Solving Problems

in the History of

Chinese Astronomy and Astrology

N. Sivin


The purpose of this guide is to facilitate the study of early knowledge of the sun, moon, planets and stars in ancient China. The first part lists reference sources; the second provides instructions for using a planetarium program, usable on any computer, to view ancient solar and lunar eclipses.

Reference Sources

Constellations and Stars

• The handiest source for descriptions of each Chinese constellation is

Schlegel, Gustave. 1875. Uranographie chinoise. La Haye: Martinus Nijhoff.

• A fine reconstruction of the sky as seen in the 2nd century B.C., with star maps and many illustrations, is

Sun Xiaochun; Jacob Kistemaker. 1997. The Chinese Sky during the Han. Constellating Stars & Society. Leiden: E. J. Brill.

• A good orientation to ancient celestial mapping is

F. Richard Stephenson, "Chinese and Korean Star Maps and Catalogs," in The History of Cartography. Vol. 2, book 2. Cartography in the Traditional East and Southeast Asian Societies, ed. Harley, J. B.; David Woodward, pp. 511-78 (University of Chicago Press, 1994).

• There are excellent detailed maps and lists with an index in

I Shih-t’ung 伊世同. 1981. Chung-hsi tui-chao heng-hsing t’u piao 1950.0 中西对照恒星图表 (Maps and tables with Chinese and Western fixed stars juxtaposed, epoch 1950.0). 2 vols. B: K’o-hsueh Ch'u-pan-she. This work is based on an excellent mid-18th-century compilation that also included European identifications of stars.

• For good reproductions of ancient star maps, some in color, see

Ch’en Mei-tung 陈美东. 1996. Chung-kuo ku hsing t’u 中国古星图 ("Star charts in ancient China"). Shenyang: Liao-ning chiao-yü Ch'u-pan-she.

Planetary Phenomena

To compute the times of stations, occultations, conjunctions, etc., use the tables in

Tuckerman, Bryant. 1962-1964. Planetary, Lunar, and Solar Positions. 2 vols.; Philadelphia: American Philosophical Society. This work covers 601 B.C. to A.D. 1649. It gives longitude and latitude at 5- or 10-day intervals. Exact times of phenomena may be determined by linear interpolation or by graphing. Thus to find a conjunction of Venus and Mercury, graph the longitudes of each planet, determine the point at which the orbits cross, and estimate the time.

The values for longitude and latitude of Mars have been improved in

Houlden, Michael A.; Stephenson, F. Richard. 1986. A Supplement to the Tuckerman tables. Memoirs of the American Philosophical Society, 170. Philadelphia: American Philosophical Society

Lunar Phenomena

Goldstine, Herman H. 1973. New and Full Moons. 1001 B.C. to A.D. 1651. Philadelphia: American Philosophical Society. A complete list based on the same elements as Tuckerman. Note that this may be used as a quick check on eclipses, since solar eclipses take place at new moon (conjunction) and lunar eclipses at full moon (opposition).


The best ready reference for solar eclipses visible in East Asia only is

F. R. Stephenson & M. A. Houlden, Atlas of Historical Eclipse Maps. East Asia 1500 BC - AD 1900. Cambridge UP, 1986.

Not a ready reference, but useful for a great number of eclipses, is

Stephenson, F. Richard. 1997. Historical Eclipses and the Earths Rotation. Cambridge University Press. Detailed theoretical and empirical study of historic records. Argues for variable non-tidal changes in day length.

For the full elements of solar and lunar eclipses, and somewhat more detailed maps, see

Watanabe Toshio 渡邊敏夫 . 1979. Nihon. Chōsen. Chūgoku. Nisshoku gesshoku hōten 日本。朝鮮。中国。日食月食宝典 (Canon of solar and lunar eclipses for Japan, Korea, and China). Tokyo: Yūzankaku.

You can look up the local time and magnitude of solar eclipses in eight Chinese capitals through history in

Chang P’ei-yü . 1997. San-ch’ien-wu-pai-nien li-jih t’ien-hsiang (Calendrical days and celestial phenomena for 3500 years). 2d ed. Cheng-chou: Ta Hsiang Ch'u-pan-she. Orig. publ., Cheng-chou: Ho-nan Chiao-yü Ch'u-pan-she, 1970. The scope of information and the accuracy of its astronomical data make this book far superior to its predecessors. In addition to using excavated materials, it provides unprecedented data, e.g., dates and times of new as well as full moons and the 8 main divisions of the solar year (pa chieh 八節), and the maximal phases and magnitudes of eclipses as seen from 8 ancient capitals. It is also exceptionally easy to use.

To check visibility of a past eclipse from a given site, the most reliable sources are Hermann Mucke & Jean Meeus, Canon of Solar Eclipses. -2003 to +2526, and Meeus & Mucke, Canon of Lunar Eclipses. -2002 to +2526 (Wien: Astronomisches Büro, 1983). The former gives Besselian elements from which you can calculate the important phenomena of a solar eclipse. Since lunar eclipses may be viewed from a whole hemisphere of the earth’s surface, no computation is necessary when using the latter.

The most accurate online lists of historical eclipses are those of Fred Espenak at

Espenak, following F. R. Stephenson, uses a different value than Mucke & Meeus for the important time constant (Δt); which is better is still a matter for argument. I find the latter more reliable for a broad range of periods.


There is a list based on computation and European records in Hermann Mucke, Helle Kometen von -86 bis +1950 (Wien: Astronomisches Büro, 1972, 1976).

Reference Books For Computation

Two books that give basic formulas in a useful form are Jean Meeus, Astronomial Formulae for Calculators (2d ed., Richmond, VA: Willmann-Bell, 1982), an excellent introduction, and Almanac for Computers (Nautical Almanac Office, U.S. Naval Observatory, 1980 and later), with tables of data for the year published.

Viewing Ancient Eclipses

It is possible to generate a simple table or map for any eclipse—although not to observe it as it would appear from the earth—with a rough-and-ready freeware program for personal computers called EMAPWIN. You can download it from

Planetarium programs allow you to actually view eclipses, even ancient ones, with high accuracy, although not as high as you can reach by using Mucke & Meeus to compute. But the difference for an eclipse two thousand years ago is between half an hour and an hour. That is roughly equal to the uncertainty due to secular changes in the lunar orbit; but of course one can never be sure whether the two discrepancies add or subtract.

By far the best PC application is Starry Night Pro for both PC and Macintosh, now in v. 4. The procedure is roughly the same for most planetarium programs. These are the main steps:

Þ1. There is a text file called "LocationsEarthE.txt" that records longitude, latitude, and altitude (if you know it) for the various observatories and other sites you want to use. Using the large list of ancient East Asian capitals in Watanabe 1979, you can add those you want, and get rid of listings for sites you don’t expect to use.

Another datum you will need: Keep in mind that before 1912 China did not have time zones. Watanabe and other historians of astronomy have tended to list times in China’s standard time (Greenwich Mean Time + 8 hours), but that is incorrect; most ancient capitals were to the west of that meridian. You will need to determine local time, by dividing longitude by 15.

2. Once you have fired up the program, go to the Tool Palette. Click on Location to set the site of observation, and then use Lookup to find it on the list and set it automatically. For most purposes you will want to set the angle of view (the button that by default says 100°) and set it to 7 or 15°

3. Then go to the Planets Palette and lock on either sun or moon, depending on what you want to do. That will keep the one you want centered on the screen while the rest of the sky moves past it.

4. Finally go to the Time Palette and set the year, month, day, and time of the phenomenon you want to see. You will probably want to begin an hour or half an hour before the maximum phase of the eclipse. Then set the time interval, in the upper left of the palette, to one that lets you view it as you wish. I usually begin at between 3 and 1 minutes. When the eclipse approaches totality, you may want to stop the viewing (using the buttons next to the time), go closer (say 3°), and move more slowly (perhaps between 10 and 3 seconds).

5. When everything is set, push the forward button, relax and let it happen. Keep in mind that you can print what you see. By setting options that the manual outlines, you can include what data you want on the printed version.

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Last Modified 2003.8.23