NASA - Eclipses During 2006 (original) (raw)

Fred Espenak

Published in Observer's Handbook 2006, Royal Astronomical Society of Canada

Two central solar and two lunar eclipses occur in 2006 as follows:

Predictions for the eclipses are summarized in Figures 1 through 6. World maps show the regions of visibility for each eclipse. The lunar eclipse diagrams also include the path of the Moon through Earth's shadows. Contact times for each principal phase are tabulated along with the magnitudes and geocentric coordinates of the Sun and Moon at greatest eclipse.

All times and dates used in this publication are in Universal Time or UT. This astronomically derived time system is colloquially referred to as Greenwich Mean Time or GMT. To learn more about UT and how to convert UT to your own local time, see Time Zones and Universal Time.

Penumbral Lunar Eclipse of March 14

The first lunar eclipse of 2006 is a deep penumbral event best visible from Europe and Africa. First and last penumbral contacts occur at 21:22 UT and 02:14 UT (Mar 15), respectively. The Moon's path through Earth's penumbra as well as a map showing worldwide visibility of the event is shown in Figure 1. Observers throughout most of North America will find the eclipse already in progress as the Moon rises on the evening of March 14. However, no eclipse will be visible from westernmost North America (Yukon, British Columbia, Alaska, Washington, Oregon and California) since the event ends there before moonrise. This particular event is unusual since it is a total penumbral eclipse. The whole Moon will lie completely within the penumbral shadow from 23:18 UT to 00:18 UT (Mar 15). According to Belgian eclipse expert Jean Meeus [1997] this is one of only five such events during the 21st century. Greatest eclipse occurs at 23:48 UT with a penumbral magnitude of 1.0565. At that instant, the Moon will stand midway in the penumbral shadow. The Moon's northern limb will lie 1.6 arc-minutes from the shadow's outer edge while the southern limb be 1.6 arc-minutes from the edge of the umbra.

Penumbral eclipses are difficult to observe, especially during the early and late stages. Nevertheless, a subtle yet distinct shading should be visible across the southern half of the Moon, especially during the two hour period centered on greatest eclipse.

Total Solar Eclipse of March 29

The year's first solar eclipse occurs on Wednesday, March 29. A total eclipse will be visible from within a narrow corridor, which traverses half the Earth. The path of the Moon's umbral shadow begins in Brazil and extends across the Atlantic, northern Africa, and central Asia, where it ends at sunset in western Mongolia. A partial eclipse will be seen within the much broader path of the Moon's penumbral shadow, which includes the northern two thirds of Africa, Europe, and central Asia (Figure 2 and Figure 3).

The central eclipse track begins in eastern Brazil, where the Moon's umbral shadow first touches down on Earth at 08:36 UT. Along the sunrise terminator, the duration is 1 minute 53 seconds from the center of the 129-kilometre wide path. Traveling over 9 km/s, the umbra quickly leaves Brazil and races across the Atlantic Ocean (with no landfall) for the next half hour. After crossing the equator, the Moon's shadow enters the Gulf of Guinea and encounters the coast of Ghana at 09:08 UT. The Sun stands 44° above the eastern horizon during the 3 minute 24 second total phase. The path width has expanded to 184 kilometres while the shadow's ground speed has decreased to 0.958 km/s. Located about 50 kilometres south of the central line, the 1.7 million inhabitants of Ghana's capital city Accra can expect a total eclipse lasting 2 minute 58 seconds (09:11 UT).

Moving inland the umbra enters Togo at 09:14 UT. Unfortunately, the capital city Lome lies just outside the southern limit so its inhabitants will only witness a grazing partial eclipse. Two minutes later, the leading edge of the umbra reaches Benin whose capital Porto-Novo experiences a deep partial eclipse of magnitude 0.985. Continuing northeast, the shadow's axis enters Nigeria at 09:21 UT. At this time, the central duration has increased to 3 minutes 40 seconds, the Sun's altitude is 52°, the path of totality is 188 kilometres wide and the velocity is 0.818 km/s. Since Lagos is situated about 120 kilometres outside the umbra's southern limit, its population of over eight million will witness a partial eclipse of magnitude 0.968.

The umbra's axis takes about sixteen minutes to cross western Nigeria before entering Niger at 09:37 UT. The central duration is 3 minutes 54 seconds as the umbra's velocity continues to decrease (0.734 km/s). During the next hour, the shadow traverses some of the most remote and desolate deserts on the planet. When the umbra reaches northern Niger (10:05 UT), it briefly enters extreme northwestern Chad before crossing into southern Libya.

The instant of greatest eclipse[1] occurs at 10:11:18 UT when the axis of the Moon's shadow passes closest to the center of Earth (gamma[2] = +0.384). Totality reaches its maximum duration of 4 minutes 7 seconds, the Sun's altitude is 67°, the path width is 184 kilometres and the umbra's velocity is 0.697 km/s. Continuing on a northeastern course, the umbra crosses central Libya and reaches the Mediterranean coast at 10:40 UT. Northwestern Egypt also lies within the umbral path where the central duration is 3 minutes 58 seconds.

Passing directly between Crete and Cyprus, the track reaches the southern coast of Turkey at 10:54 UT. With a population of nearly 3/4 million people, Antalya lies 50 kilometres northwest of the central line. The coastal city's inhabitants are positioned for a total eclipse lasting 3 minutes 11 seconds while observers on the central line receive an additional 35 seconds of totality. Konya is 25 kilometres from path center and experiences a 3 minute 36 second total phase beginning at 10:58 UT. Crossing mountainous regions of central Turkey, the Moon's shadow intersects the path of the 1999 Aug 11 total eclipse. A quarter million people in Sivas have the opportunity of witnessing a second total eclipse from their homes in less than seven years.

At 11:10 UT, the shadow axis reaches the Black Sea along the northern coast of Turkey. The central duration is 3 minutes 30 seconds, the Sun's altitude is 47°, the path width is 165 kilometres and the umbra's velocity is 0.996 km/s. Six minutes later, the umbra encounters the western shore of Georgia. Moving inland, the track crosses the Caucasus Mountains, which form the highest mountain chain of Europe. Georgia's capital, Tbilisi, is outside the path and experiences a magnitude 0.949 partial eclipse at 11:19 UT. As the shadow proceeds into Russia, it engulfs the northern end of the Caspian Sea and crosses into Kazakhstan. At 11:30 UT, the late afternoon Sun's altitude is 32°, the central line duration is 2 minutes 57 seconds and the umbral velocity is 1.508 km/s and increasing.

In the remaining seventeen minutes, the shadow rapidly accelerates across central Asia while the duration dwindles. It traverses northern Kazakhstan and briefly re-enters Russia before lifting off Earth's surface at sunset along Mongolia's northern border at 11:48 UT. Over the course of 3 hours and 12 minutes, the Moon's umbra travels along a path approximately 14,500 kilometres long and covers 0.41% of Earth's surface area. Path coordinates and central line circumstances are presented in Table 1.

Local circumstances for a number of cities within the zone of partial eclipse are given in Table 2. All times are given in Universal Time. The Sun's altitude and azimuth, the eclipse magnitude[3] and obscuration[4] are all given at the instant of maximum eclipse. Additional maps, tables, and prediction details are available at NASA's 2006 total solar eclipse web site:

http://eclipse.gsfc.nasa.gov/SEmono/TSE2006/TSE2006.html

This is the 29th eclipse of Saros series 139. The series began with 7 partial eclipses, the first of which was on 1501 May 17. Quite remarkably, the first dozen central eclipses of Saros 139 were all hybrid with the duration of totality steadily increasing during each successive event. The first total eclipse occurred on 1843 Dec 21. The series continues to produce total eclipses which culminates with an extraordinarily long total eclipse of 2186 July 16. The 7 minute 29 second duration falls just 3 seconds short of the theoretical maximum [Meeus, 2005]. The last central eclipse of Saros 139 occurs on 2601 Mar 26 with a 36 second duration. The final nine eclipses are all partial events visible from the Southern Hemisphere. The series ends with the partial eclipse of 2763 Jul 03. Complete details for Saros 139 may be found at:

http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros139.html

Partial Lunar Eclipse of September 07

The second lunar eclipse of the year is a rather small partial eclipse. The penumbral phase begins at 16:42 UT, but most observers will not be able to visually detect the faint shadow until about 17:30 UT. A timetable for the major phases of the eclipse is as follows:

Penumbral Eclipse Begins: 16:42:23 UT Partial Eclipse Begins: 18:05:03 UT Greatest Eclipse: 18:51:21 UT Partial Eclipse Ends: 19:37:41 UT Penumbral Eclipse Ends: 21:00:20 UT

In spite of the fact that the eclipse is shallow (the Moon's northern limb dips just 6.3 arc-minutes into Earth's dark umbral shadow), the partial phase lasts over 1 1/2 hours. This is due to the grazing geometry of the Moon and umbra.

At the instant of greatest eclipse (18:51 UT), the Moon will stand near the zenith for observers in the central Indian Ocean. At that time, the umbral eclipse magnitude will be 0.190. The event is best seen from Africa, Asia, Australia and Eastern Europe. Unfortunately, none of the eclipse is visible from North America. The Moon's path through Earth's shadows as well as a map illustrating worldwide visibility is shown in Figure 4.

Annular Solar Eclipse of September 22

The final eclipse of 2006 is an annular eclipse of the Sun. The track of the Moon's antumbral shadow begins in northern South America and crosses the South Atlantic with no further landfall. A partial eclipse will be seen from a much larger region including South America, the eastern Caribbean, western Africa, and Antarctica (Figure 5). The path of the annular eclipse begins in Guyana at 09:48 UT when the Moon's antumbral shadow meets Earth and forms a 323 kilometre wide corridor (Figure 6). Guyana's capitol city Georgetown lies just a few kilometres outside the path's northern limit. Here, a magnitude 0.920 partial eclipse will be seen at sunrise. On the central line 160 kilometres south, the duration of annularity is 5 minutes 31 seconds.

Rushing east, the antumbra quickly enters Surinam where its capital city Paramaribo lies deep within the antumbral path. Maximum eclipse in Paramaribo occurs at 09:51 UT, the Sun's altitude is 5° and the duration of annularity is 5 minutes 1 seconds. Continuing into French Guiana, the capitol city Cayenne stands just 10 kilometres south of the central line. Maximum eclipse occurs at 09:53 UT as the Sun stands 8° above the eastern horizon during an annular phase lasting 5 minutes 42 seconds.

The southern edge of the antumbra briefly clips the north coast of Brazil before spending the next three and a half hours sweeping across the South Atlantic. Greatest eclipse occurs at 11:40:11 UT. The annular duration is 7 minutes 9 seconds, the path width is 261 kilometres and the Sun is 66° above the featureless horizon of the open ocean. The central track runs south of the African continent and nearly reaches Kerguelen Island before ending at local sunset (13:31 UT). During its 3 hour 40 minute flight across our planet, the Moon's antumbra travels about 13,800 kilometres and covers 0.83% of Earth's surface area. Path coordinates and central line circumstances are presented in Table 3.

Partial phases of the eclipse are visible primarily from South America and Africa. Local circumstances for a number of cities are listed in Table 4. All times are given in Universal Time. The Sun's altitude and azimuth, the eclipse magnitude and obscuration are all given at the instant of maximum eclipse. Additional maps, tables, and prediction details are available at NASA's 2006 annular solar eclipse web site:

http://eclipse.gsfc.nasa.gov/SEmono/ASE2006/ASE2006.html

This is the 16th eclipse of Saros 144. The series began with the first of eight partial eclipses on 1736 Apr 11. The first central eclipse was annular in the Southern Hemisphere on 1880 Jul 07. The series will produce 39 annular eclipses the last of which is 2565 Aug 27. The series terminates on 2980 May 05 after 23 more partial eclipses. Complete details for Saros 144 may be found at:

http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros144.html

Solar Eclipse Figures

For each solar eclipse, an orthographic projection map of Earth shows the path of penumbral (partial) and umbral (total or annular) eclipse. North is to the top in all cases and the daylight terminator is plotted for the instant of greatest eclipse. An asterisk (*) indicates the sub-solar point[5] on Earth.

The limits of the Moon's penumbral shadow delineate the region of visibility of the partial solar eclipse. This irregular or saddle shaped region often covers more than half of the daylight hemisphere of Earth and consists of several distinct zones or limits. At the northern and/or southern boundaries lie the limits of the penumbra's path. Partial eclipses have only one of these limits, as do central eclipses when the Moon's shadow axis falls no closer than about 0.45 radii from Earth's centre. Great loops at the western and eastern extremes of the penumbra's path identify the areas where the eclipse begins/ends at sunrise and sunset, respectively. If the penumbra has both a northern and southern limit, the rising and setting curves form two separate, closed loops. Otherwise, the curves are connected in a distorted figure eight. Bisecting the 'eclipse begins/ends at sunrise and sunset' loops is the curve of maximum eclipse at sunrise (western loop) and sunset (eastern loop). The points P1 and P4 mark the coordinates where the penumbral shadow first contacts (partial eclipse begins) and last contacts (partial eclipse ends) Earth's surface. If the penumbral path has both a northern and southern limit, then points P2 and P3 are also plotted. These correspond to the coordinates where the penumbral shadow cone becomes internally tangent to Earth's disk.

A curve of maximum eclipse is the locus of all points where the eclipse is at maximum at a given time. Curves of maximum eclipse are plotted at each half-hour Universal Time. They generally run between the penumbral limits in the north/south direction, or from the 'maximum eclipse at sunrise and sunset' curves to one of the limits. If the eclipse is central (i.e. total or annular), the curves of maximum eclipse run through the outlines of the umbral shadow, which are plotted at ten-minute intervals. The curves of constant eclipse magnitude delineate the locus of all points where the magnitude at maximum eclipse is constant. These curves run exclusively between the curves of maximum eclipse at sunrise and sunset. Furthermore, they are parallel to the northern/southern penumbral limits and the umbral paths of central eclipses. In fact, the northern and southern limits of the penumbra can be thought of as curves of constant magnitude of 0.0. The adjacent curves are for magnitudes of 0.2, 0.4, 0.6 and 0.8. For total eclipses, the northern and southern limits of the umbra are curves of constant magnitude of 1.0. Umbral path limits for annular eclipses are curves of maximum eclipse magnitude.

Greatest eclipse is defined as the instant when the axis of the Moon's shadow passes closest to Earth's centre. Although greatest eclipse differs slightly from the instants of greatest magnitude and greatest duration (for total eclipses), the differences are negligible. The point on Earth's surface intersected by the axis at greatest eclipse is marked by an asterisk symbol. For partial eclipses, the shadow axis misses Earth entirely, so the point of greatest eclipse lies on the day/night terminator and the Sun appears on the horizon.

Data pertinent to the eclipse appear with each map. At the top are listed the instant of conjunction of the Sun and Moon in right ascension and the instant of greatest eclipse, expressed in Universal Times and Julian Dates. The eclipse magnitude is defined as the fraction of the Sun's diametre obscured by the Moon at greatest eclipse. For central eclipses (total or annular), the magnitude is replaced by the geocentric ratio of diametres of the Moon and the Sun. Gamma is the minimum distance of the Moon's shadow axis from Earth's centre in Earth radii at greatest eclipse. The Saros series of the eclipse is listed, followed by the member position. The first member number identifies the sequence position of the eclipse in the Saros, while the second is the total number of eclipses in the series.

In the upper left and right corners are the geocentric coordinates of the Sun and the Moon, respectively, at the instant of greatest eclipse. They are:

R.A. - Right Ascension
Dec. - Declination
S.D. - Apparent Semi-Diameter
H.P. - Horizontal Parallax

To the lower left are exterior/interior contact times of the Moon's penumbral shadow with Earth, which are defined:

P1 - Instant of first exterior tangency of Penumbra with Earth's limb. (Partial Eclipse Begins)
P2 - Instant of first interior tangency of Penumbra with Earth's limb.
P3 - Instant of last interior tangency of Penumbra with Earth's limb.
P4 - Instant of last exterior tangency of Penumbra with Earth's limb. (Partial Eclipse Ends)

Not all eclipses have P2 and P3 penumbral contacts. They are only present in cases where the penumbral shadow falls completely within Earth's disk. For central eclipses, the lower right corner lists exterior/interior contact times of the Moon's umbral shadow with Earth's limb which are defined as follows:

U1 - Instant of first exterior tangency of Umbra with Earth's limb. (Umbral [Total/Annular] Eclipse Begins)
U2 - Instant of first interior tangency of Umbra with Earth's limb.
U3 - Instant of last interior tangency of Umbra with Earth's limb.
U4 - Instant of last exterior tangency of Umbra with Earth's limb. (Umbral [Total/Annular] Eclipse Ends)

At bottom centre are the geographic coordinates of the position of greatest eclipse along with the local circumstances at that location (i.e. - Sun altitude, Sun azimuth, path width and duration of totality/annularity). At bottom left are a list of parameters used in the eclipse predictions, while bottom right gives the Moon's geocentric libration (optical + physical) at greatest eclipse.

Lunar Eclipse Figures

Each lunar eclipse has two diagrams associated with it along with data pertinent to the eclipse. The top figure shows the path of the Moon through Earth's penumbral and umbral shadows. Above this figure are listed the instant of conjunction in right ascension of the Moon with Earth's shadow axis and the instant of greatest eclipse, expressed as both Universal Times and Julian Dates. The penumbral and umbral magnitudes are defined as the fraction of the Moon's diameter immersed in the two shadows at greatest eclipse. The radii of the penumbral and umbral shadows P. Radius and U. Radius are also listed. Gamma is the minimum distance in Earth radii of the Moon's centre from Earth's shadow axis at greatest eclipse while Axis is the same parameter expressed in degrees. The Saros series of the eclipse is listed, followed by a pair of numbers. The first number identifies the sequence position of the eclipse in the Saros, while the second is the total number of eclipses in the series.

In the upper left and right corners are the geocentric coordinates of the Sun and the Moon, respectively, at the instant of greatest eclipse. They are:

R.A. - Right Ascension
Dec. - Declination
S.D. - Apparent Semi-Diameter
H.P. - Horizontal Parallax

To the lower left are the semi or half durations of the penumbral and umbral (partial) eclipses. Below them are the Sun/Moon ephemerides used in the predictions, followed by the extrapolated value of �T (the difference between Terrestrial Time and Universal Time). To the lower right are the contact times of the Moon with Earth's penumbral and umbral shadows, defined as follows:

P1 - Instant of first exterior tangency of Moon with Penumbra. (Penumbral Eclipse Begins)
U1 - Instant of first exterior tangency of Moon with Umbra. (Partial Umbral Eclipse Begins)
U4 - Instant of last exterior tangency of Moon with Umbra (Partial Umbral Eclipse Ends)
P4 - Instant of last exterior tangency of Moon with Penumbra. (Penumbral Eclipse Ends)

The bottom figure is an equidistant cylindrical projection map of Earth which shows the regions of visibility for each stage of the eclipse. In particular, the moonrise/moonset terminator is plotted for each contact and is labeled accordingly. The point where the Moon is in the zenith at greatest eclipse is indicated by an asterisk symbol. The unshaded region will afford a view of the entire eclipse while the darkly shaded area will witness none of the event. The remaining lightly shaded areas will experience moonrise or moonset while the eclipse is in progress. The shaded zones east of the '*' will witness moonset before the eclipse ends while the shaded zones west will witness moonrise after the eclipse has begun.

Eclipse Altitudes and Azimuths

The altitude a and azimuth A of the Sun or Moon during an eclipse depend on the time and the observer's geographic coordinates. They are calculated as follows:

h = 15 (GST + UT - α ) + λ a = arcsin [sin δ sin φ + cos δ cos h cos φ] A = arctan [-(cos δ sin h)/(sin δ cos φ - cos δ cos h sin φ)]

where

h = hour angle of Sun or Moon a = altitude A = azimuth GST = Greenwich Sidereal Time at 0:00 UT UT = Universal Time α = right ascension of Sun or Moon δ = declination of Sun or Moon λ = observer's longitude (east +, west -) φ = observer's latitude (north +, south -)

During the eclipses of 2006, the values for GST and the geocentric right ascension and declination of the Sun or the Moon (at greatest eclipse) are as follows:

Eclipse Date GST α δ Penumbral Lunar 2006 Mar 14 11.497 11.678 3.088 Total Solar 2006 Mar 29 12.445 0.525 3.403 Partial Lunar 2006 Sep 07 23.114 23.110 -6.741 Annular Solar 2006 Sep 22 0.080 11.959 0.266

Eclipses During 2007

Next year, there will be two solar and two lunar eclipses:

A full report on eclipses during 2007 will be published next year in the Observer's Handbook 2007.

NASA Solar Eclipse Bulletins

Special bulletins containing detailed predictions and meteorological data for future solar eclipses of interest are prepared by F. Espenak and J. Anderson and are published through NASA's Publication series. The bulletins are provided as a public service to both the professional and lay communities, including educators and the media. A list of currently available bulletins and an order form can be found at:

http://eclipse.gsfc.nasa.gov/SEpubs/RPrequest.html

The latest bulletin in the series is Total Solar Eclipse of 2006 March 29. Single copies of the eclipse bulletins are available at no cost by sending a 9 x 12-in. self-addressed envelope stamped with postage for 11 oz. (310 g). Please print the eclipse year on the envelope's lower left corner. Use stamps only, since cash and cheques cannot be accepted. Requests from outside the United States and Canada may include 10 international postal coupons. Mail requests to: Fred Espenak, NASA's Goddard Space Flight Center, Code 693, Greenbelt MD 20771, USA.

The NASA eclipse bulletins are also available over the Internet, including out-of-print bulletins. Using a Web browser, they can be read or downloaded through the World Wide Web from the GSFC/SDAC (Solar Data Analysis Center) eclipse page:

Eclipse Web Sites

A special Web site for solar and lunar eclipse is available through the Internet at:

http://eclipse.gsfc.nasa.gov/eclipse.html

The site features predictions and maps for all solar and lunar eclipses well into the 21st century, with special emphasis on eclipses occurring during the next two years. Detailed path maps, tables, graphs, and meteorological data are included. A world atlas of solar eclipses provides maps of all central eclipse paths from 2000 BC to AD 3000. Additional catalogues list every solar and lunar eclipse over a 5000-year period.

Detailed information on solar and lunar eclipse photography and tips on eclipse observing and eye safety may be found at:

http://www.mreclipse.com/

Acknowledgments

All eclipse predictions were generated on an Apple G4 iMac computer using algorithms developed from the Explanatory Supplement (1974) with additional algorithms from Meeus, Grosjean, and Vanderleen (1966). The solar and lunar ephemerides were generated from Newcomb and the Improved Lunar Ephemeris by Eckert, Jones, and Clark (1954). For lunar eclipses, the diameter of the umbral shadow was enlarged by 2% to compensate for Earth's atmosphere; corrections for the effects of oblateness have been included.

All calculations, diagrams, tables, and opinions presented in this paper are those of the author, and he assumes full responsibility for their accuracy.

Special thanks to National Space Club summer intern Sumit Dutta for his valuable assistance in preparing the web page (July 2005).

Footnotes

[1] The instant of greatest eclipse occurs when the distance between the Moon's shadow axis and Earth's geocentre reaches a minimum.

[2] Minimum distance of the Moon's shadow axis from Earth's center in units of equatorial Earth radii.

[3] Eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon

[4] Eclipse obscuration is defined as the fraction of the Sun's surface area occulted by the Moon.

[5] The sub-solar point is the geographic location where the Sun appears directly overhead (zenith).

References

Eckert, W.J., Jones, R., and Clark, H.K., Improved Lunar Ephemeris 1952-1959, U. S. Naval Observatory, Washington, DC, 1954.

Espenak, F., Fifty Year Canon of Solar Eclipses: 1986-2035, Sky Publishing Corp., Cambridge, MA, 1988.

Espenak, F., Fifty Year Canon of Lunar Eclipses: 1986-2035, Sky Publishing Corp., Cambridge, MA, 1989.

Espenak, F. and J. Anderson, 2004, Total Solar Eclipse of 2006 March 29, NASA TP2004-212762, Washington DC.

Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Her Majesty's Nautical Almanac Office, London, 1974.

Littmann, M., Willcox, K., & Espenak, F., Totality-Eclipses of the Sun, Oxford University Press, New York, 1999.

Meeus, J., Grosjean, C.C., & Vanderleen, W., Canon of Solar Eclipses, Pergamon Press, New York, 1966.

Meeus, J. & Mucke, H., Canon of Lunar Eclipses: -2002 to +2526, Astronomisches Buro, Wien, 1979.

Meeus, J., Mathematical Astronomy Morsels, Willmann-Bell, Richmond, 1997.

Newcomb, S., "Tables of the Motion of the Earth on its Axis Around the Sun," Astron. Papers Amer. Eph., Vol. 6, Part I, 1895.