History Online - Eclipses

Example 1. Consider the three famous eclipses of Thucydides (the so-called triad). They are linked into one triad by their having been described in one historical text, namely the History of the Peloponnesian War. The descriptive characteristics of the triad, which are extracted from Thucydides' text unambiguously, are of the following form.

(1) All three eclipses were observed in the Mediterranean region, namely, in a square approximately bounded by the longitudes 15° E. and 30° E. and the latitudes 30° N. and 42° N.
(2) The first eclipse was solar.
(3) The second eclipse was solar.
(4) The third eclipse was lunar.
(5) The time interval between the first and second eclipses was 7 years.
(6) The time interval between the second and third eclipses was 11 years.
(7) The first eclipse occurred in summer.
(8) The first (solar) eclipse was total (since 'the stars were visible'), i.e., its phase $ is 12'.
(9) The first eclipse occurred in the afternoon (local time).
(10) The second (solar) eclipse occurred at the beginning of summer.
(11) The third (lunar) eclipse occurred at the end of summer.
(12) The second eclipse occurred approximately in March.
Condition 12 is not clearly determined from Thucydides' text and, therefore, is not included in the final list of conditions.
The problem arises to find a triad of eclipses completely satisfying all conditions 1-11. Work gives the traditional astronomical solution, namely, 431, 424, and 413 B.C. However, as has been known long ago, it does not satisfy all the data of the problem.

As a matter of fact, the eclipse of 431 B.C. was not total as required by condition 8. It was only annular with phase 10' for the observation zone and could not be observed as total anywhere on the earth's surface (pp. 176-177). This important circumstance was noted by many authors, e.g., J. Zech, E. Heis, N. Struyck, G. Riccioli, F. Ginzel, and I. Hoffman . A considerable number of astronomical papers were devoted to the recalculation of the phase $ of the eclipse of 431 B.C., for which various admissible corrections were introduced into the equations of the lunar theory in order to make the phase close to 12'. Thus, Dionysius Petavius obtained $ = 10'25 for the observation zone, Struyck 11' (p. 176), Zech 10'38 Hoffman 10'72 (p. 176), and Heis even 7'9(!) (p. 176). In the modern literature, the phase value is assumed to be 10' . We stress once again that, due to its annular form, the first eclipse in 431 B.C. was total nowhere on earth for any latitude and longitude. Accordingly, Ginzel wrote:

'The insignificance of the eclipse phase was somewhat shocking. ... According to the new calculations, the phase was equal to 10'. ...' .

Besides, certain other conditions were not fulfilled either. For example, the umbra passed through the observation zone only after 17 hours local time, and even after 18 hours according to Heis which means that condition 9 (the eclipse occurring in the afternoon) is satisfied only approximately.

Certain authors (; see the survey) carried out the calculation of the coordinates of bright planets, thinking that they could have been seen during the annular eclipse, in order to satisfy the important condition 8. However, the obtained results showed clearly that the planets' positions on the celestial sphere during the eclipse of 431 B.C. did not provide for their reliable visibility. If Venus could have been visible, then, for example, Mars was only 3° over the horizon (Heis's computation), while Jupiter and Saturn were below the horizon, and so forth. Johnson suggested another astronomical solution for Thucydides' first eclipse, namely, 433 B.C. Although it soon became clear that this solution still did not satisfy the data of the problem posed, it was now for other reasons . Besides, this eclipse had a short phase, namely, 7'8 .

The largest variation possible of certain constants in the lunar equations, with the purpose to increase the phase of the eclipse in 431 B.C., was made by Stockwell. However, it yielded only 11'06 for the observation zone, which did not account for the completeness of the eclipse either. The computations were questioned in the literature, too .

In this connection, an attempt to revise Thucydides' text itself, and, in particular, condition 8, should be noted also. However, its detailed analysis carried out at the author's request by E.V. Alexeeva (Faculty of Philology, Moscow University) showed that the eclipse characteristics were unambiguously determined from Thucydides. This circumstance had not been questioned earlier, though.

No other astronomical solutions in 600-200 B.C., which would be more suitable than the traditional solution of 431, 424, 413 B.C., seem to have been found. It is because of this fact that this incorrect 'solution' has been retained in spite of the above contradiction repeatedly discussed in the literature.

Meanwhile, the application of the formal astronomical dating method and the extension of the search interval (for astronomical solutions) to 900 B.C.-A.D. 1600 yield two and only two exact solutions, the first having been given in paper (Vol. 4, pp. 509, 493-512), while the second one was given by the author of the present work during the repeated analysis of all the eclipses from the indicated interval and the construction of their trajectories on the diagram.

Thus the first solution yields August 2, 1133, March 20, 1140, and August 28, 1151, whereas the second is August 22, 1039, April 9, 1046, and September 15, 1057. Note that the fact of the availability of exact solutions itself is nontrivial. In both exact solutions found, even condition 12 is fulfilled, the one not originally included in the list of basic data. Besides, the first eclipse is total in both solutions (for the observation zone), which is just what was required by condition 8.