 

U.Mag. = 0.6897 

Gam. = -0.6515 

!"#$%&'()*+,(-()*+./(0$1,%(2.3"4'&(5,4'(,16(78,16,%6(2%%9%(:!;("1(!<

!"#/()*+, !"#/()*+= !"#/()*+.

"T = 46150 s [= 12h49m] 23:32 UT* "T1 = 49826 s [= 13h50m] 22:31 UT* "T2 = 42474 s [= 11h48m] 00:33 UT 

("T1 = "T + ! = 46150 + 3676! ("T2 = "T – ! = 46150 – 3676! std.err. (!) = ± 3676 s [= ± 15.3°]

* Universal Time corresponds to previous day (-1987 Apr 15)

"T

"T2 = "T– !

"T1 = "T+ ! "T1 "T2

UT = TD – "T = 12:21 – 12h49m = 23:32 UT = TD – "T1 = 12:21 – 13h50m = 22:31 UT = TD – "T2 = 12:21 – 11h48m = 00:30

1.7 Visual Appearance of Lunar Eclipses

The visual appearance of penumbral, partial, and total lunar eclipses differs significantly from each other. While penumbral eclipses are pale and difficult to see, partial eclipses are easy naked-eye events, while total eclipses are colorful and

dramatic.

 12 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
1.7.1 Appearance of Penumbral and Partial Lunar Eclipses

Earth’s penumbral shadow forms a diverging cone that expands into space in the anti-solar direction. From within this 

zone, Earth blocks part but not the entire disk of the Sun. Thus, some fraction of the Sun’s direct rays continues to reach 

the most deeply eclipsed parts of the Moon during a penumbral eclipse.

The primary penumbral contacts (P1 and P4), as well as the early and late stages of a penumbral eclipse, are completely 

invisible to the eye with or without optical aid. A penumbral magnitude greater than ~0.6 is needed before skilled observers can detect faint shading across the Moon’s disk.

Even when one edge of the Moon is 9/10 of the way into the penumbral shadow, approximately 10% of the Sun’s rays still 

reach the Moon’s deepest limb. Under such conditions, the Moon remains relatively bright with only a subtle gradient 

across its disk. The penumbral eclipse only becomes readily apparent when it is within ~0.05 magnitudes of becoming a 

partial eclipse.

In comparison, partial eclipses are easy to see with the naked eye. The lunar limb extending into the umbral shadow usually appears very dark or black. This is primarily due to a contrast effect because the remaining portion of the Moon in 

the penumbra may be brighter by a factor of ~500x. Because the umbral shadow’s diameter is typically ~2.7x the Moon’s 

diameter, it appears as though a semi-circular bite has been taken out of the Moon.

Aristotle (384–322 BCE) first proved that Earth was round using the curved umbral shadow seen at partial eclipses. In 

comparing observations of several eclipses, he noted that Earth’s shadow was round no matter where the eclipse took 

place, whether the Moon was high in the sky or low near the horizon. Aristotle correctly reasoned that only a sphere casts 

a round shadow from every angle.

1.7.2 Appearance of Total Lunar Eclipses

The total lunar eclipse is the most dramatic and visually compelling type of lunar eclipse. The Moon’s appearance can 

vary enormously throughout the period of totality and from one eclipse to the next. Obviously, the geometry of the Moon’s 

path through the umbra plays an important role. Not as apparent is the effect that Earth’s atmosphere has on a total eclipse.

Although the physical mass of Earth blocks all direct sunlight from the umbra, the planet’s atmosphere filters, attenuates 

and bends some of the Sun’s rays into the shadow.

The molecules in Earth’s atmosphere scatter short wavelength light (e.g., yellow, green, blue) more than long wavelength

light (e.g., orange, red). This process, which is responsible for making sunsets red, also gives total eclipses their characteristic red-orange color. However, the exact color can vary considerably in both hue and brightness.

Because the lowest layers of the atmosphere are thicker than the upper layers, they absorb more sunlight and refract it 

through larger angles. About 75% of the atmosphere’s mass is concentrated in the bottom 10 km (troposphere) as well as 

most of the water vapor, which can form massive clouds that block even more light. Just above the troposphere lies the 

stratosphere (~10 km to 50 km), a rarified zone above most of the planet’s weather systems. The stratosphere is subject 

to important photochemical reactions due to the high levels of solar ultraviolet radiation that penetrates the region. The 

troposphere and stratosphere act together as a ring-shaped lens that refracts heavily reddened sunlight into Earth’s umbral 

shadow. Because the higher atmospheric layers in the stratosphere contain less gas, they refract sunlight through progressively smaller angles into the outer parts of the umbra. In contrast, lower atmospheric layers containing more gas refract 

sunlight through larger angles to reach the inner parts of the umbra.

As a consequence of this lensing effect, the amount of light refracted into the umbra tends to increase radially from center 

to edge. However, inhomogeneities in the form of asymmetric amounts of cloud and dust at differing latitudes can cause 

significant variations in brightness throughout the umbra.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 13

FIGURES AND PREDICTIONS
Besides water (clouds, mist, precipitation), Earth’s atmosphere also contains aerosols or tiny particles of organic debris, 

meteoric dust, volcanic ash, and photochemical droplets. This material can significantly attenuate sunlight before it is refracted into the umbra. For instance, major volcanic eruptions in 1963 (Agung) and 1982 (El Chichón) each dumped huge 

quantities of gas and ash into the stratosphere and were followed by several years of very dark eclipses (Keen, 1983).

The same thing occurred after the eruption of the Philippine volcano Pinatubo in 1991. While most of the solid ash fell to 

Earth several days after circulating through the troposphere, a sizable volume of sulphur dioxide (SO2) and water vapor 

reached the stratosphere where it produced sulfuric acid (H2SO4). This high-altitude volcanic haze layer can severely dim 

sunlight that must travel several hundred kilometers horizontally through the layer before being refracted into the umbral 

shadow. Consequently, the total eclipsesfollowing large volcanic eruptions are unusually dark. For instance, the total lunar

eclipse of 1992 Dec 09 (1.5 years after Pinatubo) was so dark that the Moon’s dull gray disk was difficult to see with the 

naked eye (Espenak, 2008, personal observation).

1.7.3 Danjon Scale of Lunar Eclipse Brightness

The French astronomer A. Danjon proposed a useful five-point scale for evaluating the visual appearance and brightness 

of the Moon during total lunar eclipses. The L values for various luminosities are defined as follows:

L=0 Very dark eclipse

(Moon is almost invisible, especially at mid-totality)

L=1 Dark eclipse, gray or brownish in coloration

(Details are distinguishable only with difficulty)

L=2 Deep red or rust-colored eclipse

(Very dark central shadow, while outer umbra is relatively bright)

L=3 Brick-red eclipse

(Umbral shadow usually has a bright or yellow rim)

L=4 Very bright copper-red or orange eclipse

(Umbral shadow has a bluish, very bright rim)

The Danjon scale illustrates the range of colors and brightness the Moon can take on during a total lunar eclipse. It is also 

a useful tool to visual observers in characterizing the appearance of an eclipse. The evaluation of an L value is best done

with the naked eye, binoculars, or a small telescope near the time of mid-totality. It is also helpful to examine the Moon’s 

appearance just after the beginning and just before the end of totality. The Moon is then near the edge of the shadow, 

providing an opportunity to assign an L value to the outer umbra. In making such evaluations, the instrumentation and 

the time must be also recorded.

1.8 Lunar Eclipse Canon Online

This report, Five Millennium Canon of Lunar Eclipses: –1999 to +3000 (NASA/TP–2009–214172), is available online in

PDF format and may be downloaded at: <http://eclipse.gsfc.nasa.gov/eclipse/SEpubs/5MCLE.html>.

1.9 Lunar Eclipse Catalog Online

A supplemental publication to the Five Millennium Canon of Lunar Eclipses is also available. The Five Millennium Catalog of Lunar Eclipses: –1999 to +3000 (NASA/TP–2009–214173, Espenak and Meeus, 2009) contains all the data found

on the Canon figures in the Appendix including calendar date, Dynamical Time, eclipse type, Saros number, duration 

 14 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

FIGURES AND PREDICTIONS
of eclipse phases, gamma, and the penumbral and umbral eclipse magnitudes. In addition, a number of other useful data 

are listed such as the sequential catalog number, ∆T, the lunation number, the Quincena Solar Eclipse parameter, and the 

geographic coordinates of greatest eclipse (Moon in zenith). The eclipse type is augmented to indicate the first/last eclipse 

in a Saros series, central total eclipses and total penumbral eclipses.

The Five Millennium Catalog of Lunar Eclipses: –1999 to +3000 (NASA/TP–2009–214173) is available online in PDF 

format and may be downloaded at:

<http://eclipse.gsfc.nasa.gov/eclipse/SEpubs/5MKLE.html>.

In addition, a Web-based version of the lunar eclipse catalog is available online at:

<http://eclipse.gsfc.nasa.gov/eclipse/LEcat5/catalog.html>.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 15

FIGURES AND PREDICTIONS

SECTION 2: TIME

2.1 Greenwich Mean Time

For thousands of years, time has been measured using the length of the solar day. This is the interval between two successive returns of the Sun to an observer’s local meridian. Unfortunately, the length of the apparent solar day can vary by 

tens of seconds over the course of a year. Earth’s elliptical orbit around the Sun and the 23.5° inclination of Earth’s axis 

of rotation are responsible for these variations. Apparent solar time was eventually replaced by mean solar time because 

it provides for a uniform time scale. The key to mean solar time is the mean solar day, which has a constant length of 24 

hours throughout the year.

Mean solar time on the 0° longitude meridian in Greenwich, England is known as Greenwich Mean Time (GMT). At the

International Meridian Conference of 1884, GMTa was adopted as the reference time for all clocks around the world. It 

was also agreed that all longitudes would be measured east or west with respect to the Greenwich meridian. In 1972, GMT 

was replaced by Coordinated Universal Time (UTC) as the international time reference. Nevertheless, UTC is colloquially 

referred to as GMT although this is technically not correct.

2.2 Ephemeris Time

During the 20th century, it was found that the rotational period of Earth (length of the day) was gradually slowing down.

For the purposes of orbital calculations, time using Earth’s rotation was abandoned for a more uniform time scale based 

on Earth’s orbit about the Sun. In 1952, the International Astronomical Union (IAU) introduced Ephemeris Time (ET) to 

address this problem. The ephemeris second was defined as a fraction of the tropical year for 1900 Jan 01, as calculated 

from Newcomb’s tables of the Sun (1895). Ephemeris Time was used for Solar System ephemeris calculations until it was 

replaced by TD in 1979.

2.3 Terrestrial Dynamical Time

TD was introduced by the IAU in 1979 as the coordinate time scale for an observer on the surface of Earth. It takes into 

account relativistic effects and is based on International Atomic Time (TAI), which is a high-precision standard using 

several hundred atomic clocks worldwide. As such, TD is the atomic time equivalent to its predecessor ET and is used in

the theories of motion for bodies in the solar system. To ensure continuity with ET, TD was defined to match ET for the 

date 1977 Jan 01. In 1991, the IAU refined the definition of TD to make it more precise. It was also renamed Terrestrial 

Time (TT), although in the Canon, the older name Terrestrial Dynamical Time is preferred and used.

2.4 Universal Time

For many centuries, the fundamental unit of time was the rotational period of Earth with respect to the Sun. GMT was 

the standard time reference based on the mean solar time on the 0° longitude meridian in Greenwich, England. Universal 

Time (UT) is the modern counterpart to GMT and is determined from Very Long Baseline Interferometry (VLBI) observations of the diurnal motion of quasars. Unfortunately, UT is not a uniform time scale because Earth’s rotational period 

is (on average) gradually increasing.

The change is primarily due to tidal friction between Earth’s oceans and its rocky mantle through the gravitational attraction of the Moon and, to a lesser extent, the Sun. This secular acceleration (Sect. 1.4) gradually transfers angular 

a. GMT was originally reckoned from noon to noon. In 1925, some countries shifted GMT by 12 h so that it would begin at 

Greenwich midnight. This new definition is the one in common usage for world time and in the navigational publications of 

English-speaking countries. The designation Greenwich Mean Astronomical Time (GMAT) is reserved for the reckoning 

of time from noon (and previously called GMT).

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 17

 TIME
 18 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

TIME

momentum from Earth to the Moon. As Earth loses energy and slows down, the Moon gains this energy and its orbital 

period and distance from Earth increase. Shorter period fluctuations in terrestrial rotation also exist, which can produce 

an accumulated clock error of ±20 s in one or more decades. These decade variations are attributed to several geophysical 

mechanisms including fluid interactions between the core and mantle of Earth. Climatological changes and variations in 

sea-level may also play significant roles because they alter Earth’s moment of inertia. 

The secular acceleration of the Moon implies an increase in the length of day (LOD) of about 2.3 milliseconds per century.

Such a small amount may seem insignificant, but it has very measurable cumulative effects. At this rate, time as measured 

through Earth’s rotation is losing about 84 seconds per century squared when compared to atomic time.

2.5 Coordinated Universal Time

Coordinated Universal Time (UTC) is the present day basis of all civilian time throughout the world. Derived from TAI, 

the length of the UTC second is defined in terms of an atomic transition of the element cesium and is accurate to approximately 1 ns (billionth of a second) per day. Because most daily life is still organized around the solar day, UTC was 

defined to closely parallel Universal Time. The two time systems are intrinsically incompatible, however, because UTC 

is uniform while UT is based on Earth’s rotation, which is gradually slowing. In order to keep the two times within 0.9 s 

of each other, a leap second is added to UTC about once every 12 to 18 months.

2.6 Delta T ($T)

The orbital positions of the Sun and Moon required by eclipse predictions, are calculated using TD because it is a uniform 

time scale. World time zones and daily life, however, are based on UTa. In order to convert eclipse predictions from TD 

to UT, the difference between these two time scales must be known. The parameter delta-T ($T) is the arithmetic difference, in seconds, between the two as:

 $T = TD – UT. (2–1)

Past values of $T can be deduced from the historical records. In particular, hundreds of eclipse observations (both solar 

and lunar) were recorded in early European, Middle Eastern, and Chinese annals, manuscripts, and canons. In spite of 

their relatively low precision, these data represent the only evidence for the value of $T prior to 1600 CE. In the centuries 

following the introduction of the telescope (circa 1609 CE), thousands of high quality observations have been made of 

lunar occultations of stars. The number and accuracy of these timings increase from the 17th through the 20th century, 

affording valuable data in the determination of $T. A detailed analysis of these measurements fitted with cubic splines 

for $T from –500 to +1950, is presented in Table 2-1, and includes the standard error for each value (Morrison and Stephenson, 2004).

a. World time zones are actually based on UTC. It is an atomic time synchronized and adjusted to stay within 0.9 s of astronomically determined UT. Occasionally, a “leap second” is added to UTC to keep it in sync with UT (which changes because 

of variations in Earth’s rotation rate).
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 19

 TIME

Table 2-1. Values of $T Derived from Historical Records

Year

∆T

(seconds)

Standard 

Error

(seconds)

–500 17,190 430

–400 15,530 390

–300 14,080 360

–200 12,790 330

–100 11,640 290

 0 10,580 260

 100 9,600 240

 200 8,640 210

 300 7,680 180

 400 6,700 160

 500 5,710 140

 600 4,740 120

 700 3,810 100

 800 2,960 80

 900 2,200 70

1000 1,570 55

1100 1,090 40

1200 740 30

1300 490 20

1400 320 20

1500 200 20

1600 120 20

1700 9 5

1750 13 2

1800 14 1

1850 7 <1

1900 –3 <1

1950 29 <0.1

In modern times, the determination of $T is made using atomic clocks and radio observations of quasars,so it is completely

independent of the lunar ephemeris. Table 2-2 gives the value of $T every five years from 1955 to 2005 (Astronomical

Almanac for 2006 [2004], page K9).
 20 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

TIME

Table 2-2. Recent Values of $T from Direct Observations

Year

$T

(seconds)

5-Year Change

(seconds)

Average

1-Year Change

(seconds)

1955.0 +31.1 — —

1960.0 +33.2 2.1 0.42

1965.0 +35.7 2.5 0.50

1970.0 +40.2 4.5 0.90

1975.0 +45.5 5.3 1.06

1980.0 +50.5 5.0 1.00

1985.0 +54.3 3.8 0.76

1990.0 +56.9 2.6 0.52

1995.0 +60.8 3.9 0.78

2000.0 +63.8 3.0 0.60

2005.0 +64.7 0.9 0.18

The average annual change of $T was 0.99 s from 1965 to 1980, however, the average annual increase was just 0.63 s from 

1985 to 2000, and only 0.18 s from 2000 to 2005. Future changes and trends in $T can not be predicted with certainty 

because theoretical models of the physical causes are not of high enough precision. Extrapolations from the table weighted 

by the long period trend from tidal braking of the Moon offer reasonable estimates of +67 s in 2010, +93 s in 2050, +203 

s in 2100, and +442 s in 2200.

Outside the period of observations (500 BCE to 2005 CE), the value of $T can be extrapolated from measured values using 

the long-term mean parabolic trend:

$T = –20 + 32 u2 s, (2–2)

where u = (year – 1820)/100, and is defined as time measured in centuries.

2.7 Polynomial Expressions for $T

Using the ∆T values derived from the historical record and from direct observations (Tables 2-1 and 2-2, respectively), a 

series of polynomial expressions have been created to simplify the evaluation of $T for any time during the interval –1999 

to +3000. The decimal year “y” is defined as follows:

y = year + (month – 0.5)/12. (2–3)

This gives y for the middle of the month, which is accurate enough given the precision in the known values of $T. The 

following polynomial expressions can be used to calculate the value of $T (in seconds) over the interval of the Catnon.

Before the year –500, calculate

$T = –20 + 32 u2, (2–4)

where u = (y – 1820)/100.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 21

 TIME

Between years –500 and +500, the data from Table 2-1 are used, except for the year –500 where the value 17,190 is changed

to 17,203.7 in order to avoid a discontinuity with the previous formula (2–4) at that epoch. The value for ∆T is given by a 

polynomial of the 6th degree, which reproduces the values in Table 2-1 with an error not larger than 4 s:

$T = 10583.6 – 1014.41u + 33.78311u2 – 5.952053 u3

 –0.1798452u4 + 0.022174192 u5 + 0.0090316521u6 (2–5)

where u = y/100.

Between years 500 and 1600, the data is again used from Table 2-1. Calculate u = (y – 1000)/100. The value for ∆T is given 

by the following polynomial of the 6th degree with a divergence from Table 2-1 not larger than 4 s:

$T = 1574.2 – 556.01u + 71.23472u2 + 0.319781 u3

 – 0.8503463u4 – 0.005050998u5 + 0.0083572073 u6, (2–6)

where u = (y – 1000)/100.

Between years 1600 and 1700, calculate

$T = 120 – 0.9808 t – 0.01532t

2

 + (t

3

 / 7129), (2–7)

where t = y – 1600, and is defined as time measured in years.

Between years 1700 and 1800, calculate

$T = 8.83 + 0.1603t – 0.0059285 t

2

 + 0.00013336 t

3

 – (t

4

 / 1,174,000), (2–8)

where t = y – 1700.

Between years +1800 and +1860, calculate

$T = 13.72 – 0.332447t + 0.0068612t

2

 + 0.0041116t

3

 – 0.00037436t

4

 + 0.0000121272 t

5 – 0.0000001699t6 + 0.000000000875t7

, (2–9)

where t = y – 1800.

Between years 1860 and 1900, calculate

$T = 7.62 + 0.5737t – 0.251754 t

2

 + 0.01680668t

3 –0.0004473624t4 +(t5

 / 233,174), (2–10)

where t = y – 1860.

Between years 1900 and 1920, calculate

$T = –2.79 + 1.494119t – 0.0598939t

2

 + 0.0061966 t

3

 – 0.000197t

4

, (2–11)

where t = y – 1900.

Between years 1920 and 1941, calculate 

$T = 21.20 + 0.84493t – 0.076100 t

2

 + 0.0020936t

3

, (2–12)
 22 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

TIME

where t = y – 1920.

Between years 1941 and 1961, calculate

$T = 29.07 + 0.407t – (t

2

/233) + (t

3

 / 2547), (2–13)

where t = y – 1950.

Between years 1961 and 1986, calculate

$T = 45.45 + 1.067t – (t

2

/260) – (t

3

 / 718), (2–14)

where t = y – 1975.

Between years 1986 and 2005, calculate

$T = 63.86 + 0.3345 t – 0.060374 t

2

 + 0.0017275t

3

 + 0.000651814 t

4

 + 0.00002373599t

5

, (2–15)

where t = y – 2000.

Between years 2005 and 2050, calculate

$T = 62.92 + 0.32217t + 0.005589t

2

, (2–16)

where t = y – 2000.

This expression is derived from estimated values of $T in the years 2010 and 2050. The value for 2010 (66.9 s) is based 

on a linear extrapolation from 2005 using 0.39 s/y (average from 1995 to 2005)

a

. The value for 2050 (93 s) is linearly 

extrapolated from 2010 using 0.66 s/y (average rate from 1901 to 2000).

Between years 2050 and 2150, calculate

$T = –20 + 32[(y – 1820)/100]

2

 – 0.5628 (2150 – y). (2–17)

The last term is introduced to eliminate the discontinuity at 2050.

After 2150, calculate

$T = –20 + 32u2, (2–18)

where u = (y – 1820)/100.

All values of $T, based on Morrison and Stephenson (2004), assume a value for the Moon’s secular acceleration of –26 

arcsec/cy2. However, the ELP-2000/82 lunar ephemeris employed in the Canon uses a slightly different value of –25.858 

arcsec/cy2. Thus, a small correction “c” must be added to the values derived from the polynomial expressions for $T before 

they can be used in the Canon:

c = –0.000012932(y – 1955)

2

. (2–19)

a. Although ∆T values are available through 2008, the 2005 value is used here to be consistent with the values used in the Five 

Millennium Canon of Solar Eclipses: –1999 to +2000, NASA Tech. Pub. 2006–214141 (Espenak and Meeus, 2006).
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 23

 TIME

Because the values of $T for the interval 1955 to 2005 were derived independent of any lunar ephemeris, no correction

is needed for this period.

2.8 Uncertainty in $T

The uncertainty in the value of $T is of particular interest in the calculation of eclipse paths in the distant past and future.

Unfortunately, estimating the standard error in $T prior to 1600 CE is a difficult problem. It depends on a number of factors, which include the accuracy of determining $T from historical eclipse records and modeling the physical processes 

producing changes in Earth’s rotation. Morrison and Stephenson (2004) propose a simple parabolic relation to estimate 

the standard error (S), which is valid over the period 1000 BCE to 1200 CE:

S = 0.8t

2

 s, (2–20)

where t = (year – 1820)/100.

Table 2-3 gives the errors in $T, along with the corresponding uncertainties in the longitude of the zones of eclipse

visibility.

Table 2-3. Uncertainty of $T, Part I

Year

S

(seconds)

Longitude

–1000 636 2.65°

–500 431 1.79°

 0 265 1.10°

+500 139 0.58°

+1000 54 0.22°

+1200 31 0.13°

The decade fluctuations in $T result in an uncertainty of approximately 20 s (0.08°) for the period 1300 to 1600 CE.

During the telescopic era (1600 CE to present), records of astronomical observations pin down the decade fluctuations 

with increasing reliability. The uncertainties in $T are presented in Table 2-4 (Stephenson and Houlden, 1986).

Table 2-4. Uncertainty of ∆T, Part II

Year

S

(seconds)

Longitude

+1700 5 0.021°

+1800 1 0.004°

+1900 0.1 0.0004°

The estimation in the uncertainty of $T prior to 1000 BCE must rely on a certain amount of modeling and theoretical arguments because no measurements of $T are available for this period. Huber (2000) proposed a Brownian motion model, 

including drift, to estimate the standard error in $T for periods outside the epoch of measured values. The intrinsic variability in the LOD during the 2,500 years of observations (500 BCE to 2000 CE) is 1.780 ms/cy with a standard error of 

0.56 ms/cy. This rate is not due entirely to tidal friction, but includes a drift in LOD from imperfectly understood effects, 

such as changes in sea level due to variations in polar ice caps. Presumably, the same mechanisms operating during the

present era also operated prior to 1000 BCE, as well as one millennium into the future.
 24 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

TIME

Huber’s derived estimate for the total standard error (fluctuations plus drift) in $T is as follows.

S = 365.25 N SQRT [(N Q / 3) ( 1 + N / M)] / 1000, (2–21)

where:

N = Difference between target year and calibration year; 

M = 2500 years (–500 to +2000)—this covers the period of observed ∆T measurements; and

Q = 0.058 ms

2

/yr.

The calibration year is taken as –500 for target years before 500 BCE, while the calibration year is 2005 CE for target years 

in the future. Evaluation of this expression at 500-year intervals is found in Table 2-5. It shows estimates in the standard 

error of $T along with the equivalent shift in longitude.

Table 2-5. Uncertainty of $T, Part III

Year

S

(seconds)

Longitude

–4500 20,717 86.3°

–4000 16,291 67.9°

–3500 12,378 51.6°

–3000 8,978 37.4°

–2500 6,094 25.4°

–2000 3,732 15.6°

–1500 1,900 7.9°

–1000 622 2.6°

— — —

+2500 612 2.6°

+3000 1,885 7.9°

+3500 3,711 15.6°

+4000 6,068 25.3°

+4500 8,946 37.3°

+5000 12,341 51.4°
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 25

LUNAR ECLIPSE STATISTICS

SECTION 3: LUNAR ECLIPSE STATISTICS

3.1 Statistical Distribution of Lunar Eclipse Types

Eclipses of the Moon can only occur during the Full Moon phase. It is then possible for the Moon to pass through Earth’s 

penumbral and umbral shadows thereby producing an eclipse. There are three types of lunar eclipses:

1) Penumbral—Moon passes partially or completely into Earth’s penumbral shadow.

2) Partial—Moon passes partially into Earth’s umbral shadow.

3) Total—Moon passes completely into Earth’s umbral shadow

During the 5,000-year period from –1999 to +3000 (2000 BCE to 3000 CE), Earth will experience 12,064 eclipses of the 

Moon. The statistical distribution of the three eclipse types over this interval is shown in Table 3-1.

Table 3-1. Distribution of Basic Lunar Eclipse Types

Eclipse Type Abbreviation Number Percent

All Eclipses – 12064 100.0%

Penumbral N 4378 36.3%

Partial P 4207 34.9%

Total T 3479 28.8%

During most penumbral eclipses, only part of the Moon passes through Earth’s penumbral shadow. Examples of such 

partial penumbral eclipses include: 2009 Feb 09, 2009 Jul 07, 2009 Aug 06, and 2012 Nov 28. However, it is also possible 

to have a penumbral eclipse in which the Moon passes completely within Earth’s penumbral shadow without entering the 

inner umbral shadow. Such total penumbral eclipses are quite rare compared to normal (or partial) penumbral eclipses.

During the 21st century, there are 87 partial penumbral eclipses, but only 5 total penumbral eclipses: 2006 Mar 14, 2053

Aug 29, 2070 Apr 25, 2082 Aug 08, and 2099 Sep 29. Table 3-2 shows the distribution of the two penumbral eclipse types 

during the period covered by the Canon. For more on total penumbral eclipses, see Section 3.11.

Table 3-2. Statistics of Penumbral Lunar Eclipses

Eclipse Type Number Percent

All Penumbral Eclipses 4378 100.0%

Partial Penumbral 4237 96.8%

Total Penumbral 141 3.2%

Total lunar eclipses through Earth’s umbral shadow can be categorized as:

a) Central—The Moon passes through the central axis of Earth’s umbral shadow.

b) Non-Central—The Moon misses the central axis of Earth’s umbral shadow.

Using the above categories, the distribution of the 3,479 total eclipses is shown in Table 3-3.
 26 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

Table 3-3. Statistics of Total Lunar Eclipses

Eclipse Type Number Percent

All Total Eclipses 3479 100.0%

Central Total 2074 59.6%

Non-Central Total 1405 40.4%

Examples of central total eclipses include: 2000 Jul 16, 2011 Jun 15, 2018 Jul 27, and 2022 May 16. Several examples of 

non-central total eclipses are: 2010 Dec 21, 2011 Dec 10, 2014 Apr 15, and 2014 Oct 08.

3.2 Distribution of Lunar Eclipse Types by Century

Table 3-4 summarizes 5,000 years of eclipses by eclipse type over 100-year intervals. The average century contains 241 

lunar eclipses of which 88 are penumbral, 84 are partial and 70 are total. Individual centuries deviate from these mean 

values in interesting ways. For instance, the total number of eclipses in a century varies from a minimum of 225 (century 

beginning –0899) to a maximum of 259 (centuries beginning 1101 and 2801). The number of penumbral eclipses varies 

from 76 (century 0301) to 100 (century 2801), while the number of partial eclipses ranges from 54 (century –1599) to 102 

(centuries –0699, 1101, and 2801). Finally, the number of total lunar eclipses per century varies from 57 (centuries 0001 

and 2801) to 89 (century 0801). Note that century 2801 not only has the most number of eclipses (259), it also has the 

maximum number of penumbral (100) and partial (102) eclipses, but the minimum number of total eclipses (57).

The last column of Table 3-4 lists the number of total lunar eclipse tetrads per century. A tetrad is a grouping of four 

consecutive total lunar eclipses each separated by six lunations. Their frequency is quite variable with some centuries 

having 0 tetrads, while others may have as many as 8. For more on tetrads, see Section 3.16.

When the data in Table 3-4 is displayed graphically (Figure 3-1), other important relationships are revealed. The most apparent feature is a periodic oscillation in the number of all lunar eclipses (Figure 3-1a), as well as in the individual types.

By inspection, the period is about 600 years. Using tables from von Oppolzer's Canon der Finsternisse (1887) the Dutch

astronomer G. van den Bergh (1954) calculated a period of 586 years. By studying the distributions of tetrad eclipse groups 

(Section 3.16), Meeus derived an empirical expression showing that this period is slowly decreasing (Meeus 2004b). While 

its current value is actually 565 years, the period was 618 years in –1999 and it will decrease to 552 years by +3000. A 

theoretical study by T. Hughes (Hughes 2004) demonstrates that the period is caused by the eccentricity of Earth’s orbit, 

which is gradually decreasing.

There are other interesting features in Figure 3-1. For instance, the number of total lunar eclipses as well as deep central 

total eclipses is highest when the number of all lunar eclipses is at a minimum. In contrast, numbers of penumbral eclipses, 

partial eclipses and non-central total eclipses all appear to be synchronized with the overall number of lunar eclipses.

Finally, the number of total penumbral eclipses, and total lunar eclipse tetrads are most frequent during epochs when the 

overall number of lunar eclipses is at a minimum.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 27

LUNAR ECLIPSE STATISTICS

Table 3-4. Number of Lunar Eclipse Types by Century: –1999 to +3000 (2000 BCE to 3000 CE)

Century Interval All Lunar 

Eclipses

All 

Penumbral 

Eclipses

Partial 

Penumbral 

Eclipses

Total 

Penumbral 

Eclipses

All Partial 

Eclipses

All Total 

Eclipses

Central 

Total 

Eclipses

Non-Central 

Total 

Eclipses

Total 

Eclipse 

Tetrads

–1999 to –1900 242 88 84 4 92 62 13 49 1

–1899 to –1800 255 98 97 1 97 60 11 49 0

–1799 to –1700 254 94 94 0 99 61 12 49 0

–1699 to –1600 244 90 87 3 87 67 21 46 3

–1599 to –1500 226 85 81 4 54 87 62 25 8

–1499 to –1400 228 86 78 8 60 82 55 27 6

–1399 to –1300 239 83 80 3 90 66 23 43 2

–1299 to –1200 251 92 91 1 99 60 9 51 0

–1199 to –1100 252 96 95 1 95 61 13 48 0

–1099 to –1000 240 88 81 7 86 66 18 48 4

–0999 to–0900 228 80 72 8 61 87 59 28 7

–0899 to –0800 225 79 76 3 62 84 57 27 7

–0799 to –0700 239 87 85 2 88 64 21 43 1

–0699 to –0600 253 91 91 0 102 60 10 50 0

–0599 to –0500 255 95 95 0 100 60 11 49 0

–0499 to –0400 242 88 86 2 90 64 19 45 1

–0399 to –0300 229 80 79 1 61 88 54 34 7

–0299 to –0200 228 79 76 3 64 85 55 30 6

–0199 to –0100 240 85 84 1 86 69 21 48 3

–0099 to 0000 253 94 93 1 98 61 11 50 0

0001 to 0100 251 93 92 1 101 57 7 50 0

0101 to 0200 239 84 82 2 88 67 23 44 3

0201 to 0300 228 83 75 8 63 82 53 29 6

0301 to 0400 227 76 72 4 69 82 58 24 4

0401 to 0500 244 83 82 1 95 66 18 48 3

0501 to 0600 254 97 96 1 95 62 12 50 0

0601 to 0700 255 97 94 3 100 58 10 48 0

0701 to 0800 240 84 82 2 88 68 23 45 3

0801 to 0900 228 79 74 5 60 89 65 24 8

0901 to 1000 230 82 79 3 70 78 45 33 6

1001 to 1100 246 87 84 3 97 62 14 48 0

1101 to 1200 259 98 98 0 102 59 10 49 0

1201 to 1300 251 95 94 1 96 60 12 48 0

1301 to 1400 231 81 73 8 73 77 41 36 6

1401 to 1500 228 80 77 3 65 83 60 23 4

1501 to 1600 233 82 79 3 74 77 39 38 6

1601 to 1700 249 91 88 3 97 61 11 50 0

1701 to 1800 256 98 98 0 98 60 13 47 0

1801 to 1900 249 90 88 2 97 62 11 51 0

1901 to 2000 229 83 74 9 65 81 48 33 5

2001 to 2100 228 86 81 5 57 85 61 24 8

2101 to 2200 238 81 77 4 88 69 24 45 4

2201 to 2300 252 94 93 1 97 61 11 50 0

2301 to 2400 253 95 95 0 98 60 12 48 0

2401 to 2500 237 83 77 6 85 69 23 46 4

2501 to 2600 227 82 77 5 58 87 64 23 8

2601 to 2700 230 81 80 1 70 79 44 35 7

2701 to 2800 241 86 83 3 91 64 16 48 0

2801 to 2900 259 100 99 1 102 57 9 48 0

2901 to 3000 249 89 89 0 97 63 13 50 1
 28 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

0

10

20

30

40

50

60

10

20

30

40

50

60

50

60

70

80

90

50

60

70

80

90

100

0

10

70

80

90

100

70

80

90

100

220

230

240

250

260

Number of Lunar Eclipses 

Figure 3–1. Number of Lunar Eclipses Per Century: -1999 to +3000

Year

a) all eclipses

b) all penumbral

c) partial penumbral

d) total penumbral

e) all partial

f) all total

g) central total

h) non-central total

i) tetrads

 -2000 -1000 0 1000 2000 3000
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 29

LUNAR ECLIPSE STATISTICS

3.3 Distribution of Lunar Eclipse Types by Month

Table 3-5 summarizes 5,000 years of eclipses by eclipse type in each month of the year. The first value in each column 

is the number of eclipses of a given type for the corresponding month. The second value, in square brackets [ ], is the 

number of eclipses divided by the number of days in that month. This normalization allows direct comparison of eclipse 

frequencies in different months.

A brief examination of the normalized values in the column “Number of All Lunar Eclipses” shows that eclipses are 

equally distributed around the year. The same holds true for partial eclipses; however, the columns for penumbral and 

total eclipses reveal something interesting. Penumbral eclipses are about 6% more likely during the period of December–

January–February compared to the months June–July–August. This effect is attributed to Earth’s elliptical orbit. Earth 

currently reaches perihelion in early January and aphelion in early July. Consequently, the Sun’s apparent diameter varies from 1,952 to 1,887 arcsec between perihelion and aphelion. The Sun’s larger apparent diameter at perihelion makes 

Earth’s penumbral shadow larger so penumbral eclipses are more frequent at that time.

The opposite argument holds true for total eclipses that are about 4% more likely during the period April to August, 

compared to the months November to February. In this case, the Sun’s smaller apparent size around aphelion increases 

the diameter of Earth’s umbral shadow so the frequency of total eclipses is slightly higher at that time.

Table 3-5. Lunar Eclipse Types by Month: –1999 to +3000 (2000 BCE to 3000 CE)

Month Number of All 

Lunar Eclipses

Number of 

Penumbral Eclipses

Number of 

Partial Eclipses

Number of Total 

Eclipses

January 1027 [33.1] 379 [12.2] 352 [11.4] 296 [ 9.5]

February 936 [33.4] 343 [12.2] 333 [11.9] 260 [ 9.3]

March 1028 [33.2] 376 [12.1] 361 [11.6] 291 [ 9.4]

April 986 [32.9] 354 [11.8] 342 [11.4] 290 [ 9.7]

May_ 1025 [33.1] 370 [11.9] 358 [11.5] 297 [ 9.6]

June 992 [33.1] 351 [11.7] 347 [11.6] 294 [ 9.8]

July 1025 [33.1] 368 [11.9] 356 [11.5] 301 [ 9.7]

August 1015 [32.7] 361 [11.6] 355 [11.5] 299 [ 9.6]

September 990 [33.0] 364 [12.1] 341 [11.4] 285 [ 9.5]

October 1023 [33.0] 377 [12.2] 356 [11.5] 290 [ 9.4]

November 993 [33.1] 350 [11.7] 357 [11.9] 286 [ 9.5]

December 1024 [33.0] 385 [12.4] 349 [11.3] 290 [ 9.4] 

 Numbers in square brackets [ ] are the number of eclipses divided by the number of days in the month.

3.4 Lunar Eclipse Frequency and the Calendar Year

There are two to five lunar eclipses in every calendar year. Table 3-6 shows the distribution in the number of eclipses per 

year for the 5,000 years covered in the Canon.
 30 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

Table 3-6. Number of Lunar Eclipses per Year

Number of 

Eclipses per Year

Number 

of Years

Percent

2 3,541 70.8%

3 887 17.7%

4 539 10.8%

5 33 0.7%

When two eclipses occur in one calendar year, they can be in any combination of N, P, or T (penumbral, partial, or total, 

respectively). Table 3-7 lists the frequency of each eclipse combination, along with five recent years when the combination 

occurs. The table makes no distinction in the order of any two eclipses. For example, the eclipse combination PT includes 

all years where the order is either PT or TP.

Over 71% of all years containing two eclipses are composed of the combinations PP (34.2%) or TT (37.2%). The NT pair

is the rarest combination with only six instances, all within the first two millennia of the Canon, and with five of the six 

involving a total penumbral eclipse.

Table 3-7. Two Lunar Eclipses in One Year

Eclipse 

Combinationsa

Number 

of Years

Percent Examples (Years)b

NN 116 3.3% ..., 1987, 2016, 2042, 2045, 2053, ...

NP 373 10.5% ..., 1999, 2005, 2006, 2012, 2017, ...

NT 6 0.2% [–1989, –1971, –1423, –1403, –1385, –0186]

PP 1211 34.2% ..., 1980, 2039, 2041, 2046, 2057, ...

PT 516 14.6% ..., 1997, 2008, 2010, 2019, 2021, ...

TT 1319 37.2% ..., 2003, 2007, 2011, 2014, 2015, ...

a. N = Penumbral, P = Partial, and T = Total.

b. When years are surrounded by square brackets [ ], there are no other examples outside this 

 range.

When three eclipses occur in one calendar year, there are nine possible combinations of N, P, or T. Table 3-8 lists the 

frequency of each eclipse combination along with five recent years when each combination occurs. The table makes no 

distinction in the order of eclipses in any combination. For example, the eclipse combination NPT includes all years where 

the order is NPT, NTP, PNT, PTN, TPN, and TNP. The rarest combinations—NNT and NTT—each occurs six times or 

less in the five-millennium span of this work. Interestingly, no PPP combinations occur.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 31

LUNAR ECLIPSE STATISTICS

Table 3-8. Three Lunar Eclipses in One Year

Eclipse

Combinationsa

Number 

of Years

Percent Examples (Years)b

NNN 382 43.1% ..., 2002, 2027, 2031, 2049, 2060, ...

NNP 159 17.9% ..., 1958, 2013, 2147, 2168, 2186, ...

NNT 4 0.5% [–1991, –1405, –0168, 0418]

NPP 158 17.8% ..., 1871, 2075, 2140, 2151, 2169, ...

NPT 27 3.0% ..., 1963, 2001, 2048, 2066, 2504, ...

NTT 6 0.7% [–1953, –1432, –1367, –0846, 0977, 2466]

PPT 51 5.7% ..., 1898, 2028, 2113, 2178, 2531, ...

PTT 75 8.5% ..., 1852, 2094, 2159, 2224, 2243, ...

TTT 25 2.8% ..., 1917, 1982, 2485, 2550, 2615]

a. N = Penumbral, P = Partial, and T = Total.

b. When a year is bounded by a square bracket “[” or “]”, there are no other examples beyond that year.

When four eclipses occur in one calendar year, there are three possible combinations of eclipse types N, P, and T. Table 3-9 

liststhe frequency of each eclipse combination along with five recent years when each combination occurs. The table makes

no distinction in the order of eclipses in the seven combinations. The rarest combination NNPP occurs just 32 times.

Table 3-9. Four Lunar Eclipses in One Year

Eclipse 

Combinationsa

Number 

of Years

Percent Examples (Years)

NNNN 390 72.4% ..., 1944, 2020, 2038, 2056, 2085, ...

NNNP 117 21.7% ..., 1991, 2009, 2150, 2197, 2215, ...

NNPP 32 5.9% ..., 1684, 2205, 2411, 2726, 2819, ...

 a. N = Penumbral, P = Partial, and T = Total.

The maximum number of five lunar eclipsesin one calendar year is quite rare. Over the 5,000-yearspan of the Canon, there 

are only 33 years containing five lunar eclipses. They occur in two possible combinations of eclipse types where four out

of the five eclipses are always of type N. The first eclipse of such a quintet always occurs in the first half of January, while 

the last eclipse falls in the latter half of December. Table 3-10 lists the frequency of the two eclipse combinations, along 

with recent years when each combination occurs. The rarest combination NNNPP (actually either PNPNN or NNPNP) 

occurred just three times. Once again, the table makes no distinction in the order of eclipses in any combination.

Table 3-10. Five Lunar Eclipses in One Year

Eclipse 

Combinationsa

Number 

of Years

Percent Examples (Years)b

NNNNP 30 90.9% ..., 1879, 2132, 2262, 2400, 2653, ...

NNNPP 3 9.1% [0475, 1694, 1749]

 a. N = Penumbral, P = Partial, and T = Total.

 b. When years are surrounded by square brackets [ ], there are no other examples outside this 

 range. 
 32 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

3.5 Extremes in Eclipse Magnitude—Penumbral Lunar Eclipses

The penumbral eclipse magnitude is defined asthe fraction of the Moon’s diameter immersed in Earth’s penumbralshadow.

It is a unitless parameter that can be expressed numerically by

Mp = xp/dm, (3–1)

where Mp is the penumbral eclipse magnitude, dm is the apparent diameter of the Moon, and xp is the distance measured 

from the edge of the penumbral shadow to the edge of the Moon deepest in the penumbra.

The penumbral eclipse magnitude reaches its maximum value at the instant of greatest eclipse. This is the value shown in 

the figures in the Appendix. A search through the 12,064 eclipses in the Canon reveals some interesting cases involving

extreme values of the penumbral eclipse magnitude.

Seven penumbral eclipses have a maximum magnitude less than 0.0020 (Table 3-11). These events are all the first or last 

members in a Saros series. The smallest magnitude was the penumbral eclipse of –0780 Dec 13 with a magnitude of just 

0.0004.

Table 3-11. Penumbral Lunar Eclipses with Magnitude ≤ 0.0020

Date 

(Dynamical 

Time)

Saros Gamma Penumbral Eclipse 

Magnitude

Penumbral Eclipse 

Duration

–0780 Dec 13 61 –1.5529 0.0004 5.2m

–0411 Jan 23 27 1.5791 0.0013 11.0m

–0331 May 07 74 1.5502 0.0008 7.8m

–0103 Feb 07 80 1.5540 0.0019 12.0m

0859 May 20 112 1.5700 0.0007 8.1m

2027 Jul 18 110 –1.5758 0.0014 11.8m

2791 Feb 11 175 –1.5670 0.0006 7.4m

Table 3-12 lists the nine penumbral eclipses having a maximum magnitude greater than 1.0800. The greatest penumbral 

eclipse occurred on 1322 Nov 24 with a maximum magnitude of 1.0951. Because the penumbral magnitudes of these 

eclipses are all greater than 1, they are classified as total penumbral eclipses, i.e., the Moon is completely immersed within 

the penumbral shadow.

Table 3-12. Total Penumbral Lunar Eclipses with Magnitude ≥ 1.0800 

Date 

(Dynamical 

Time)

Saros Gamma Penumbral Eclipse 

Magnitude

Penumbral Eclipse 

Duration

–1517 Jan 12 0 –0.9901 1.0858 291.2m

–1348 Jan 03 32 0.9948 1.0831 294.4m

–1058 Oct 29 19 0.9917 1.0860 291.6m

0348 Oct 24 90 0.9890 1.0946 296.1m

1322 Nov 24 95 0.9897 1.0951 296.5m

1340 Dec 04 95 0.9970 1.0820 295.1m

1988 Mar 03 113 0.9885 1.0907 293.8m

2429 Dec 11 132 –0.9904 1.0853 290.1m

2732 Apr 02 163 –0.9928 1.0814 293.2m
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 33

LUNAR ECLIPSE STATISTICS

3.6 Extremes in Eclipse Magnitude—Partial Lunar Eclipses

The umbral eclipse magnitude is defined as the fraction of the Moon’s diameter immersed in Earth’s umbral shadow. It is 

a unitless parameter that can be expressed numerically by

Mu = xu/dm (3–2)

where Mu is the umbral eclipse magnitude, dm is the apparent diameter of the Moon, and xu is the distance measured from 

the edge of the umbral shadow to the edge of the Moon deepest in the umbra.

The umbral eclipse magnitude reaches its maximum value at the instant of greatest eclipse. This is the value shown in 

the figures in the Appendix. A search through the 12,064 eclipses in the Canon reveals some interesting cases involving

extreme values of the umbral eclipse magnitude in partial and total lunar eclipses.

Eleven partial eclipses have a maximum magnitude (at greatest eclipse) lessthan or equal to 0.0020 (Table 3-13). The partial

eclipse with the smallest magnitude (at greatest eclipse) occurred on 1553 Jul 25 and had a magnitude of just 0.0001.

Table 3-13. Partial Lunar Eclipses with Magnitude ≤ 0.0020

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Partial Eclipse 

Duration

–0602 May 03 31 0.9940 0.0015 9.7m

–0519 May 15 32 –1.0261 0.0004 4.3m

–0292 Mar 27 66 1.0016 0.0010 7.5m

1050 Feb 09 108 0.9861 0.0013 8.9m

1416 Nov 05 97 1.0107 0.0019 9.9m

1430 Sep 02 128 1.0229 0.0008 6.3m

1553 Jul 25 131 –1.0253 0.0001 2.5m

1890 Nov 26 114 –0.9994 0.0017 9.8m

2157 Feb 24 145 –0.9868 0.0005 5.6m

2421 Jun 16 156 1.0225 0.0011 7.3m

2627 May 22 160 0.9914 0.0011 8.0m

Nine partial eclipses have a maximum magnitude (at greatest eclipse) greater than or equal to 0.9980 (Table 3-14). The 

partial eclipse with the largest magnitude (at greatest eclipse) occurred on –1972 Jun 27 with a magnitude of 0.9998

Table 3-14. Partial Lunar Eclipses with Magnitude ≥ 0.9980 

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Partial Eclipse 

Duration

–1972 Jun 27 –2 –0.4505 0.9998 209.0m

–1021 May 16 24 –0.4758 0.9986 192.6m

–0247 Oct 03 52 –0.4532 0.9988 202.7m

0145 Sep 18 78 0.4511 0.9994 205.0m

0274 Apr 08 65 0.4523 0.9993 207.1m

0778 Sep 11 98 0.4670 0.9993 195.0m

1001 Mar 12 87 0.4728 0.9995 191.1m

1165 May 27 107 –0.4727 0.9986 194.5m

2413 Nov 08 152 0.4733 0.9993 189.5m
 34 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

3.7 Extremes in Eclipse Magnitude—Total Lunar Eclipses

Twelve total eclipses have a maximum magnitude less than or equal to 1.0020 (Table 3-15). The smallest magnitude was 

the total eclipse of 1529 Oct 17 with a value of just 1.0001 (note the upcoming total eclipse of 2015 Apr 04 and its magnitude of 1.0008). Because the Moon’s passage through the umbral shadow is so shallow, these events all have short total 

phases less than 7 min.

Table 3-15. Total Lunar Eclipses with Magnitude ≤ 1.0020

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Total Eclipse 

Duration

–1573 Jan 31 18 0.4776 1.0008 4.2m

–1338 Jun 09 28 0.4622 1.0012 5.5m

–0318 Aug 10 62 0.4474 1.0009 4.9m

–0200 Mar 30 48 –0.4790 1.0019 6.6m

0767 Apr 19 92 0.4581 1.0002 2.4m

0792 Dec 03 96 0.4413 1.0004 3.1m

1529 Oct 17 109 0.4775 1.0001 1.7m

2015 Apr 04 132 0.4460 1.0008 4.7m

2155 Sep 11 130 –0.4752 1.0003 2.6m

2366 May 25 146 0.4817 1.0007 3.9m

2565 Sep 11 156 0.4700 1.0009 4.6m

2905 Jun 08 164 0.4748 1.0018 6.5m

Eight total eclipses have a maximum magnitude greater than or equal to 1.8700. Their total phase durations all last 98 to

99 min and gamma values are all close to 0.0 indicating that the Moon passes centrally through the middle of the umbral 

shadow. These eclipses all take place when the Moon is near perigee—the time when the ratio of the Moon’s to umbra’s 

diameters is at maximum. The total eclipse with the largest magnitude (1.8821) occurs on 2756 Jun 05.

Table 3-16. Total Lunar Eclipses with Magnitude ≥ 1.8700

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Total Eclipse 

Duration

–0731 Apr 19 39 –0.0054 1.8766 99.4m

–0630 Nov 06 45 –0.0002 1.8703 98.3m

–0051 Apr 01 60 –0.0009 1.8774 99.7m

0564 Sep 06 85 0.0017 1.8764 98.9m

1092 Apr 24 97 0.0080 1.8702 99.3m

1226 Aug 09 106 –0.0021 1.8770 99.6m

1631 May 15 115 0.0052 1.8721 99.8m

2756 Jun 05 152 0.0018 1.8821 99.3m

3.8 Greatest Duration—Penumbral Lunar Eclipses

Nine penumbral eclipses each have durations of 292 min or more. Because the penumbral eclipse magnitude of each of 

these events is greater than 1, they are all classified as total penumbral eclipses. Each eclipse in Table 3-17 occurs near 
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 35

LUNAR ECLIPSE STATISTICS

lunar apogee and within several weeks of aphelion. Earth’s penumbra is then largest, while the Moon exhibits a small 

angular diameter and travels relatively slowly, thereby extending the length of the eclipse.

Table 3-17. Penumbral Lunar Eclipses with a Duration ≥ 292 min

Date 

(Dynamical 

Time)

Saros Gamma Penumbral 

Eclipse Magnitude

Penumbral 

Eclipse Duration

–1367 Dec 23 32 1.0089 1.0588 292.2m

–1348 Jan 03 32 0.9948 1.0831 294.4m

0348 Oct 24 90 0.9890 1.0946 296.1m

1322 Nov 24 95 0.9897 1.0951 296.5m

1340 Dec 04 95 0.9970 1.0820 295.1m

1358 Dec 16 95 1.0039 1.0693 293.6m

1376 Dec 26 95 1.0104 1.0569 292.1m

1988 Mar 03 113 0.9885 1.0907 293.8m

2732 Apr 02 163 –0.9928 1.0814 293.2m

3.9 Greatest Duration—Partial Lunar Eclipses

Seven partial eclipses have durations of 209 min or more. All of these events occur with the Moon close to apogee so its

slow trajectory through the umbra tends to prolong the partial phase.

Table 3-18. Partial Lunar Eclipses with a Duration ≥ 209 min

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Partial Eclipse 

Duration

–1274 Jun 21 19 0.4611 0.9768 209.3m

–1133 May 24 22 –0.4592 0.9814 209.6m

–0764 Jan 26 31 0.4540 0.9771 209.1m

–0387 Oct 20 59 –0.4458 0.9908 209.3m

0303 Sep 12 71 0.4510 0.9864 209.6m

1382 Sep 23 117 –0.4458 0.9977 209.6m

2669 Feb 08 144 –0.4424 0.9951 210.0m

3.10 Greatest Duration—Total Lunar Eclipses

Eighteen total eclipses have durations greater than or equal to 106 min. The most recent one was 2000 Jul 16, while the 

next is 2123 Jun 09. All of these eclipses occur near aphelion and with the Moon close to apogee. Consequently, the Moon 

has a small angular diameter coupled with a relatively slow orbital motion with respect to the umbra. Furthermore, the 

umbral shadow is largest when Earth is at aphelion. Such conditions prolong the Moon’s passage through the umbra to 

produce long total lunar eclipses (Meeus, 2002).

Earth’s tropical longitude of perihelion is currently increasing by 1.72° per century. This means that the date of aphelion 

occurred ~17 days earlier for each 1000 years backwards from the present. This too is reflected in the dates seen in Table 

3-19.
 36 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

Table 3-19. Total Lunar Eclipses with a Duration ≥ 106 min

Date 

(Dynamical 

Time)

Saros Gamma Umbral Eclipse 

Magnitude

Total Eclipse 

Duration

–1921 Apr 07 1 0.0302 1.7681 106.2m

–1646 Jun 24 13 0.0164 1.7946 106.3m

–1505 May 27 16 –0.0171 1.7948 106.5m

–1364 Apr 28 19 0.0187 1.7910 106.4m

–0380 Jun 06 53 –0.0308 1.7703 106.2m

–0239 May 09 56 0.0301 1.7713 106.1m

–0098 Apr 11 59 –0.0016 1.8212 106.1m

0054 Aug 07 68 –0.0147 1.7924 106.2m

0177 Jun 28 71 –0.0198 1.7874 106.5m

0318 May 31 74 0.0160 1.7951 106.6m

0459 May 03 77 0.0033 1.8167 106.5m

1443 Jun 12 111 –0.0098 1.8097 106.2m

1584 May 24 114 –0.0065 1.8145 106.1m

1859 Aug 13 126 0.0038 1.8148 106.5m

2000 Jul 16 129 0.0302 1.7684 106.4m

2123 Jun 09 132 0.0406 1.7487 106.1m

2141 Jun 19 132 –0.0446 1.7415 106.1m

2264 May 12 135 0.0121 1.7979 106.2m

3.11 Total Penumbral Lunar Eclipses

During most penumbral eclipses, only part of the Moon passes through Earth’s penumbral shadow. However, it is also possible to have a penumbral eclipse in which the entire Moon passes completely within Earth’s penumbral shadow without 

entering the inner umbral shadow. The geocentric apparent diameter of the Moon ranges from an extreme minimum of 

1763.0 arcsec (apogee) to an extreme maximum of 2011.8 arcsec (perigee). The penumbral annulus formed by the zone 

between the outer edges of the penumbra and umbra also undergoes extremes ranging from 1887.7 arcsec (aphelion) to 

1951.9 arcsec (perihelion). From these values, it is apparent that the Moon cannot fit entirely within the penumbral annulus when it is near perigee (Meeus, 1997). As a consequence of the restrictive geometry and conditions, total penumbral 

eclipses are quite rare and account for just 3.2 %, or 141 out of 4378 penumbral eclipses in the Canon. Table 3-20 lists the 

dates of all 141 total penumbral eclipses.

The frequency of total penumbral eclipse varies considerably with time. If the 5,000-year period covered by the Canon

is divided into 100-year intervals, the number of total penumbral eclipses per century varies from 0 to a maximum of 9 

(Table 3.4). For instance, the number of total penumbral eclipses in centuries beginning in 1701, 1801, and 1901 are 0, 2, 

and 9, respectively. The number of total penumbral eclipses appears to be correlated with the number of total eclipses, 

as well as the number of tetrads per century, and inversely correlated with the overall number of all lunar eclipses per 

century. When a century has a relatively large number of lunar eclipses, it has fewer total lunar eclipses and few or no 

total penumbral lunar eclipses or tetrads (Figure 3.1)
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 37

LUNAR ECLIPSE STATISTICS

Table 3-20. Total Penumbral Lunar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE)

–1989 Dec 01 –1142 Jun 02 –0274 Oct 02 0682 Apr 27 1455 Oct 25 2103 Jan 23

–1981 Jul 07 –1058 Oct 29 –0263 Aug 31 0711 Oct 01 1496 Jul 25 2121 Feb 02

–1971 Dec 12 –1040 Nov 08 –0205 Jan 26 0729 Oct 11 1502 Apr 22 2128 Mar 16

–1953 Dec 23 –1022 Nov 19 –0186 Jun 22 0805 Mar 19 1513 Sep 15 2139 Feb 13

–1840 Jun 08 –1018 Mar 14 –0045 May 25 0816 Aug 11 1542 Aug 25 2222 Aug 23

–1699 May 11 –1007 Aug 07 0096 Apr 26 0822 May 09 1607 Mar 13 2429 Dec 11

–1669 Sep 05 –1004 Nov 30 0154 Sep 09 0823 Sep 24 1637 Jul 07 2447 Dec 22

–1604 Mar 13 –1001 May 05 0197 Nov 12 0862 Sep 12 1665 Jul 27 2458 May 28

–1575 Aug 17 –0986 Dec 11 0215 Nov 24 0945 Mar 31 1806 Jun 30 2466 Jan 01

–1564 Jul 16 –0968 Dec 21 0219 Mar 18 0974 Sep 04 1900 Jun 13 2484 Jan 13

–1558 Apr 13 –0964 Oct 10 0233 Dec 04 0996 Jan 08 1901 May 03 2498 Sep 30

–1517 Jan 12 –0949 Jan 02 0248 Aug 21 1014 Jan 19 1908 Dec 07 2502 Jan 24

–1499 Jan 22 –0946 Oct 21 0251 Dec 15 1032 Jan 30 1926 Dec 19 2520 Feb 04

–1457 Oct 30 –0943 Sep 17 0265 Apr 18 1097 Jul 27 1944 Dec 29 2523 Nov 24

–1452 Jul 08 –0931 Jan 12 0269 Dec 26 1221 May 08 1948 Oct 18 2538 Feb 15

–1439 Nov 10 –0925 Sep 29 0288 Jan 06 1322 Nov 24 1963 Jan 09 2562 Nov 12

–1435 Mar 05 –0860 Apr 06 0312 Oct 02 1340 Dec 04 1981 Jan 20 2656 Oct 25

–1421 Nov 21 –0838 Jul 29 0330 Oct 13 1344 Mar 29 1988 Mar 03 2714 Mar 23

–1406 Aug 09 –0831 Sep 10 0348 Oct 24 1358 Dec 16 1999 Jan 31 2732 Apr 02

–1403 Dec 01 –0755 Feb 15 0388 Mar 09 1373 Sep 02 2006 Mar 14 2761 Sep 06

–1385 Dec 13 –0726 Jul 22 0417 Aug 13 1376 Dec 26 2053 Aug 29 2885 Jun 18

–1367 Dec 23 –0461 Apr 05 0512 Jun 15 1390 Apr 29 2070 Apr 25

–1348 Jan 03 –0432 Sep 08 0653 May 18 1395 Jan 06 2082 Aug 08

–1283 Jun 30 –0356 Feb 14 0681 Jun 07 1413 Jan 17 2099 Sep 29

3.12 Lunar Eclipse Duos

A duo is a pair of eclipses separated by one lunation (synodic month). Of the 12,064 eclipses in the Canon, 3,054 eclipses

(25.3%) belong to a duo. One eclipse of a duo always passes north of Earth’s shadow axis, while the other eclipse passes

to the south. In most cases, both eclipses in a duo are penumbral eclipses; however, there are 51 instances (3.3% of duos)

in the Canon where one eclipse is penumbral and the other is partial. In each of these pairs, the penumbral magnitude of 

the penumbral eclipse is quite small, as is the umbral magnitude of the partial eclipse. The dates and eclipse combinations 

of all lunar eclipse duos are listed in Table 3-21.
 38 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

Table 3-21. Lunar Eclipse Duos of Two Types

–1952 May–Jun – NP –0668 May–Jun – NP 0475 Jun–Jul – NP 1296 Apr–May – NP 2288 Jul–Aug – PN

–1811 Apr–May – NP –0527 Apr–May – NP 0483 Jul–Aug – PN 1427 Apr–May – PN 2411 Jun–Jul – PN

–1774 May–May – PN –0519 May–Jun – PN 0606 May–Jun – PN 1430 Aug–Sep – NP 2429 Jun–Jul – PN

–1670 Mar–Apr – NP –0252 Jul–Jul – NP 0624 Jun–Jul – PN 1553 Jun–Jul – NP 2552 May–Jun – PN

–1492 Mar–Apr – PN –0111 Jun–Jul – NP 0747 Apr–May – PN 1608 Jul–Aug – PN 2819 Jun–Jul – NP

–1358 Jun–Jul – PN –0074 Jun–Jul – PN 0888 Mar–Apr – PN 1694 Jun–Jul – NP 2827 Jul–Aug – PN

–1217 May–Jun – PN 0030 May–Jun – NP 0891 Jul–Aug – NP 1749 Jun–Jul – PN 2960 Jun–Jun – NP

–1076 Apr–May – PN 0067 May–Jun – PN 1014 Jun–Jul – NP 1835 May–Jun – NP

–0935 Mar–Apr – PN 0153 Mar–Apr – NP 1022 Jul–Aug – PN 1958 Apr–May – NP

–0932 Jul–Aug – NP 0208 Apr–May – PN 1155 May–Jun – NP 2013 Apr–May – PN

–0809 Jun–Jul – NP 0428 Jun–Jul – NP 1163 Jun–Jul – PN 2147 Aug–Sep – PN

3.13 Lunar Eclipses Duos in One Calendar Month

There are 57 instances where both members of an eclipse duo occur in one calendar month. In most cases, both eclipses

in the duos are penumbral. In three instances, the duo consists of the NP combination (–1774 May, –0252 Jul, and 2960 

Jun). The year and month of each duo appears in Table 3-22.

Table 3-22. Two Lunar Eclipses in One Calendar Month

–1883 Sep –1033 Jan –0078 Mar 0768 Sep 1694 Dec 2566 Aug

–1861 Jul –0765 Aug 0019 Dec 0790 Jul 1705 Nov 2577 Jul

–1807 Aug –0686 May 0074 Jan 0877 May 1716 Oct 2838 Jan

–1796 Jul –0675 Apr 0269 Jul 1116 Jan 1817 May 2848 Dec

–1785 May –0599 Mar 0291 May 1126 Dec 1904 Mar 2957 Aug

–1774 Jun –0512 Jan 0356 May 1213 Oct 2172 Oct 2960 Jun

–1706 Mar –0502 Dec 0367 Apr 1289 Sep 2208 May 2968 Jul

–1286 Aug –0447 Jan 0443 Mar 1300 Aug 2284 Apr

–1275 Jul –0252 Jul 0595 Jan 1311 Jul 2295 Mar

–1185 Mar –0165 May 0605 Dec 1376 Jul 2382 Jan

3.14 January–March Lunar Eclipse Duos

The mean length of one synodic month is 29.5306 days (in year 2000). Because this is longer than the month of February, 

it is possible to have one member of an eclipse duo in January followed by the second in March. There are six instances 

of such a rare January/March duo in the Canon: –1109, –0523, –0002, 1915, 2306, and 2371. In all cases, both eclipses in 

the duos are penumbral.

3.15 Total Lunar Eclipse Multiplets

A total lunar eclipse is usually preceded or succeeded by at least one other total lunar eclipse. Of the 3479 total eclipses 

in the Canon, 1798 of them (51.7%) are part of a doublet. Another 1023 eclipses (29.4%) belong to a triplet. Finally, 568 

total eclipses (16.3%) are part of a quadruplet known as a tetrad. In comparison, only 90 total eclipses (2.6%) occur as 

solitary singlets.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 39

LUNAR ECLIPSE STATISTICS

A key feature of total lunar eclipse multiplets is that the individual members are always separated by six lunations. A 

summary of the muliplet statistics appears in Table 3-23.

Table 3-23. Total Lunar Eclipse Multiplets

Total Eclipse 

Multiplet

Number of 

Eclipses Per 

Multiplet

Number of 

Multiplets

Number 

of Total 

Eclipses

Percent 

of Total 

Eclipses

Recent Examples

All Total Eclipses – – 3479 100.0 %

Singlet 1 90 90 2.6 % 1997 Sep 16; 2021 May 26

Doublet 2 899 1798 51.7 % 1978; 1996; 2022; 2040

Triplet 3 341 1023 29.4 % 2007 to 2008; 2010 to 2011

Tetrad 4 142 568 16.3 % 2003 to 2004; 2014 to 2015

3.16 Lunar Eclipse Tetrads

When four consecutive lunar eclipses are all total, the group is termed a tetrad. As discussed previously, 16.3% (568 out of 

3479) of all total eclipses are members of a tetrad. These 142 groupings of total eclipses occur because of the eccentricity 

of Earth’s orbit in conjunction with the timing of eclipse seasons (Section 3.18). During the first 1,000 years of the Canon, 

the first eclipse of every tetrad occurs sometime from December to May. In later millennia, the first eclipse date occurs 

later in the year because of precession—during the 3rd Millennium, the period for the first date extends from February to 

July. For a detailed description of tetrad geometry and an explanation of why tetrads happen, see Meeus (2004b).

Italian astronomer Giovanni Schiaparelli first pointed out that the frequency of tetrads is variable over time. He noticed 

that tetrads were relatively plentiful during one 300-year interval, while none occurred during the next 300 years. For example, there are no tetrads from 1582 to 1908, but 17 tetrads occur during the following 2 1⁄2 centuries from 1909 to 2156.

This can be seen graphically in Figure 3-1 (i). The 565-year period of the tetrad “seasons” is tied to the slowly decreasing 

eccentricity of Earth’s orbit. Consequently, the tetrad period is gradually decreasing (Hughes, 2004). In the distant future, 

when Earth’s eccentricity is 0, tetrads will no longer be possible.

The umbral magnitudes of the total eclipses making up a tetrad are all relatively small. For the 300-year period 1901 to 

2200, the largest umbral magnitude of a tetrad eclipse is 1.4251 on 1949 Apr 13. For comparison, some other total eclipses 

during this period are much deeper. Two examples are the total eclipses of 2000 Jul 16 and 2029 Jun 26 with umbral 

magnitudes of 1.7684 and 1.8436, respectively.

Table 3-24 lists the date of the first total lunar eclipse in each of the 142 tetrads in the Canon.
 40 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE STATISTICS

Table 3-24. Date of First Eclipse in Lunar Eclipse Tetrads

–1991 Dec 22 –0999 Mar 14 –0283 Mar 18 0766 Apr 29 1457 Mar 11 2137 Mar 07

–1661 Apr 12 –0981 Mar 25 –0272 Feb 16 0784 May 09 1475 Mar 22 2155 Mar 19

–1643 Apr 22 –0963 Apr 04 –0243 Jan 26 0795 Apr 09 1493 Apr 02 2448 Jun 17

–1625 May 04 –0945 Apr 16 –0225 Feb 06 0802 May 21 1504 Mar 01 2466 Jun 28

–1596 Apr 13 –0923 Feb 12 –0207 Feb 16 0813 Apr 19 1515 Jan 30 2477 May 28

–1585 Mar 13 –0916 Mar 26 –0189 Feb 28 0824 Mar 18 1522 Mar 12 2495 Jun 08

–1578 Apr 24 –0905 Feb 24 –0168 Dec 27 0842 Mar 30 1533 Feb 09 2506 May 08

–1574 Feb 10 –0887 Mar 06 –0149 Jan 07 0860 Apr 09 1562 Jan 20 2524 May 19

–1567 Mar 24 –0876 Feb 03 0162 Apr 17 0878 Apr 20 1580 Jan 31 2542 May 30

–1556 Feb 21 –0869 Mar 17 0180 Apr 27 0889 Mar 21 1909 Jun 04 2564 Mar 29

–1538 Mar 04 –0858 Feb 14 0198 May 08 0900 Feb 18 1927 Jun 15 2571 May 11

–1520 Mar 14 –0847 Jan 14 0227 Apr 19 0918 Feb 28 1949 Apr 13 2582 Apr 09

–1473 Mar 06 –0840 Feb 25 0238 Mar 18 0936 Mar 11 1967 Apr 24 2589 May 21

–1462 Feb 02 –0829 Jan 25 0245 Apr 29 0947 Feb 08 1985 May 04 2600 Apr 20

–1444 Feb 13 –0782 Jan 15 0256 Mar 28 0965 Feb 18 2003 May 16 2611 Mar 20

–1433 Jan 13 –0453 May 06 0267 Feb 26 0976 Jan 19 2014 Apr 15 2618 May 01

–1415 Jan 23 –0377 Apr 06 0285 Mar 08 0994 Jan 30 2032 Apr 25 2629 Mar 31

–1405 Dec 24 –0359 Apr 17 0332 Feb 28 1305 May 09 2043 Mar 25 2640 Feb 29

–1386 Jan 04 –0341 Apr 28 0350 Mar 10 1323 May 21 2050 May 06 2647 Apr 11

–1368 Jan 15 –0330 Mar 28 0361 Feb 06 1341 May 31 2061 Apr 04 2658 Mar 11

–1057 Apr 24 –0319 Feb 24 0390 Jan 17 1352 Apr 30 2072 Mar 04 2676 Mar 22

–1039 May 05 –0312 Apr 07 0408 Jan 29 1370 May 11 2090 Mar 15 2987 Jul 02

–1028 Apr 03 –0301 Mar 07 0437 Jan 08 1399 Apr 20 2101 Feb 14

–1010 Apr 14 –0290 Feb 04 0455 Jan 19 1428 Mar 31 2119 Feb 25

3.17 Lunar Eclipses on February 29

There are six instances of a lunar eclipse occurring on February 29. Two eclipses are penumbral, two are partial, and two 

are total. A list of eclipses on February 29 with physical parameters appears in Table 3-25.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 41

LUNAR ECLIPSE STATISTICS

Table 3-25. Lunar Eclipses on February 29

Date 

(Dynamical 

Time)

Eclipse Type Saros Gamma Umbral Eclipse 

Magnitude

–0664 Feb 29 N 22 –1.3596 0.3819a

–0588 Feb 29 N 62 1.4929 0.1363a

–0124 Feb 29 P 50 –0.5634 0.8114

1420 Feb 29 P 94 –0.9205 0.1614

2268 Feb 29 T– 137 –0.1142 1.6602

2640 Feb 29 T 143 0.3353 1.2478

a. Penumbral Eclipse Magnitude

3.18 Eclipse Seasons

The 5.1° inclination of the lunar orbit around Earth means that the Moon’s orbit crosses the ecliptic at two points or nodes.

If Full Moon takes place within about 17° of a node a, then a lunar eclipse will be visible from a portion of Earth.

The Sun makes one complete circuit of the ecliptic in 365.24 days, so its average angular velocity is 0.99° per day. At this 

rate, it takes 34.5 days for the Sun—and at the opposite node, Earth’s umbral and penumbral shadows—to cross the 34° 

wide eclipse zone centered on each node. Because the Moon’s orbit with respect to the Sun has a mean duration of 29.53 

days, there will always be one, and possibly two, lunar eclipses during each 34.5-day interval when the Sun (and Earth’s

shadows) pass through the nodal eclipse zones. These time periods are called eclipse seasons.

The mid-point of each eclipse season is separated by 173.3 days because this is the mean time for the Sun to travel from 

one node to the next. The period is a little less that half a calendar year because the lunar nodes slowly regress westward 

by 19.3° per year.

3.19 Quincena

The mean time interval between New Moon and Full Moon is 14.77 days. This is less than half the duration of an eclipse 

season. As a consequence, the same Sun–node alignment geometry responsible for producing a lunar eclipse alwaysresults

in a complementary solar eclipse within a fortnight. The solar eclipse may either precede or succeed the lunar eclipse. In 

either case, the pair of eclipses is referred to here as a quincena

b

. The Quincena Solar Eclipse (QSE) parameter identifies 

the type of the solar eclipse and whether it precedes or succeeds a particular lunar eclipse. There are four basic types of

solar eclipses:

1) p = partialsolar eclipse (Moon’s penumbralshadow traverses Earth; umbral/antumbralshadow completely misses 

Earth)

2) a = annular solar eclipse (Moon’s antumbral

c shadow traverses Earth; Moon is too far from Earth to completely 

cover the Sun)

3) t = total solar eclipse (Moon’s umbral shadow traverses Earth; Moon is close enough to Earth to completely cover 

the Sun)

4) h = hybrid solar eclipse (Moon’s umbral and antumbralshadows traverse different parts of Earth; eclipse appears either 

total or annular along different sections of its path—hybrid eclipses are also known as annular-total eclipses)

a. The actual value ranges from 15.3° to 17.1° of a node because of the eccentricity of the Moon's (and Earth's) orbit.

b. Quincena is a Spanish word for a period of about 15 days.

c. The cone-shaped umbra gradually narrows to a point. Extending the sides of the umbra beyond this vertex forms an inverted 

cone. This zone is known as the antumbra. It corresponds to the region in the Moon’s shadow where the Moon appears 

smaller than the Sun. The Moon is then seen in complete silhouette against the Sun’s photospheric disk.
 42 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT

The QSE is a two character string consisting of one or more of the above solar eclipse types. The first character in the QSE 

identifies a solar eclipse preceding a lunar eclipse while the second character identifies a solar eclipse succeeding a lunar 

eclipse. In most instances, one of the two characters is “–” indicating a single solar eclipse either precedes or succeeds 

the lunar eclipse. On rare occasions, a double quincena occurs in which a lunar eclipse is both preceded and succeeded 

by solar eclipses.

3.20 Quincena Combinations with Total Lunar Eclipses

A total lunar eclipse can be preceded or succeeded by a total solar eclipse (7.7%), an annular solar eclipse (10.2%), a hybrid 

solar eclipse (0.4%), or a partial solar eclipse (42.5%). Double quincenas (a lunar eclipse is both preceded and succeeded 

by a solar eclipse) occur with a frequency of 39.1% and usually consist of two partial solar eclipses (38.7%). In rare instances, a double quincena consists of a total and a partial solar eclipse (0.4%). A complete list of all QSE combinations

with total lunar eclipses appears in Table 3-26. The most recent years when each quincena combination occurs are given 

in the last column.

Table 3-26 Quincena Combinations with Total Lunar Eclipses

Quincena Solar 

Eclipse QSE Number Percent Examples (Years)a

– total –t 127 3.7% ..., 1985, 2003, 2043, 2061, 2072,...

total – t– 139 4.0% ..., 1957, 1968, 2015, 2033, 2044,...

– annular –a 178 5.1% ..., 1891, 2003, 2014, 2021, 2032,...

annular – a– 178 5.1% ..., 1990, 2008, 2026, 2044, 2102,...

– hybrid –h 12 0.3% ..., 1627, 1645, 1768, 1909, 2050,...

hybrid – h– 5 0.1% [ –1989, –1848, –1642, 0163, 1986]

– partial –p 730 21.0% ..., 2000, 2007, 2010, 2014, 2018,...

partial – p– 749 21.5% ..., 2001, 2004, 2011, 2015, 2019,...

total – partial tp 8 0.2% ..., –0434, –0159, 1248, 1928, 2912]

partial – total pt 6 0.2% [ –1310, –1169, –1028, –0026, 2195, 2459]

partial – partial pp 1347 38.7% ..., 1982, 2000, 2011, 2018, 2029,...

a. When a year is bounded by a square bracket “[” or “]”, there are no other examples beyond that year.

3.21 Quincena Combinations with Partial Lunar Eclipses

A partial lunar eclipse can be preceded or succeeded by a total solar eclipse (37.6%), an annular solar eclipse (55.1%), or a 

hybrid solar eclipse (6.9%). In rare instances, a partial lunar eclipse can be followed by a partialsolar eclipse (0.3%). Double

quincenas do not occur with partial lunar eclipses. A list of quincena solar eclipse combinations with partial lunar eclipses 

appears in Table 3-27. The most recent years when each quincena combination occurs are given in the last column.
FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 43

ECLIPSES AND THE MOON’S ORBIT

Table 3-27. Quincena Combinations with Partial Lunar Eclipses

Quincena 

Solar Eclipse QSE Number Percent Examples (Years)

– total –t 782 18.6% ..., 1992, 1999, 2010, 2017, 2021,...

total – t– 801 19.0% ..., 2001, 2008, 2019, 2026, 2037,...

– annular –a 1149 27.3% ..., 1995, 2006, 2009, 2013, 2024,...

annular – a– 1171 27.8% ..., 1994, 2005, 2012, 2023, 2030,...

– hybrid –h 167 4.0% ..., 1912, 1930, 2209, 2350, 2368,...

hybrid – h– 124 2.9% ..., 1827, 1845, 2164, 2182, 2323,...

– partial –p 13 0.3% ..., –0754, –0196, 2086, 2607, 2625,...

3.22 Quincena Combinations with Penumbral Lunar Eclipses

A penumbral lunar eclipse can be preceded or succeeded by a total solar eclipse (39.5%), an annular solar eclipse (51.9%), 

or a hybrid solar eclipse (8.7%). There are no instances of a quincena involving a partial solar and a penumbral lunar 

eclipse, nor are there any double quincenas in the Canon. A list of quincena solar eclipse combinations with penumbral 

lunar eclipses appears in Table 3-28. The most recent years when each quincena combination occurs are given in the last

column.

Table 3-28. Quincena Combinations with Penumbral Lunar Eclipses

Quincena 

Solar Eclipse QSE Number Percent Examples (Years)a

– total –t 878 20.1% ..., 2002, 2006, 2009, 2020, 2024,...

total – t– 848 19.4% ..., 1998, 2009, 2012, 2016, 2027,...

– annular –a 1144 26.1% ..., 1999, 2002, 2017, 2020, 2031,...

annular – a– 1128 25.8% ..., 2001, 2002, 2009, 2013, 2016,...

– hybrid –h 176 4.0% ..., 1846, 1908, 2013, 2031, 2049,...

hybrid – h– 204 4.7% ..., 1987, 2005, 2023, 2172, 2190,...

SECTION 4: ECLIPSES AND THE MOON’S ORBIT

4.1 Introduction

The Moon revolves around Earth in an elliptical orbit with a mean eccentricity of 0.0549. Thus, the Moon’s center-tocenter distance from Earth varies with mean values of 363,396 km at perigee to 405,504 km at apogee. The lunar orbital

period with respect to the stars (sidereal month) is 27.32166 days (27d 07h 43m 12s). However, there are three other orbital 

periods or months that are crucial to the understanding and prediction of eclipses. These three cycles and the harmonics 

between them determine when, where, and how solar (and lunar) eclipses occur.

The mutual gravitational force between the Sun and Moon is over twice as large as between the Moon and Earth. For 

this reason, the Sun plays a dominant role in perturbing the Moon’s motion. The ever-changing distances and relative 

positions between the Sun, Moon, and Earth; the inclination of the Moon’s orbit; the oblateness of Earth; and (to a lesser 

extent) the gravitational attraction of the other planets all act to throw the Moon’s orbital parameters into a constant state 

of change. Although the Moon’s position and velocity can be described by the classic Keplerian orbital elements, such 

osculating elements are only valid for a single instant in time (Chapront-Touzé and Chapront, 1991). Nevertheless, these 

instantaneous parameters are of value in understanding the Moon’s complex motions, particularly with respect to the 

three major orbital cycles that govern eclipses.

4.2 Synodic Month

The most familiar lunar cycle is the synodic month because it governs the well-known cycle of the Moon’s phases. The 

Moon has no light of its own, but shines by reflected sunlight. As a consequence, the geometry of its orbital position relative to the Sun and Earth determines the Moon’s apparent phase.

The mean length of the synodic month is 29.53059 days (29d 12h 44m 03s). This is nearly 2.21 days longer than the sidereal month. As the Moon revolves around Earth, both objects also progress in orbit around the Sun. After completing one 

revolution with respect to the stars, the Moon must continue a little farther along its orbit to catch up to the same position it started from relative to the Sun and Earth. This explains why the mean synodic month is longer than the sidereal 

month.

According to astronomical convention, New Moon is defined as the instant when the geocentric ecliptic longitudes of the 

Sun and Moon are equal. When the synodic month is measured from New Moon to New Moon, it is sometimes referred 

to as a lunation, and that usage will be followed here. Historically, the phases of the Moon have been used as the basis of 

lunar calendars by many cultures around the world. The major problem with such calendars is that the year, based on the 

solar calendar, is not evenly divisible by a whole number of lunations. Consequently, most lunar calendars are actually 

lunisolar calendars (e.g., Chinese, Hebrew, and Hindu) that include intercalary months to keep the seasons in step with 

the year.

The duration of the lunation actually varies from its mean value by up to 7 h. For instance, Table 4-1 contains details for 

all lunations in 2008. The first column lists the decimal date of every New Moon throughout the year (Terrestrial Dynamical Time), while the second column gives the duration of each lunation. The third column is the difference between the 

actual and mean lunation. The first lunation of the year (Jan 08) was 03h 23m longer than the mean. Continuing through

2008, the length of each lunation drops and reaches a minimum of 05h 48m shorter than the mean value (Jun 03). The 

duration now increases with each succeeding lunation until the maximum value of the year is reached of 06h 49m longer

than the mean (Dec 27).

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 45

ECLIPSES AND THE MOON’S ORBIT
Table 4-1 New Moon and Lunation Length in 2008

Date of New Moon 

(Dynamical Time)

Length of Lunation Difference From 

Mean Lunation

Moon’s 

True 

Anomaly

 2008 Jan 08.4849 29d 16h 07m +03h 23m 242.4°

 2008 Feb 07.1567 29d 13h 30m +00h 46m 280.0°

 2008 Mar 07.7190 29d 10h 41m –02h 03m 310.8°

 2008 Apr 06.1642 29d 08h 23m –04h 21m 332.7°

2008 May 05.5134 29d 07h 04m –05h 40m 349.4°

 2008 Jun 03.8081 29d 06h 56m –05h 48m 4.4°

 2008 Jul 03.0970 29d 07h 54m –04h 50m 20.1°

 2008 Aug 01.4261 29d 09h 45m –02h 59m 39.2°

 2008 Aug 30.8327 29d 12h 14m –00h 30m 64.9°

 2008 Sep 29.3426 29d 15h 02m +02h 18m 98.7°

 2008 Oct 28.9687 29d 17h 41m +04h 57m 133.4°

 2008 Nov 27.7053 29d 19h 28m +06h 44m 161.9°

 2008 Dec 27.5163 29d 19h 33m +06h 49m 186.6°

What is the cause of this odd behavior? The last column in Table 4-1 gives a clue; it contains the Moon’s true anomaly at 

the instant of New Moon. The true anomaly is the angle between the Moon’s position and the point of perigee along its 

orbit. In other words, it is the orbital longitude of the Moon with respect to perigee. Table 4-1 shows that when New Moon 

occurs near perigee (true anomaly = 0°), the length of the lunation is at a minimum (e.g., Jun 03). Similarly, when New 

Moon occurs near apogee (true anomaly = 180°), the length of the lunation reaches a maximum (e.g., Dec 27).

Thisrelationship is quite apparent when viewed graphically. Figure 4-1 plotsthe difference from mean lunation (histogram)

and the Moon’s true anomaly (diagonal curves) for every New Moon from 2008 through 2010. The left-hand scale is for 

the difference from mean lunation, while the right-hand scale is for the true anomaly. The shortest lunations are clearly 

correlated with New Moon at perigee, while the longest lunations occur at apogee. From the figure, the length of this cycle 

appears to be about 412 days. The reason why must wait until the next section.

The Moon’s orbital period with respect to perigee is the anomalistic month and has a duration of approximately 27.55 days.

The lock-step rhythm between the lunation length and true anomaly can be explained with the help of the anomalistic 

month and Figure 4-2. It illustrates the Moon’s orbit around Earth and Earth’s orbit around the Sun. The relative sizes and 

distances of the Sun, Moon, and Earth, as well as the eccentricity of the Moon’s orbit are all exaggerated for clarity. The

major axis of the Moon’s orbit marks the positions of perigee and apogee.

 46 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT
Year

 -8

 -6

 -4

 -2

 0

 2

 4

 6

 8

Difference from Mean Lunation (hours) 

[mean = 29d 12h 44m 03s]

Figure 4–1: Length of Lunation for 2008 – 2010 

 2008 2009 2010 2011

 0°

 90°

 180°

 270°

 360°

True Anomaly at New Moon

difference from 

mean lunation 

True Anomaly

at New Moon

Sun

Orbit of Earth

New Moon

New Moon

New Moon

New Moon

A

B

C

D

Earth

Line of Apsides

(Direction of Perigee)

Moon

Case 1: 

New Moon

Near Perigee

Case 2: 

New Moon

Near Apogee

b1

b2

b

d1

d2

d

a1 c1

Figure 4–2: Moon's Orbit and the Synodic Month

Orbit of Moon

Two distinct cases—each consisting of two revolutions of the Moon around Earth—are depicted in Figure 4-2. The first 

case covers the New Moon geometry around perigee. The orbit marked A shows New Moon taking place near perigee at 

position a1. One anomalistic month later (orbit B), the Moon has returned to the same position relative to perigee (marked 

b1). However, Earth has traveled about 30° around its orbit so the Sun’s direction relative to the Moon’s major axis has 

shifted. The Moon must travel an additional distance of $b in its orbit before reaching the New Moon phase at b2. This 

graphically demonstrates why the synodic month is longer (~1.98 days) than the anomalistic month.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 47

ECLIPSES AND THE MOON’S ORBIT
The second case takes place about half a year later. New Moon then occurs near apogee (orbit C, position c1). After one 

anomalistic month, the Moon has returned to the same location with respect to apogee (orbit D, position d1). Once again, 

Earth has traveled about 30° around its orbit so the Moon must revolve an additional distance of ∆d before reaching the

New Moon phase at position d2.

An inspection of orbits B and D reveals that the orbital arc $d is longer that $b. This means that the Moon must cover a 

greater orbital distance to reach New Moon near apogee as compared to perigee. Furthermore, the Moon’s orbital velocity 

is slower at apogee so it takes longer to travel a given distance. Thus, the length of the lunation is shorter than average 

when New Moon occurs near perigee, and longer than average when New Moon occurs near apogee.

Earth’s elliptical orbit around the Sun also factors into the length of the lunation. With an eccentricity of 0.0167, Earth’s

orbit is about one third as elliptical as the Moon’s orbit. Nevertheless, it affects the length of the lunation by producing 

shorter lunations near aphelion, and longer lunations near perihelion.

During the 5000-year period covered in the Canon, there are 61,841 complete lunations. The shortest lunation began on 

–1602 Jun 03 and lasted 29.26574 days (29d 06h 22m 40s; 6h 21m 23s shorter than the mean). The longest lunation began

on –1868 Nov 27 and lasted 29.84089 days (29d 20h 10m 53s; 7h 26m 50s longer than the mean). Thus, the duration of 

the lunation varies over a range of 13h 48m 13s during this time interval.

The histogram presented in Figure 4-3 shows the distribution in the length of the lunation over 5000 years. To create the

histogram, the durations of individual lunations were binned into 30-minute groups. It might seem reasonable to expect 

a simple bell-shaped Gaussian curve. However, the results are surprising because the distribution in lunation length has 

two distinct peaks. This bifurcation can be understood if the lunation length, which depends primarily on the Moon’s 

distance, is considered as a series of sine functions. The extremes of a sine function always occur more frequently than 

the mean, which is just what is seen in Figure 4-3. For a more detailed discussion, see Meeus (1997).

 -8 -6 -4 -2 0 2 4 6 8

 0

 500

 1000

 1500

 2000 Number

Difference from Mean Lunation (hours) 

[mean = 29d 12h 44m 03s]

Figure 4–3: Length of Lunation Over 5000 Years

61,841 Lunations from 

2000 BCE to 3000 CE

Mean Lunation 

29d 12h 44m 03s

4.3 Anomalistic Month

The anomalistic month is defined as the revolution of the Moon around its elliptical orbit as measured from perigee to 

perigee. The length of this period can vary by several days from its mean value of 27.55455 days (27d 13h 18m 33s).

 48 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT
Figure 4-4 plots the difference of the anomalistic month from the mean value for the 3-year interval 2008 through 2010.

Also plotted is the difference between the mean longitudes of the Sun and perigee. This is just the angle between the Sun 

and the Moon’s major axis in the direction of perigee. The left-hand scale is the length of the anomalistic month minus 

the mean value, while the right-hand scale is for the difference in longitude (Sun–perigee). For comparison, the lunation 

length minus its mean value is also plotted (light gray).

 2008 2009 2010 2011

 0°

 90°

 180°

 270°

 360°

 Difference in Mean Longitude (Sun - Perigee) 

 2008 2009 2010 2011

 0°

 90°

 180°

 270°

 360°

 Difference in Mean Longitude (Sun - Perigee) 

difference from 

mean anomalistic 

month difference from 

mean lunation 

difference in

mean longitude

(Sun - Perigee)

Difference from Mean Anomalistic Month (days)

[mean = 27d 13h 18m 33s]

Figure 4–4: Length of Anomalistic Month for 2008 – 2010 

The variation in the length of the anomalistic month is much larger than that of the lunation. Figure 4-4 shows the 

anomalistic month is typically within 1 day of its mean value. Once or twice every 7 to 8 months, however, the anomalistic month is significantly shorter than the mean by two to nearly three days. The difference in longitude of the Sun and 

perigee show that the shortest anomalistic months are correlated with values of 90° and 270°, when the line of apsides is 

perpendicular to the Sun’s direction.

In comparison, the longest anomalistic months take place when the difference in longitude passes through 0° or 180°.

The line of apsides is then directed towards, or away, from the Sun. The maximum duration of the anomalistic month is 

then about 28.5 days (1.0 day longer than the mean). The Earth–Sun distance also influences the anomalistic month by 

causing greater extremes near perihelion. This currently occurs in early January each year.

In an earlier discussion on the synodic month, it was assumed that the lunar orbit’s line of apsides has a fixed and permanent direction in space. In fact, the length of the mean anomalistic month (27.55 days) exceeds the mean sidereal month 

(27.32 days) by 0.23 days. Thus, the Moon’s major axis slowly shifts with a mean rate of 0.11140° per day in the direct 

sense, that is, in the same direction as the Moon’s orbital motion. This corresponds to an average of 40.7° per year, so it 

takes 8.85 years (3231.6 days) for the line of apsides to make one complete revolution with respect to the stars.

What impact do the varying length of the anomalistic month and the direct (eastward) rotation of the Moon’s elliptical orbit

have on the length of the lunation? To answer this, one must first consider Earth’s elliptical orbit around the Sun, which

has a mean eccentricity of 0.0167. The center-to-center distance between Earth and the Sun varies with mean values of 

147,098,074 km at perihelion, to 152,097,701 km at aphelion. The direction of Earth’s orbital line of apsides also changes,

but at a rate far slower than the Moon’s. Having a direct (eastward) shift with a mean value of 0.0172° per year, it takes 

about 20,500 years for Earth’s major axis to make one complete revolution. This is only 0.0004 of the lunar rate, so it can 

be treated as fixed for the purpose of the following discussion.

At certain times, the perigee of the lunar orbit and the perihelion of Earth’s orbit can have the same ecliptic longitude.

Ignoring the 5.1° tilt of the Moon’s obit, the major axes are then essentially parallel to each other and point in the same 

direction. As time passes, the major axis of the lunar orbit slowly rotates east with respect to Earth’s major axis until it 

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 49

ECLIPSES AND THE MOON’S ORBIT
becomes perpendicular to it 2.21 years later. In another 2.21 years (4.42 years from the start), the major axes of the orbits

are again parallel to each other, but the perigee and the perihelion are 180° apart as they point in opposite directions. After 

an additional period of 2.21 years, the axes are once more perpendicular. Finally, the Moon’s perigee and Earth’s perihelion 

again share the same ecliptic longitude after a total interval of 8.85 years.

The length of each lunation minus the mean lunation is plotted in Figure 4-5 for the 20-year period from 2008 through 

2027. The periodic rhythm between the lunation length and the true anomaly, as described earlier (via Figure 4-1), can 

now be seen over the course of two decades. The 412-day mean period of this cycle corresponds to the time between two 

consecutive alignments of the major axis in the direction of the Sun. It is slightly longer than a year because of the slow 

eastward shift of the Moon’s major axis.

 2010 2015 2020 2025

 0°

 90°

 180°

 270°

 360°

Difference in Longitude of Perigee & Perihelion

Year

Figure 4–5: Length of Lunation for 2008 – 2027

 -8

 -6

 -4

 -2

 0

 2

 4

 6

 8

Difference from Mean Lunation (hours) 

[mean = 29d 12h 44m 03s]

difference in mean longitude 

of perigee & perihelion

difference from 

mean lunation 

difference in true longitude 

of perigee & perihelion

An interesting feature revealed in Figure 4-5 is how the extremes in the lunation length slowly vary over a period of nearly 

9 years. The envelope defined by the minima and maxima appears to oscillate over a range of values from ±2 h to ±6 h. 

This behavior is evidence revealing the influence of the 8.85-year cycle in the alignment of the major axes of the orbits of 

the Moon and Earth.

The amplitude of the envelope is due to the eccentricity of Earth’s orbit. When Earth is at perihelion, its orbital velocity is 

at its maximum value so Earth travels a larger distance around its orbit in a given time as compared to aphelion. Thus, the 

Moon must travel a greater distance to align with the Sun, which results in a longer lunation. Near aphelion, the opposite

conditions produce a shorter lunation.

Using the axis scale on the right, the diagonal lines in Figure 4-5 plot the angle between the Moon’s perigee and Earth’s 

perihelion. This is the difference between the Moon’s mean longitude of perigee and Earth’s true longitude of perihelion.

When the angle between the perigee and perihelion is 0°, the length of the lunation varies from a minimum of 29.273 days 

(–6.17 hours from mean) to a maximum of 29.820 days (+6.93 hours from mean). Similarly, when the angle between the 

perigee and perihelion is 180°, the length of the lunation varies from a minimum of 29.452 days (–1.88 hours from mean) 

to a maximum of 29.628 days (+2.33 hours from mean). To summarize, the greatest extremes in the length of the lunation 

occur when the longitudes of the Moon’s perigee and Earth’s perihelion are equal. The smallest extremes in the lunation

length occur when their longitudes differ by 180°.

Although the Moon’s major axis rotates eastward at a mean rate of 0.1114° per day, the true rate varies considerably. Figure 

4-5 illustrates the variation by plotting the difference between the true longitudes of the Moon’s perigee and Earth’s perihelion. This quasi-sinusoidal oscillation about the difference in the mean longitudes shows peak departures of ±30° from 

 50 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT
average. Indeed, the Moon’s major axis can swing both east and west of its mean value, taking on an actual retrograde 

shift west during some anomalistic months.

This dynamic behavior is due to the gravitational pull of the Sun on the Moon as it orbits Earth. Consequently, a continuous torque is applied to the lunar orbit in an unsuccessful effort to permanently align the major axis towards the Sun. The 

annual orbit of the Earth–Moon system around the Sun coupled with the Moon’s synodic orbit around Earth mean that 

the conditions for such a permanent alignment are always changing. The overall effect is to twist and distort the shape 

and orientation of the Moon’s elliptical orbit.

It was stated earlier that the Moon’s mean orbital eccentricity is 0.0549, but this too is subject to large changes because of 

solar perturbations. Figure 4-6 plots the variation in the Moon’s orbital eccentricity from 2008 through 2010. The instantaneous eccentricity (light gray curve) oscillates with a period tied to the synodic month and ranges from 0.0266 to 0.0762 

over this 3-year interval. Superimposed on the instantaneous eccentricity isthe eccentricity at the instant of perigee, which

occurs at the beginning of each anomalistic month (heavy black curve). The straight diagonal linesrepresent the difference

between the mean longitudes of the Sun and perigee. In other words, it is the angle between the Moon’s perigee-directed 

major axis and the Sun. Oscillating about this line is the difference between the true longitudes of Sun and perigee. The 

scale for these angles appears along the right side of Figure 4-6. The extreme range of the Moon’s orbital eccentricity at 

perigee during the 5000 years of the Canon is 0.0255 to 0.0775.

 0.00

 0.02

 0.04

 0.06

 0.08

 0.10 Eccentricity

 2008 2009 2010 2011

Year

 90°

 180°

 270°

 360°

Difference in Longitude (Sun - Perigee)

 0.00 0°

 0.02

 0.04

 0.06

 0.08

 0.10 Eccentricity

eccentricity

at perigee

instantaneous

eccentricity

Figure 4–6: Moon's Eccentricity for 2008 – 2010

difference in

mean longitude

(Sun - Perigee)

difference in

true longitude

(Sun - Perigee)

Figure 4-6 showsthat the eccentricity reaches a maximum when the major axis of the lunar orbit is pointed directly towards

or directly away from the Sun (angles of 0° and 180°, respectively). This occurs at a mean interval of 205.9 days, which 

is somewhat longer than half a year because of the eastward shift of the major axis. The eccentricity reaches a minimum 

when the major axis of the lunar orbit is perpendicular to the Sun (angles of 90° and 270°).

Such changes in orbital eccentricity produce significant variations in the Moon’s distance at perigee and apogee. Figure 

4-7 plots the Moon’s distance for all perigees and apogees from 2008 through 2010. Also shown is the orbital eccentricity 

at perigee as well as the angle between the perigee directed major axis and the Sun. The closest perigee (minimum perigee 

distance) and farthest apogee (maximum apogee distance) occur when the eccentricity is at maximum. This corresponds 

to times when the Moon’s major axis points directly towards or directly away from the Sun (angles of 0° and 180°, respectively). The farthest perigee (maximum perigee distance) and closest apogee (minimum apogee distance) occur when the 

eccentricity is at minimum. At such times, the major axis is oriented perpendicular to the Sun. During the 3-year interval 

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 51

ECLIPSES AND THE MOON’S ORBIT
covered in Figure 4-7, the Moon’s perigee distance ranges from 356,568 to 370,216 km while the apogee distance ranges 

from 404,168 to 406,602 km.

difference in

mean longitude

(Sun - Perigee)

 90°

 180°

 270°

 360°

Difference in Longitude (Sun - Perigee)

 0°

eccentricity

at perigee

 380

 350

 360

 370

 390

 400

 410 Distance of Moon ( x 1000 km )

perigee

apogee

 2008 2009 2010 2011

Year

Figure 4–7: Perigee & Apogee for 2008 – 2010

Over the 5000-year period of the Canon, there are 66,276 perigees and apogees. During this epoch, the distance of the 

Moon’s perigee variesfrom 356,355 to 370,399 km while the apogee variesfrom 404,042 to 406,725 km. The minimum and

maximum extremes in orbital eccentricity are 0.0255 to 0.0775 and the extremes in the length of the anomalistic month are 

24.629 days (2.925 days shorter than the mean) to 28.565 days (1.011 days longer than the mean). A histogram showing the 

distribution in the length of the anomalistic month is presented in Figure 4-8 where the durations of individual anomalistic 

months have been binned into 2-hour groups. The sharply asymmetric distribution shows that anomalistic months longer 

than the mean cluster over a much shorter range of values compared to anomalistic months shorter than the mean. Number

 -80 -60 -40 -20 0 20 40

 0

 2000

 4000

 6000

 8000

 10000

Difference from Mean Anomalistic Month (hours)

[mean = 27d 13h 18m 33s]

Figure 4–8: Length of Anomalistic Month Over 5000 Years

66,276 Anomalistic Months from 

2000 BCE to 3000 CE

Mean Anomalistic Month

27d 13h 18m 33s

4.4 Draconic Month 

The plane of the Moon’s orbit is inclined at a mean angle of 5.145° to the plane of Earth’s orbit around the Sun. The intersection of these planes defines two points or nodes on the celestial sphere. The node where the Moon’s path crosses the 

 52 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT
ecliptic from south to north is the ascending node, while the node where the Moon’s path crosses the ecliptic from north 

to south is the descending node.

The draconic month is defined as one revolution of the Moon about its orbit with respect to the ascending node. The mean 

length of this nodical period is 27.21222 days (27d 05h 05m 36s). However, the actual duration can vary by over 6 h from 

the mean. Figure 4-9 plots the duration of the draconic month minus its mean value for 2008 through 2010. The shortest

month over this 3-year period is 27.05115 days (27d 01h 14m), while the longest month is 27.38409 days (27d 09h 13m).

 2008 2009 2010 2011

Year

 -6

 -4

 -2

 0

 2

 4

 6

Difference from Mean Draconic Month (hours)

[mean = 27d 05h 05m 36s]

Figure 4–9: Length of Draconic Month for 2008 – 2010

 2008 2009 2010 2011

Year

 0°

 90°

 180°

 270°

 360°

Difference in Mean Longitude (Sun - Ascending Node)

difference from 

mean draconic 

month

difference in

mean longitude

(Sun - Asc. Node)

The most significant characteristic of this variation is that it is synchronized with the ascending node relative to the Sun’s 

position along the ecliptic. The mean angle between the Sun and the ascending node (i.e., difference in mean longitude) is 

also plotted in Figure 4-9 (diagonal lines) to illustrate thisrelationship. The longitude difference at the start of each draconic

month is plotted as a black dot. Longitude values can be read using the scale along the right side of the figure. The longest 

draconic months occur when the difference in the mean longitudes of the Sun and the ascending node is either 0° or 180°.

In contrast, the shortest months occur when the angle between the Sun and the ascending node is either 90° or 270°.

The mean draconic month is 0.10944 day (2h 36m 36s)shorter than the sidereal month. Consequently, the lunar nodesslowly

rotate west or retrograde (opposite the Moon’s orbital motion) along the ecliptic at a rate of 0.05295° per day. One complete 

rotation of the ascending node about the ecliptic requires 18.6 years (6793.48 days) with respect to the fixed stars.

Figure 4-10 plotsthe instantaneousinclination of the lunar orbit over the 3-year period 2008–2010. The mean angle between

the Sun and the ascending node (i.e., difference in mean longitude) is also plotted. The largest inclination of 5.30° occurs 

when the difference in longitude is either 0° or 180°. In other words, the inclination is always near its maximum value for 

both solar and lunar eclipses. The smallest inclination of 5.00° occurs when the difference in longitude is either 90° or 

270°. Note the small monthly oscillations in the inclination when near its minimum. The figure also plots the longitude 

of the instantaneous ascending node. Its westward motion draws to a near standstill whenever the Sun aligns with either

of the nodes. This corresponds to a difference in longitude of either 0° or 180°.

The mean interval in the periodic variation of both the draconic month and the orbital inclination is 173.3 days. This is the 

average time it takes for the Sun to travel from one node to the other. It is also equivalent to the interval between the midpoints of two eclipse seasons. The period is slightly less than half a year because of the retrograde motion of the nodes.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 53

ECLIPSES AND THE MOON’S ORBIT
 2008 2009 2010 2011

Year

 0°

 90°

 180°

 270°

 360°

Difference in Mean Longitude (Sun - Ascending Node)

 2008 2009 2010 2011

Year

 4.9°

 5.0°

 5.1°

 5.2°

 5.3°

 5.4°

Inclination

[mean = 5.145°]

instantaneous 

inclnation

difference in

mean longitude

(Sun - Asc. Node)

Figure 4–10: Lunar Orbit Inclination for 2008 – 2010

instantaneous 

ascending node

The length of the draconic month is strongly modulated by the position of the nodes with respect to the major axis of the 

Moon’s orbit. The histogram in Figure 4-11 shows how the draconic month changes from 2008 through 2017. The 173-day 

alignment of the Sun with a node appears as the rapid oscillation in the month length. The quasi-sinusoidal envelopes 

surrounding the minima and maxima form two longer period oscillations. Over the 10-year period covered in this figure, 

the minimum month duration varies from 27.089 to 27.011 days (3.0 to 4.8 hours shorter than the mean). The maximum 

month duration ranges from 27.261 to 27.472 days (1.2 to 6.2 hours longer than the mean).

 2008 2013 2018

Year

 -8

 -6

 -4

 -2

 0

 2

 4

 6

 8

Difference from Mean Draconic Month (hours)

[mean = 27d 05h 05m 36s]

 2008 2013 2018

Year

0°

 90°

 180°

 270°

 360°

Difference in Mean Longitude (Perigee - Ascending Node)

difference from 

mean draconic 

month

difference in

mean longitude

(Perigee - Asc. Node)

Figure 4–11: Draconic Month and Perigee for 2008 – 2017

The difference in the mean longitudes of perigee and the ascending node appear as diagonal lines in Figure 4-11. This 

is the angle between these orbital parameters measured along the ecliptic. The greatest extremes in the draconic month 

occur when the angle between perigee and the ascending node is 0°. Likewise, the smallest extremes of the month take 

place when the difference in longitude is 180°. The mean rates of the major axis and the ascending node are 0.11140° east 

and 0.05295° west per day, respectively. Therefore, the mean period between alignments of the axis and node is 2190.4 

days or 6.0 years. This period is clearly seen in Figure 4-11.

 54 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

 ECLIPSES AND THE MOON’S ORBIT
There are 67,111 draconic months during the 5000 years covered in the Canon. The shortest and longest months are 27.004 

days (0.208 days or 5.0 hours shorter than the mean) and 27.487 days (0.275 days or 6.6 hours longer than the mean), 

respectively. A histogram of the distribution in the length of the draconic month over the five millennia appears in Figure 

4-12 where the duration of individual draconic months have been binned into 30-min groups. The width and bifurcated 

symmetry of the distribution resemble the distribution for the lunation (synodic month) in Figure 4-4.

 -8 -6 -4 -2 0 2 4 6 8

 0

 1000

 2000

 3000 Number

Difference from Mean Draconic Month (hours)

[mean = 27d 05h 05m 36s]

Figure 4–12: Length of Draconic Month Over 5000 Years

67,111 Draconic Months from 

2000 BCE to 3000 CE

Mean Draconic Month

27d 05h 05m 36s

4.5 Eclipse Cycles

The interaction and harmonics of the synodic, anomalistic, and draconic months not only determine how frequently eclipses

occur, but they also control the geometric characteristics and classification of each eclipse. The commensurability of these 

periods over long time scales results in several important eclipse cycles, which will be the subject of the next section.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 55

ECLIPSES AND THE MOON’S ORBIT

SECTION 5: LUNAR ECLIPSE PERIODICITY

5.1 Interval Between Two Successive Lunar Eclipses

The time interval between any two successive lunar eclipses can be either 1, 5, or 6 lunations (synodic months). The distribution of these 12,063 intervals in the Canon is found in Table 5-1.

Table 5-1. Interval Between Successive Eclipses

Number of 

Lunations

Number of 

Eclipses

Percent

1 1,527 12.7%

5 2,909 24.1%

6 7,627 63.2%

5.2 Lunar Eclipse Repetition

Lunar eclipses separated by 1, 5, or 6 lunations are usually quite dissimilar. They are frequently of unlike types (i.e., 

penumbral, partial, or total) with diverse Sun–Moon–Earth alignment geometries, and with different lunar orbital characteristics (i.e., longitude of perigee and longitude of ascending node). More importantly, these short periods are of no 

value as predictors of future eclipses because they do not repeat in a recognizable pattern.

A simple lunar eclipse repetition cycle can be found by requiring that certain orbital parameters be repeated. The Moon 

must be in the full phase with the same longitude of perigee and same longitude of the ascending node. These conditions 

are met by searching for an integral multiple in the Moon’s three major periods—the synodic, anomalistic, and draconic

months. A fourth condition might require that an eclipse occur at approximately the same time of year to preserve the 

axial tilt of Earth and thus, the same season, as well as the distance from the Sun. This last factor controls the apparent 

diameter of Earth’s umbral and penumbral shadows.

5.3 Saros

The Saros arises from a harmonic between three of the Moon’s orbital cycles. All three periods are subject to slow variations over long time scales, but their values as of 2000 CE are:

Synodic Month (New Moon to New Moon) = 29.530589 days = 29d 12h 44m 03s

Anomalistic Month (perigee to perigee) = 27.554550 days = 27d 13h 18m 33s

Draconic Month (node to node) = 27.212221 days = 27d 05h 05m 36s

One Saros is equal to 223 synodic months, however, 239 anomalistic months and 242 draconic months are also equal 

(within a few hours) to this same period:

223 Synodic Months = 6585.3223 days = 6585d 07h 43m

239 Anomalistic Months = 6585.5375 days = 6585d 12h 54m

242 Draconic Months = 6585.3575 days = 6585d 08h 35m

With a period of approximately 6,585.32 days (~18 years 11 days 8 hours), the Saros is a valuable tool in investigating the 

periodicity and recurrence of eclipses. It was first known to the Chaldeans as an interval when lunar eclipses repeat, but

the Saros is applicable to solar eclipses as well.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 57

LUNAR ECLIPSE PERIODICITY
Any two eclipses separated by one Saros cycle share similar characteristics. They occur at the same node with the Moon 

at nearly the same distance from Earth and the same time of year. Because the Saros period is not equal to a whole number of days, its biggest drawback as an eclipse predictor is that subsequent eclipses are visible from different parts of the 

globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120° with each cycle. For

lunar eclipses, this results in a shift ~120° west in the visibility zones of each succeeding eclipse. Thus, a Saros series 

returns to approximately the same geographic region every three Saros periods (~54 years and 34 days). This triple Saros 

cycle is known as the Exeligmos.

Partial 1932 Sep 14

Saros 136 21:01 TD 

Par. = 204m

P.Mag. = 2.0296 

U.Mag. = 0.9752 

Gam. = 0.4664 

Total 1950 Sep 26

Saros 136 04:17 TD 

Par. = 210m

Tot. = 44m

P.Mag. = 2.1331 

U.Mag. = 1.0783 

Gam. = 0.4101 

Total 1968 Oct 06

Saros 136 11:43 TD 

Par. = 214m

Tot. = 63m

P.Mag. = 2.2242 

U.Mag. = 1.1691 

Gam. = 0.3605 

Total 1986 Oct 17

Saros 136 19:19 TD 

Par. = 217m

Tot. = 74m

P.Mag. = 2.3008 

U.Mag. = 1.2455 

Gam. = 0.3188 

Total 2004 Oct 28

Saros 136 03:05 TD 

Par. = 219m

Tot. = 80m

P.Mag. = 2.3637 

U.Mag. = 1.3081 

Gam. = 0.2846 

Total + 2022 Nov 08

Saros 136 11:00 TD 

Par. = 220m

Tot. = 85m

P.Mag. = 2.4143 

U.Mag. = 1.3589 

Gam. = 0.2570 

Figure 5–1. Lunar Eclipses from Saros 136: 1932 to 2022

1 Saros 1 Saros 

3 Saros = 1 Exeligmos

Figure 5-1 shows the path of the Moon through Earth’s shadows and the geographic regions of visibility for six lunar 

eclipses belonging to Saros 136 from 1932 through 2022. The 1932 Sep 14 eclipse was a large magnitude partial eclipse 

with a visibility zone centered on eastern Europe and Africa. One Saros period later the eclipse was total (1950 Sep 26)

with visibility centered on the Americas. After another Saros interval, the eclipse was a larger magnitude event centered 

on the Pacific Ocean (1968 Oct 06). Finally, after the lapse of one more Saros period (3 Saros = Exeligmos = ~54.1 years), 

the zone of visibility returned to eastern Europe and Africa with a deeper non-central total lunar eclipse (1986 Oct 17).

The same 54.1-year time interval in geographic visibility repeats for the Americas (1950 and 2004) and for the Pacific 

(1968 and 2022). The westward migration in the zone of eclipse visibility illustrates the effect of the extra 1/3-day in the

Saros period. The southward shift of the Moon’s path with respect to the shadow axis is due to the progressive decrease in 

gamma from 0.4664 (1932) to 0.2570 (2022). During this interval, lunar eclipses in the series change from partial (1932) 

to non-central total (1950) to central total (2022). Although the Moon’s path through Earth’s shadows is similar from 

 58 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
one eclipse to the next, it is not exact. The Moon-shadow geometry changes slowly as do the characteristics of each lunar 

eclipse in a Saros series.

Sarosseries do not last indefinitely because the synodic, draconic, and anomalistic months are not perfectly commensurate

with one another. In particular, the Moon’s node shifts eastward by about 0.48° with each eclipse in a series. The following 

narrative describes the life cycle of a typical Saros series at the Moon’s ascending node. The series begins when the Full 

Moon occurs approximately 17° east of the node.

A small fraction of the Moon’s disk passes through the northern edge of the penumbra and a small penumbral eclipse 

occurs. One Saros period later, the lunar trajectory shifts a little further south, the Moon passes deeper into the penumbra (gamma decreases) and a penumbral eclipse of slightly larger magnitude results. After ~10 penumbral eclipses, the 

first partial lunar eclipse occurs as the Moon’s southern limb passes through the umbra. Around 20 more partial eclipses

occur as the Moon swings increasingly deeper into the umbra after each Saros and the magnitude of each event grows 

larger. Finally, the Moon passes completely into the umbra and a shallow total eclipse occurs. Over the course of the next 

2 centuries, a total lunar eclipse occurs every 18.031 years (= Saros), as the Moon is displaced progressively southward 

through the umbral shadow with each eclipse. Halfway through this period, the Moon passes through the center of the 

umbra producing long total eclipses. The last of ~13 total eclipses in the series takes place just inside the southern edge 

of the umbra. The Saros series winds down now with another string of ~20 partial eclipses following by a final set of ~10 

penumbral eclipses. The last eclipse of the series is a small magnitude penumbral event just inside the southern edge of 

the penumbral shadow. In all, this typical Saros series produces 73 eclipses spanning nearly 13 centuries.

The scenario for a Saros series occurring at the Moon’s descending node is similar except that gamma increases as each 

successive eclipse shifts the Moon’s trajectory farther north of the previous one. The magnitude of the shift in gamma is 

again tied to aphelion and perihelion.

Because of the ellipticity of the orbits of Earth and the Moon, the exact duration and number of eclipses in a complete 

Saros series is not constant. A series may last 1,226 to 1,587 years and is composed of 69 to 89 eclipses. A series can begin 

with 6 to 25 penumbral eclipses, followed by 6 to 24 partial eclipses. During the mid-life of a Saros series, there are 11 

to 29 total eclipses. Finally, a series ends with 6 to 24 partial eclipses followed by 7 to 25 penumbral eclipses. At present 

(2008), there are 40 active Saros series numbered 110 to 149. The number of eclipses in each of these series ranges from 

70 to 83, however, the majority of them (80%) are composed of 70 to 73 eclipses.

5.4 Gamma and Saros Series

Gamma changes monotonically throughout any single Saros series. As mentioned previously (Sect. 1.2.6), the change in 

gamma is larger when Earth is near its aphelion (June to July) than when it is near perihelion (December to January). For 

odd numbered series (descending node), gamma increases, while for even numbered series (ascending node), gamma decreases. This simple rule describes the current behavior of gamma, but this has not always been the case. The eccentricity 

of Earth’s orbit is presently 0.0167, and is slowly decreasing. It was 0.0181 in the year –2000 and will be 0.0163 in +3000.

In the past, when the eccentricity was larger, there were Saros series in which the trend in gamma reversed for one or 

more Saros cycles before resuming its original direction. These instances occur near perihelion when the Sun’s apparent

motion is highest and may, in fact, overtake the eastward shift of the node. The resulting effect is a relative shift west of 

the node after one Saros cycle instead of the usual eastward shift. Consequently, gamma reverses direction.

The most unusual case of this occurs in Saros series 13. It began in –2313 with 11 penumbral eclipses, followed by 7 

partial eclipses. The series then reverted back to 3 more penumbral eclipse followed by another 11 partial eclipses. The 

series then produced 13 total, 20 partial, and 8 penumbral eclipses. To understand this odd behavior we must look to 

gamma. The value of gamma increased positively for the first 15 eclipses of the series. It then reversed direction after 

the fifth partial and decreased for 5 sequential eclipses while changing from partial back to penumbral. Finally resuming 

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 59

LUNAR ECLIPSE PERIODICITY
its northward motion, gamma began to increase again and continued to do so for the remainder of the series. Saros 13 

produced 73 ending in the year –1015.

Among 200 Saros series examined (–20 to 183), there are many other examples of temporary shifts in the monotonic 

nature of gamma, although none as unusual as Saros 13. In fact, the first 38 Saros series (series –20 to 17) with members 

represented in the Canon, experience short reversals in gamma. The reversals are short and rarely last for more than four 

or five eclipses in a series. Some series even have two separate reversals in gamma (e.g., series –19, –15, –14, –12, –11, 

–5, –1, 4, 7, and 25). The most recent eclipse with a gamma reversal was on 1648 Jan 10 (Saros 138). The next and last 

in the Canon will occur on 2353 Jan 20 (Saros 120). In past millennia, the gamma reversals were more frequent because 

Earth’s orbital eccentricity was larger.

5.5 Saros Series Statistics

Lunar eclipses belonging to 204 different Saros series fall within the five millennium span of the Canon. One series (183) 

has only two eclipses represented, while two series (–20 and 182) have three eclipses each. Another 81 have a larger, but 

incomplete, subset of their members included (–18 to 19, 12, 25, 139, 142, and 144 to 181). Finally, 120 complete Saros 

series are contained within the Canon (20 to 23, 26 to 138, 140, 141, and 143).

The number of lunar eclipses in each of these series ranges from 69 to 89. Almost a quarter (22.6%) of the series contain 

72 eclipses, another quarter (24.0%) has 73 eclipses, and a sixth (15.7%) consists of 71 eclipses. In other words, nearly 2/3 

(62.3%) of all Saros series are composed of 71 to 73 eclipses. If all Saros series with 70 to 74 eclipses are considered, then 

the percentage jumps to 75.0%. The remaining quarter have either 69 eclipses (Saros 181) or 75 to 89 eclipses.

Table 5-2 presents the statistical distribution of the number of eclipses in each Saros series. The approximate duration 

(years) as a function of the number of eclipses, is listed along with the first five Saros series containing the corresponding 

number of eclipses.

All Saros series begin and end with a number of penumbral eclipses. Among the 204 Saros series with members falling 

within the scope of this Canon, the number of penumbral eclipses in the initial phase ranges from 6 to 25. Similarly, the 

number of penumbral eclipses in the final phase varies from 7 to 25. The initial penumbral eclipse sequence is followed

by a series of 6 to 24 partial eclipses, while the final penumbral eclipses are preceded by a sequence of 6 to 24 partial 

eclipses. The middle life of a Saros series is composed of total (umbral) eclipses, which range in number from 11 to 29.

Saros 13 is an exception to the normal progression of eclipse types through a series. After beginning with 11 penumbral 

eclipses followed by 7 partial eclipses, the series reverts back to produce 3 more penumbral eclipses. It then resumes the 

normal pattern to produce 11 partial eclipses followed by 13 total, 20 partial, and 8 penumbral eclipses. This odd behavior 

is caused by a reversal in gamma (Sect.5.4).

Figure 5-2 presents data on the number of penumbral, partial, and total eclipsesin Sarosseries 1 through 150. The information is plotted in four separate histograms showing the numbers of all eclipses (Fig. 5-2a), penumbral eclipses (Fig. 5-2b), 

partial eclipses (Fig. 5-2c), and total eclipses (Fig. 5-2d). Several interesting relationships are revealed in these diagrams.

Figure 5-2a shows that Saros series with large numbers of lunar eclipses tend to cluster into tight groups or 3 or 4 series 

separated by 18 to 19 series. However, most series are composed of 72 to 73 eclipses as already shown in Table 5-2.

Figure 5-2b displays the numbers of both leading (solid) and following (dashed) penumbral eclipses in a series. Note 

how the two histograms are displaced from each other, but their overlapping sections coincide with Saros series with 

large numbers of eclipses. Figure 5-2c shows the numbers of leading (solid) and following (dashed) partial eclipses in a 

series, which are nearly in phase with each other and peak during periods when the number of all lunar eclipses is near 

the minimum. Finally, Figure 5-2d presents the number of total eclipses in each series, which is inversely correlated with 

the number of partial lunar eclipses.

 60 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Table 5-2. Number of Lunar Eclipses in Saros Series

Number of 

Eclipses

Duration 

(Years)

Number of 

Series Saros Series

69 1226.0 1 181

70 1244.0 10 126, 147, 148, 163, 166, ...

71 1262.1 32 59, 92, 93, 94, 95, ...

72 1280.1 46 –4, –1, 17, 20, 34, ...

73 1298.1 49 –20, –19, –17, –9, –6, ...

74 1316.2 16 –8, –7, 0, 10, 11, ...

75 1334.2 4 –18, –16, 9, 48

76 1352.2 4 3, 44, 46, 85

77 1370.3 2 5, 140

78 1388.3 2 61, 137

79 1406.3 4 100, 139, 174, 176

81 1442.4 2 156, 158

82 1460.4 5 63, 103, 119, 121, 138

83 1478.4 4 –10, 29, 101, 120

84 1496.5 7 –12, 64, 66, 82, 83, 84, 120

85 1514.5 6 4, 24, 26, 27, 43, 45

86 1532.5 4 6, 8, 47, 65

87 1550.5 3 –15, –13, 25

88 1568.6 2 –14, –11

89 1586.6 1 7

To generalize these relationships, it appearsthat Sarosseriesthat are rich in the number of total eclipses are also rich in the

number of penumbral eclipses, but poor in the number of partial eclipses. Conversely, Saros series poor in total eclipses 

are also poor in penumbral eclipses, but rich in partial eclipses. Finally, Saros series with large numbers of eclipses are 

centered on series with large numbers of total eclipses. Figure 5-2a also shows that the extremes in the minimum and 

maximum numbers of lunar eclipses in a Saros series is gradually decreasing.

A concise summary of all 204 Saros series (–20 to 183) is presented in Tables 5-3 to 5-8. The number of lunar eclipses 

in each series is listed followed by the calendar dates of the first and last eclipses in the Saros. Finally, the chronological

sequence of lunar eclipse types in the series is tabulated. The number and type of eclipses varies from one Saros series to 

the next as reflected in the sequence diversity. Note that the tables make no distinction between central and non-central 

total lunar eclipses. The following abbreviations are used in the eclipse sequences:

T = Total Lunar Eclipse

P = Partial Lunar Eclipse

N = Partial Penumbral Lunar Eclipse

N* = Total Penumbral Lunar Eclipse

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 61

LUNAR ECLIPSE PERIODICITY
 0 50 100 150

 10

 20

 30

 0

 10

 20

 0

 10

 20

 70

 80

 90

Number of Eclipses

Figure 5–2. Number of Lunar Eclipses vs. Saros Series

Saros Series

d) total eclipses

c) partial eclipses

b) penumbral eclipses

a) all lunar eclipses

leading penumbrals

following penumbrals

leading partials

following partials

maximum number of eclipses in Saros 

minimum number of eclipses in Saros 

 62 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Table 5-3. Summary of Saros Series –20 to 14

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

–20 73 –3250 Apr 01 –1952 May 18 7N 1N* 20P 13T 23P 9N

–19 73 –3221 Mar 11 –1923 Apr 28 7N 9P 27T 22P 8N

–18 75 –3228 Jan 29 –1894 Apr 08 9N 10P 27T 8P 2N* 19N

–17 73 –3109 Mar 03 –1811 Apr 20 7N 8P 26T 8P 24N

–16 75 –3116 Jan 20 –1782 Mar 31 9N 7P 29T 9P 21N

–15 87 –3322 Aug 12 –1771 Feb 27 22N 8P 29T 6P 1N* 21N

–14 88 –3239 Aug 24 –1670 Mar 23 22N 1N* 6P 27T 7P 25N

–13 87 –3192 Aug 14 –1641 Mar 03 21N 7P 29T 8P 22N

–12 84 –3199 Jul 03 –1703 Dec 18 23N 8P 29T 6P 18N

–11 88 –3134 Jul 05 –1565 Feb 01 24N 1N* 6P 26T 8P 23N

–10 83 –3069 Jul 06 –1591 Dec 10 21N 8P 29T 7P 18N

–9 73 –3058 Jun 05 –1760 Jul 23 21N 10P 28T 7P 7N

–8 74 –2993 Jun 07 –1677 Aug 05 23N 1N* 7P 24T 10P 9N

–7 74 –2946 May 28 –1630 Jul 27 9N 2N* 19P 27T 9P 8N

–6 73 –2917 May 08 –1619 Jun 25 8N 23P 18T 17P 7N

–5 73 –2852 May 09 –1554 Jun 26 9N 1N* 21P 11T 23P 8N

–4 72 –2787 May 10 –1507 Jun 17 6N 1N* 22P 14T 22P 7N

–3 73 –2776 Apr 09 –1478 May 28 7N 24P 13T 21P 1N* 7N

–2 73 –2711 Apr 11 –1413 May 29 8N 22P 11T 23P 9N

–1 72 –2646 Apr 12 –1366 May 20 6N 21P 15T 23P 7N

0 74 –2653 Mar 01 –1337 Apr 30 8N 12P 25T 18P 2N* 9N

1 73 –2570 Mar 14 –1272 Apr 30 8N 19P 14T 9P 1N* 22N

2 73 –2523 Mar 03 –1225 Apr 22 7N 8P 28T 18P 12N

3 76 –2567 Dec 30 –1214 Mar 21 11N 8P 29T 7P 1N* 20N

4 78 –2646 Oct 06 –1131 Apr 02 13N 8P 25T 7P 1N* 24N

5 77 –2455 Dec 22 –1084 Mar 24 11N 7P 29T 8P 22N

6 86 –2624 Aug 04 –1091 Feb 10 22N 8P 29T 6P 1N* 20N

7 89 –2595 Jul 16 –1008 Feb 22 25N 7P 26T 7P 24N

8 86 –2494 Aug 08 –0961 Feb 13 21N 7P 29T 7P 22N

9 75 –2501 Jun 26 –1167 Sep 05 22N 9P 28T 7P 9N

10 74 –2454 Jun 17 –1138 Aug 15 24N 1N* 7P 25T 8P 9N

11 74 –2371 Jun 29 –1055 Aug 27 20N 1N* 8P 28T 8P 9N

12 73 –2360 May 28 –1062 Jul 17 9N 22P 27T 8P 7N

13 73 –2313 May 20 –1015 Jul 06 11N 7P 3N* 11P 13T 20P 8N

14 73 –2230 Jun 01 –0932 Jul 19 8N 1N* 20P 14T 22P 8N

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 63

LUNAR ECLIPSE PERIODICITY
Table 5-4. Summary of Saros Series 15 to 49

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

15 73 –2219 Apr 30 –0921 Jun 19 7N 23P 15T 21P 7N

16 73 –2172 Apr 21 –0874 Jun 08 8N 24P 11T 21P 1N* 8N

17 72 –2089 May 04 –0809 Jun 11 6N 1N* 21P 13T 24P 7N

18 73 –2078 Apr 02 –0780 May 21 7N 21P 16T 21P 8N

19 73 –2031 Mar 24 –0733 May 11 8N 23P 11T 12P 8N* 11N

20 72 –1948 Apr 05 –0668 May 12 6N 1N* 9P 25T 22P 9N

21 74 –1955 Feb 22 –0639 Apr 23 8N 8P 28T 11P 2N* 17N

22 74 –1926 Feb 02 –0610 Apr 02 10N 9P 25T 7P 1N* 22N

23 73 –1825 Feb 25 –0527 Apr 14 7N 1N* 6P 28T 9P 22N

24 85 –2031 Sep 16 –0516 Mar 14 20N 7P 29T 8P 21N

25 87 –2038 Aug 06 –0487 Feb 21 24N 8P 26T 7P 22N

26 85 –1919 Sep 09 –0404 Mar 06 20N 1N* 6P 28T 8P 22N

27 85 –1926 Jul 28 –0411 Jan 23 22N 7P 29T 7P 20N

28 74 –1897 Jul 09 –0581 Sep 06 24N 7P 27T 7P 9N

29 83 –1814 Jul 21 –0336 Dec 24 21N 1N* 7P 27T 8P 19N

30 74 –1803 Jun 19 –0487 Aug 18 20N 10P 29T 7P 8N

31 73 –1774 May 30 –0476 Jul 17 22N 10P 24T 10P 7N

32 73 –1673 Jun 23 –0375 Aug 09 12N 7N* 10P 14T 22P 8N

33 73 –1662 May 22 –0364 Jul 10 8N 22P 17T 19P 7N

34 72 –1615 May 13 –0335 Jun 19 8N 23P 13T 20P 1N* 7N

35 72 –1532 May 25 –0252 Jul 01 7N 1N* 20P 12T 24P 8N

36 73 –1521 Apr 24 –0223 Jun 11 7N 22P 15T 22P 7N

37 72 –1492 Apr 03 –0212 May 10 8N 24P 12T 19P 1N* 8N

38 72 –1391 Apr 27 –0111 Jun 03 6N 1N* 19P 14T 23P 9N

39 73 –1380 Mar 26 –0082 May 14 7N 10P 26T 21P 9N

40 73 –1369 Feb 24 –0071 Apr 12 9N 10P 25T 8P 1N* 20N

41 73 –1268 Mar 18 0030 May 06 7N 1N* 7P 26T 9P 23N

42 74 –1275 Feb 04 0041 Apr 05 9N 7P 29T 9P 20N

43 85 –1463 Sep 07 0052 Mar 04 22N 8P 27T 7P 21N

44 76 –1199 Jan 06 0153 Mar 27 11N 1N* 6P 27T 7P 24N

45 85 –1351 Aug 29 0164 Feb 25 21N 7P 29T 7P 21N

46 76 –1358 Jul 19 –0006 Oct 08 24N 8P 27T 6P 1N* 10N

47 86 –1275 Jul 31 0258 Feb 05 23N 1N* 6P 26T 8P 22N

48 75 –1228 Jul 21 0106 Sep 30 21N 8P 29T 7P 10N

49 73 –1217 Jun 21 0081 Aug 08 22N 9P 27T 7P 1N* 7N

 64 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Table 5-5. Summary of Saros Series 50 to 84

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

50 73 –1134 Jul 03 0164 Aug 20 21N 1N* 8P 22T 12P 9N

51 73 –1105 Jun 13 0193 Jul 31 9N 2N* 19P 26T 10P 7N

52 72 –1076 May 23 0204 Jun 29 8N 23P 15T 19P 1N* 6N

53 72 –0993 Jun 05 0287 Jul 12 9N 1N* 20P 11T 23P 8N

54 72 –0946 May 26 0334 Jul 03 6N 1N* 21P 15T 22P 7N

55 72 –0935 Apr 25 0345 Jun 01 7N 24P 13T 20P 1N* 7N

56 72 –0852 May 07 0428 Jun 13 7N 1N* 21P 11T 23P 9N

57 73 –0823 Apr 16 0475 Jun 05 7N 19P 17T 22P 8N

58 73 –0812 Mar 16 0486 May 04 8N 12P 24T 12P 6N* 11N

59 71 –0711 Apr 09 0551 May 06 7N 12P 21T 8P 1N* 22N

60 73 –0700 Mar 08 0598 Apr 27 8N 8P 27T 11P 19N

61 78 –0780 Dec 13 0609 Mar 26 14N 8P 28T 7P 1N* 20N

62 74 –0624 Feb 08 0692 Apr 06 10N 7P 26T 7P 24N

63 82 –0722 Nov 03 0739 Mar 29 17N 7P 28T 8P 22N

64 84 –0783 Aug 20 0714 Feb 04 22N 8P 28T 7P 19N

65 86 –0736 Aug 11 0797 Feb 16 24N 7P 25T 8P 22N

66 84 –0671 Aug 12 0826 Jan 27 21N 7P 29T 8P 19N

67 73 –0660 Jul 11 0638 Aug 30 21N 9P 28T 7P 1N* 7N

68 72 –0595 Jul 14 0685 Aug 20 23N 8P 23T 10P 8N

69 73 –0530 Jul 15 0768 Sep 01 18N 1N* 9P 27T 10P 8N

70 72 –0519 Jun 13 0761 Jul 21 9N 21P 25T 10P 1N* 6N

71 72 –0472 Jun 04 0808 Jul 11 11N 1N* 20P 11T 21P 1N* 7N

72 72 –0389 Jun 17 0891 Jul 25 7N 1N* 20P 14T 22P 8N

73 72 –0378 May 16 0902 Jun 23 7N 23P 14T 21P 7N

74 72 –0331 May 07 0949 Jun 13 9N 22P 11T 21P 1N* 8N

75 72 –0266 May 08 1014 Jun 15 7N 21P 14T 23P 7N

76 73 –0255 Apr 07 1043 May 26 8N 19P 17T 20P 9N

77 72 –0190 Apr 09 1090 May 16 8N 21P 13T 8P 2N* 20N

78 72 –0125 Apr 10 1155 May 18 7N 9P 25T 19P 12N

79 73 –0132 Feb 27 1166 Apr 17 9N 8P 28T 8P 1N* 19N

80 74 –0103 Feb 07 1213 Apr 06 11N 8P 26T 6P 1N* 22N

81 74 –0020 Feb 19 1296 Apr 19 9N 7P 27T 9P 22N

82 84 –0208 Sep 21 1289 Mar 08 20N 8P 29T 7P 20N

83 84 –0197 Aug 22 1300 Feb 05 24N 7P 26T 7P 20N

84 84 –0096 Sep 13 1401 Feb 28 20N 1N* 6P 28T 8P 21N

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 65

LUNAR ECLIPSE PERIODICITY
Table 5-6. Summary of Saros Series 85 to 119

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

85 76 –0103 Aug 02 1249 Oct 23 22N 8P 28T 7P 11N

86 73 –0074 Jul 13 1224 Aug 30 24N 8P 25T 8P 8N

87 73 0027 Aug 06 1325 Sep 23 20N 1N* 7P 26T 10P 9N

88 72 0038 Jul 05 1318 Aug 12 12N 18P 26T 9P 7N

89 72 0067 Jun 15 1347 Jul 23 11N 21P 15T 17P 1N* 7N

90 72 0150 Jun 27 1430 Aug 04 9N 3N* 17P 13T 22P 8N

91 72 0179 Jun 07 1459 Jul 15 7N 22P 15T 21P 7N

92 71 0208 May 17 1470 Jun 13 8N 23P 12T 20P 1N* 7N

93 71 0291 May 30 1553 Jun 25 7N 1N* 20P 12T 24P 7N

94 71 0320 May 09 1582 Jun 06 6N 21P 16T 21P 7N

95 71 0349 Apr 19 1611 May 26 7N 23P 12T 12P 6N* 11N

96 71 0432 May 01 1694 Jun 07 7N 13P 20T 20P 11N

97 72 0443 Mar 31 1723 May 20 7N 9P 27T 12P 17N

98 74 0436 Feb 18 1752 Apr 28 10N 10P 25T 7P 1N* 21N

99 72 0555 Mar 24 1835 May 12 7N 1N* 7P 26T 8P 23N

100 79 0439 Dec 06 1846 Apr 11 15N 7P 29T 8P 20N

101 83 0360 Sep 11 1839 Feb 28 22N 8P 27T 6P 1N* 19N

102 84 0461 Oct 05 1958 Apr 04 20N 1N* 6P 26T 8P 23N

103 82 0472 Sep 03 1933 Feb 10 21N 7P 29T 7P 18N

104 72 0483 Aug 04 1763 Sep 22 22N 9P 26T 7P 1N* 7N

105 73 0566 Aug 16 1864 Oct 15 21N 1N* 7P 25T 9P 10N

106 73 0595 Jul 27 1893 Sep 25 19N 10P 27T 9P 8N

107 72 0606 Jun 26 1886 Aug 14 12N 20P 23T 10P 7N

108 72 0689 Jul 08 1969 Aug 27 17N 3N* 10P 12T 22P 8N

109 71 0736 Jun 27 1998 Aug 08 7N 1N* 20P 17T 19P 7N

110 72 0747 May 28 2027 Jul 18 8N 23P 13T 20P 1N* 7N

111 71 0830 Jun 10 2092 Jul 19 8N 1N* 20P 11T 23P 8N

112 72 0859 May 20 2139 Jul 12 7N 21P 15T 22P 7N

113 71 0888 Apr 29 2150 Jun 10 7N 23P 13T 18P 2N* 8N

114 71 0971 May 13 2233 Jun 22 7N 1N* 19P 13T 12P 6N* 13N

115 72 1000 Apr 21 2280 Jun 13 7N 9P 26T 19P 11N

116 73 0993 Mar 11 2291 May 14 9N 9P 27T 8P 1N* 19N

117 71 1094 Apr 03 2356 May 15 8N 9P 24T 7P 23N

118 73 1105 Mar 02 2403 May 07 9N 7P 28T 8P 21N

119 82 0935 Oct 14 2396 Mar 25 20N 8P 28T 6P 1N* 19N

 66 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Table 5-7. Summary of Saros Series 120 to 154

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

120 83 1000 Oct 16 2479 Apr 07 21N 7P 25T 7P 1N* 22N

121 82 1047 Oct 06 2508 Mar 18 19N 1N* 6P 29T 7P 20N

122 74 1022 Aug 14 2338 Oct 29 22N 8P 28T 7P 9N

123 72 1087 Aug 16 2367 Oct 08 23N 1N* 6P 25T 8P 9N

124 73 1152 Aug 17 2450 Oct 21 20N 8P 28T 8P 9N

125 72 1163 Jul 17 2443 Sep 09 17N 13P 26T 9P 7N

126 70 1228 Jul 18 2472 Aug 19 21N 1N* 8P 14T 19P 7N

127 72 1275 Jul 09 2555 Sep 02 10N 1N* 18P 16T 20P 7N

128 71 1304 Jun 18 2566 Aug 02 7N 23P 15T 19P 1N* 6N

129 71 1351 Jun 10 2613 Jul 24 9N 1N* 21P 11T 21P 8N

130 71 1416 Jun 10 2678 Jul 26 7N 1N* 20P 14T 22P 7N

131 72 1427 May 10 2707 Jul 07 7N 22P 15T 20P 8N

132 71 1492 May 12 2754 Jun 26 8N 21P 12T 11P 7N* 12N

133 71 1557 May 13 2819 Jun 29 6N 1N* 13P 21T 20P 10N

134 72 1550 Apr 01 2830 May 28 8N 10P 26T 10P 1N* 17N

135 71 1615 Apr 13 2877 May 18 9N 10P 23T 7P 1N* 21N

136 72 1680 Apr 13 2960 Jun 01 7N 1N* 7P 27T 8P 22N

137 78 1564 Dec 17 2953 Apr 20 15N 8P 28T 7P 20N

138 82 1521 Oct 15 2982 Mar 30 21N 1N* 7P 26T 6P 21N

139 79 1658 Dec 09 3065 Apr 13 16N 7P 27T 8P 21N

140 77 1597 Sep 25 2968 Jan 06 20N 8P 28T 7P 14N

141 72 1608 Aug 25 2888 Oct 11 24N 7P 26T 7P 8N

142 73 1709 Sep 19 3007 Nov 17 20N 1N* 7P 26T 9P 10N

143 72 1720 Aug 18 3000 Oct 05 19N 10P 27T 8P 8N

144 71 1749 Jul 29 3011 Sep 04 21N 1N* 9P 20T 12P 1N* 7N

145 71 1832 Aug 11 3094 Sep 16 15N 3N* 10P 15T 20P 8N

146 72 1843 Jul 11 3123 Aug 29 9N 20P 17T 19P 7N

147 70 1890 Jul 02 3134 Jul 28 8N 23P 12T 19P 1N* 7N

148 70 1973 Jul 15 3217 Aug 09 7N 1N* 20P 12T 23P 7N

149 71 1984 Jun 13 3246 Jul 20 7N 21P 15T 21P 7N

150 71 2013 May 25 3275 Jun 30 8N 23P 12T 15P 3N* 10N

151 71 2096 Jun 06 3358 Jul 13 7N 1N* 18P 14T 21P 10N

152 72 2107 May 07 3387 Jun 23 8N 10P 25T 15P 1N* 13N

153 71 2136 Apr 16 3398 May 22 9N 10P 24T 8P 1N* 19N

154 71 2237 May 10 3499 Jun 16 7N 8P 25T 8P 23N

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 67

LUNAR ECLIPSE PERIODICITY
Table 5-8. Summary of Saros Series 155 to 183

Saros 

Series

Number of 

Eclipses First Eclipse Last Eclipse Lunar Eclipse Sequence

155 73 2212 Mar 18 3510 May 17 9N 8P 28T 8P 20N

156 81 2060 Nov 08 3503 Apr 05 20N 8P 27T 6P 1N* 19N

157 73 2306 Mar 01 3604 Apr 27 11N 6P 26T 8P 22N

158 81 2154 Oct 21 3597 Mar 17 20N 7P 28T 8P 18N

159 73 2147 Sep 09 3445 Nov 07 23N 8P 26T 7P 9N

160 72 2248 Oct 03 3528 Nov 19 21N 7P 25T 8P 11N

161 73 2259 Sep 02 3557 Oct 31 20N 9P 27T 8P 9N

162 71 2288 Aug 12 3550 Sep 19 19N 12P 24T 9P 7N

163 70 2371 Aug 27 3615 Sep 20 19N 2N* 8P 13T 20P 8N

164 71 2400 Aug 05 3662 Sep 11 9N 1N* 18P 18T 18P 7N

165 71 2411 Jul 06 3673 Aug 11 9N 22P 14T 19P 7N

166 70 2494 Jul 18 3738 Aug 13 9N 1N* 19P 11T 22P 8N

167 71 2541 Jul 09 3803 Aug 16 7N 20P 15T 21P 8N

168 71 2552 Jun 08 3814 Jul 15 8N 22P 13T 18P 2N* 8N

169 70 2635 Jun 22 3879 Jul 17 7N 1N* 19P 13T 13P 4N* 13N

170 71 2664 Jun 01 3926 Jul 09 7N 11P 24T 19P 10N

171 71 2675 May 01 3937 Jun 07 8N 10P 26T 8P 1N* 18N

172 70 2758 May 15 4002 Jun 08 8N 9P 23T 8P 22N

173 72 2787 Apr 24 4067 Jun 11 8N 7P 27T 9P 21N

174 79 2635 Dec 16 4042 Apr 18 18N 8P 27T 7P 19N

175 74 2791 Feb 11 4107 Apr 20 14N 7P 25T 7P 21N

176 79 2747 Dec 09 4154 Apr 11 17N 1N* 6P 28T 8P 19N

177 73 2704 Oct 05 4002 Dec 03 21N 8P 28T 6P 1N* 9N

178 70 2769 Oct 07 4013 Nov 01 22N 7P 24T 8P 1N* 8N

179 73 2816 Sep 27 4114 Nov 26 20N 8P 27T 8P 10N

180 71 2827 Aug 28 4089 Oct 03 19N 11P 26T 8P 7N

181 69 2892 Aug 29 4118 Sep 13 21N 1N* 8P 15T 17P 7N

182 70 2957 Aug 31 4201 Sep 26 10N 4N* 14P 15T 20P 7N

183 70 2968 Jul 30 4212 Aug 26 8N 21P 16T 18P 1N* 6N

5.6 Saros and Other Periods

The numbering system used for the Saros series was introduced by van den Bergh in his book Periodicity and Variation of 

Solar(and Lunar) Eclipses(1955). He assigned the number 1 to a pair ofsolar and lunar eclipse seriesthat were in progress

during the second millennium BCE based on an extrapolation from von Oppolzer’s Canon der Finsternisse (1887).

There is an interval of 1, 5, or 6 synodic months between any sequential pair of lunar eclipses. Interestingly, the number 

of lunations between two eclipses permits the determination of the Saros series number of the second eclipse when the 

 68 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Saros series number of the first eclipse is known. Let the Saros series number of the first eclipse in a pair be “s”. The Saros 

series number of the second eclipse can be found from the relationships in Table 5-9 (Meeus, Grosjean, and Vanderleen, 

1966).

Table 5-9. Some Eclipse Periods and Their Relationships to the Saros Number

Number of 

Synodic

Months

Length of Time

Saros 

Series 

Number

Period Name

 1 ~1 month s + 38 Lunation

 5 ~5 months s – 33 Short Semester

 6 ~6 months s + 5 Semester

135 ~11 years – 1 month s + 1 Tritos

223 ~18 years + 11 days s Saros

235 ~19 years s + 10 Metonic Cycle

358 ~29 years – 20 days s + 1 Inex

669 ~54 years + 33 days s Exeligmos (Triple Saros)

5.7 Saros and Inex

A number of different eclipse cycles were investigated by van den Bergh, but the most useful were the Saros and the Inex.

The Inex is equal to 358 synodic months (~29 years less 20 days), which is very nearly 388.5 draconic months.

358 Synodic Months = 10,571.9509 days = 10,571d 22h 49m

388.5 Draconic Months = 10,571.9479 days = 10,571d 22h 55m

The extra 0.5 in the number of draconic months means that eclipses separated by one Inex period occur at opposite nodes.

Consequently, an eclipse occurring in the northern half of Earth’s shadows will be followed one Inex later by an eclipse

occurring in the southern half of Earth’s shadows, and vice versa.

The mean time difference between 358 synodic months and 388.5 draconic months making up an Inex is only 6 min. In 

comparison, the mean difference between these two cycles in the Saros is 52 min. This means that after one Inex, the 

shift of the Moon with respect to the node (+0.04°) is much smaller than for the Saros (–0.48°). While a Saros series lasts 

12 to 15 centuries, an Inex series typically lasts 225 centuries and contains about 780 eclipses.

5.8 Saros–Inex Panorama

Van den Bergh placed all 5,200 lunar eclipsesin von Oppolzer’s Canon der Finsternisse (1887) into a large two-dimensional

matrix. (Von Oppolzer did not include penumbral lunar eclipses in his Canon der Finsternisse.) Each Saros series was 

arranged as a separate column containing every eclipse in chronological order. The individual Saros columns were then 

staggered so that the horizontal rows each corresponded to a different Inex series. This “Saros–Inex Panorama” proved 

useful in organizing eclipses. For instance, one step down in the panorama is a change of one Saros period (6585.32 days) 

later, while one step to the right is a change of one Inex period (10571.95 days) later. The rows and columns were then 

numbered with the Saros and Inex numbers.

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 69

LUNAR ECLIPSE PERIODICITY
The panorama also made it possible to predict the approximate circumstances of lunar (and solar) eclipses occurring before

or after the period spanned by von Oppolzer’s Canon. The time interval “t” between any two lunar eclipses can be found 

through an integer combination of Saros and Inex periods via the following relationship:

t = a i + b s, (5–1)

where

t = interval in days,

i = Inex period of 10571.95 days (358 synodic months),

s = Saros period of 6585.32 days (223 synodic months), and

a, b = integers (negative, zero, or positive).

From this equation, a number of useful combinations of Inex and Saros periods can be employed to extend von Oppolzer’s 

Canon from –1207 back to –1600 using nothing more than simple arithmetic (van den Bergh, 1954). The ultimate goal of 

the effort was to a produce an eclipse canon for dating historical events prior to –1207. Periods formed by various combinations of Inex and Saros were evaluated in order to satisfy one or more of the following conditions:

1) The deviation from a multiple of 0.5 draconic months should be small (i.e., Moon should be nearly the 

same distance from the node).

2) The deviation from an integral multiple of anomalistic months should be small (i.e., Moon should be nearly 

the same distance from Earth).

3) The deviation from an integral multiple of anomalistic years should be small (i.e., eclipse should occur on nearly 

the same calendar date).

No single Inex–Saros combination meets all three criteria, but there are periods that do a reasonably good job for any one 

of them. Note that secular changes in the Moon’s elements cause a particular period to be of high accuracy for a limited

number of centuries. The direct application of the Saros–Inex panorama allowsfor the determination of eclipse datesin the

past (or future); however, the application of the longer Saros–Inex combinations permit the rapid estimation of a number 

of eclipse characteristics without lengthy calculations. Table 5-10 lists several of the most useful periods.

Table 5-10. Some Useful Eclipse Periods

Period Name Period

(Inex + Saros)

Period

(years) Use

Heliotrope 58i + 6s 1,787 Geographic longitude of eclipse

Accuratissima 58i + 9s 1,841 Geographic latitude of eclipse

Horologia 110i + 7s 3,310 Time of ecliptic conjunction

Modern digital computers using high precision solar and lunar ephemerides can directly predict the dates and circumstances of eclipses. Nevertheless, the Saros and Inex cycles remain useful tools in understanding the periodicity and 

frequency of eclipses.

5.9 Secular Variations in the Saros and Inex

Because of long secular variations in the average ellipticity of the Moon’s and Earth’s orbits, the mean lengths of the 

synodic, draconic, and anomalistic months are slowly changing. The mean synodic and draconic months are increasing

by approximately 0.2 and 0.4 s per millennium, respectively. Meanwhile, the anomalistic month is decreasing by about 

0.8 s per millennium.

 70 FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE)

LUNAR ECLIPSE PERIODICITY
Although small, the cumulative effects of such changes has an impact on both the Saros and Inex. Table 5-11 shows how 

the number of draconic and anomalistic months change with respect to 223 synodic months (Saros period) over an interval 

of 7000 years. Of particular interest is the last column, which shows the mean shift of the Moon’s node after a period of 1 

Saros. It is gradually increasing, which means that the average number of eclipses in a typical Saros series is decreasing.

This explains the trend in the number of lunar eclipses seen in Figure 5-2a.

Table 5-11: Number of Anomalistic and Draconic Months in 1 Saros

Year

Anomalistic Months 

(223 Lunations)

Draconic Months 

(223 Lunations)

Node Shift 

(after 1 Saros)

–3000 238.991679 241.998742 0.4529

–2000 238.991763 241.998730 0.4571

–1000 238.991854 241.998717 0.4618

 0 238.991950 241.998703 0.4668

 1000 238.992051 241.998688 0.4722

 2000 238.992157 241.998673 0.4779

 3000 238.992267 241.998656 0.4838

 4000 238.992379 241.998639 0.4899

Table 5-12 shows how the number of draconic months is changing with respect to 358 synodic months (Inex period) over a 

7000-year interval. The mean shift in the lunar node after 1 Inex is much smaller than the Saros and is gradually decreasing. This explains why the lifetime of the Inex is so much longer than the Saros and is still increasing.

Table 5-12: Number of Draconic Months in 1 Inex

Year Draconic Months 

(358 Lunations)

Node Shift 

(after 1 Inex)

–3000 388.500223 -0.0801

–2000 388.500204 -0.0734

–1000 388.500183 -0.0659

 0 388.500160 -0.0578

 1000 388.500136 -0.0491

 2000 388.500111 -0.0400

 3000 388.500085 -0.0305

 4000 388.500057 -0.0207

Although the Inex possesses a long lifespan, its mean duration is not easily characterized because of the decreasing nodal 

shift seen in Table 5-12. If the instantaneous mean durations of the synodic and draconic months for the years –2000, 

+2000, and +4000 are used to calculate the mean duration of the Inex, the resulting lengths are about 14,500, 26,600, and 

51,000 years, respectively (Meeus, 2004a).

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 71

LUNAR ECLIPSE PERIODICITY

ACRONYMS AND UNITS

arcsec Arc second

AT Hybrid eclipse that begins as annular, then changes to total.

ATA Hybrid eclipse that begins as annular, changes to total, and then reverts back to annular.

BCE Before the Common Era

CE Common Era

cm Centimeter

ET Ephemeris Time

GMAT Greenwich Mean Astronomical Time

GMT Greenwich Mean Time

IAU International Astronomical Union

ISO International Standards Organization

LLR Lunar Laser Ranging

LOD Length of Day

m Meter (or minutes in tables)

min Minutes

s Second

arcsec/cy2 Arc seconds per Julian century squared

TA Hybrid eclipse that begins as total and ends as annular.

TAI International Atomic Time

TD Terrestrial Dynamical Time

TT Terrestrial Time

UT Universal Time

UTC Coordinated Universal Time

VLBI Very Long Baseline Interferometry

FIVE MILLENNIUM CANON OF LUNAR ECLIPSES: –1999 TO +3000 (2000 BCE TO 3000 CE) 73

 ACRONYMS, UNITS, AND REFERENCES
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