Total solar eclipse of AD 1133 and ΔT

Abstract

Twenty-seven extant reports from medieval Europe and the Middle East of the total solar eclipse of AD 1133 (+1133) are analysed to set limits on the Earth rotation parameter ∆T. We conclude that at the epoch +1133, ∆T is in the range +720 <ΔT<+1110 seconds.

Keywords

Total solar eclipse AD 1133 ΔT

Introduction

Prior to the advent of accurate clocks in the 17th century, historical reports of the occurrence of total solar eclipses potentially provide the most accurate way of determining decade and long-term variations in the Earth’s rate of rotation. The paths of totality are narrow compared to the circumference of the Earth, and a definitive report of totality at a specific place fixes the observed longitude of the path and hence the rotational phase of the Earth at that epoch.

Professor Zawilski¹ has assembled an archive of reports of solar eclipses made from places in medieval Europe and the Near East. The eclipse of +1133 was widely observed and the archive contains 27 reports of that eclipse. Morrison et al.² used the two most explicit observations of totality to determine the value of the parameter ∆T, which is used to measure variations in the rate of rotation of the Earth. The purpose of the present paper is to examine the other 25 reports of the eclipse to determine whether tighter constraints can be placed on the value of ∆T obtained by Morrison et al.³

An Appendix with the original historical reports of the solar eclipse of AD 1133 together with data on the greatest phase at the various places is available as Supplementary Material in the on-line edition of the Journal.

Path of totality and ∆T

We have developed our own programs for the calculation and plotting of the eclipse tracks in Figures 1 and 2. The basic coordinates of the Sun and Moon are extracted from the Jet Propulsion Laboratory’s long-term ephemerides DE 431⁴ and the algorithms for finding their positions for the particular date and time and the position of the track of the eclipse on the Earth are taken from The Explanatory Supplement^5,6 together with routines from the International Astronomical Union’s Standards of Fundamental Astronomy.⁷ The map outlines in Figures 1 and 2 were downloaded from Natural Earth.⁸

Figure 1.

Track of totality western Europe for ∆ $T = + 1108 s$ .

Figure 2.

Track of totality across eastern Europe and the Middle East for $Δ T = + 1108 s$ .

The computed longitude of the track of totality is obtained on the uniform time-scale Terrestrial Time (TT), which is the argument of time in the Solar System ephemerides. The difference in time $(Δ T)$ measured in seconds between the TT and UT of the eclipse, due to the cumulative effect of variations in the Earth’s rate of rotation between some adopted epoch and the date of the eclipse, causes a displacement between the computed and observed longitude $(λ)$ . This displacement, measured in degrees positive to the east, is related to ∆T by

λ (computed - observed) \times 240 = (TT - UT) = Δ T .

Thus, moving the computed track east in longitude by $1^{\circ}$ requires an addition of $240 s$ to ∆T; and moving west by $1^{\circ}$ the subtraction of 240 seconds.

Using this methodology, values of ∆T were derived by Morrison et al.⁹ for the historical period $- 720$ to $+ 1600$ . The value of ∆T for the epoch $+ 1133$ August $02$ in that paper is $+ 1108$ seconds, which is obtained from a spline fit to all the values of ∆T. Figure 1 shows the computed track of totality over northern Europe for a value of $Δ T = + 1108 s$ .

The position of the umbral shadow cone is shown at 11:48 UT. Figure 2 covers southern Europe and the Middle East.

Penumbral phase and background brightness of sky

On either side of the track of totality there is a wide zone where the eclipse is partial. A measure of the size of the eclipse is given by the magnitude, which is the fraction of the solar diameter covered by the Moon at the time of greatest phase, expressed in units of the solar diameter. The greatest phase at a place in the penumbra occurs when the shadow cone passes closest to it.

To what extent stars are visible during totality and at places outside the belt of totality, depends on the sky brightness, the magnitude of the objects and the meteorological conditions. For example, haze will diminish the number of objects seen, and this could vary from place to place.

As a guide to the limiting stellar magnitude in a clear sky during the partial and total phases of an eclipse, we use the values in Table 2 of Können and Hinz,¹⁰ this shows that for an eclipse magnitude of $0.888$ only objects brighter than $- 1.5$ are clearly visible, and at $0.986$ the limit is $+ 1.0$ . Between $0.986$ and the boundary of totality the sky darkens considerably and stars brighter than $+ 2.0$ become visible. During totality the background falls to a level of brightness equivalent to that of Civil Twilight, and in mid-totality third magnitude stars can be seen.

Figures 1 and 2 include the equal contours for eclipse magnitudes $0.888$ and $0.986$ in the penumbra for $Δ T = + 1108 s$ .

Star field

Figure 3 shows the positions of the planets and stars brighter than first magnitude $(+ 1.0)$ surrounding the Sun at the time of the eclipse of $+ 1133$ . Mercury $(- 0.7)$ and Venus $(- 3.9)$ were within about $30^{\circ}$ of the Sun. Mars was less than $10^{\circ}$ from the Sun, and fainter at magnitude $+ 1.8$ .

Figure 3.

Sky chart looking from the south at the bottom for a central location (Disibodenberg), showing planets and stars brighter than magnitude $+ 1.0$ above the horizon.

For objects at an altitude of $10^{\circ}$ , atmospheric absorption reduces the limiting stellar magnitude by about 1. Below $10^{\circ}$ absorption increases steeply. Sirius would have been reduced to about $- 0.5$ , and Rigel would have been invisible even during totality. Aldebaran would have been reduced to about $+ 2.0$ .

Given Venus’s considerable brightness $(- 3.9)$ and its separation from the Sun $(29^{\circ})$ , it should have been visible around the time of greatest phase at places within the phase boundary of $0.888$ . A wide range of ∆T would bring all the places in Figures 1 and 2 within that zone. For observers at places closer to the $0.986$ boundary, Venus, Mercury $(- 0.7)$ and probably Sirius (reduced by atmospheric absorption to $- 0.5$ ) would have been seen. This depends more critically on the positioning of the path of the eclipse, and hence on the value of ∆T. At places within the $0.986$ boundary, all the stars in Figure 3 except Rigel, Aldebaran and Vega would have progressively become visible in clear sky conditions.

Observational reports

The observational reports assembled by Zawilski are given in full in the Supplemental Appendix to this paper. Table 1 lists the names of the places of the observations, together with summaries of the critical comments appertaining to the greatest phase of the eclipse at each place. They are ordered by greatest phase, beginning to the west of the track of totality and progressing eastwards. In Figures 1 and 2 the place names are contracted to the first two letters of those listed in Table 1. Plots of the crescent Sun at greatest phase for $Δ T = + 1108 s$ are included in the Supplemental Appendix.

Table 1.

Critical comments in reports ordered by greatest phase from west to east, calculated for $Δ T = + 1108 s$ . The magnitude is listed for each entry.

Place	Magnitude	Critical comment
Monte Cassino	0.893	Almost whole Sun obscured
Malmesbury	0.931	Stars around the Sun
Cambrai	0.952	Sun suddenly obscured – darkness
Dover (probably)	0.954	Like a 3-day old Moon – many stars
Bourbourg	0.959	Sun obscured – stars
Fosse	0.974	Sun obscured – stars
Floreffe	0.975	Sun obscured – stars
Gembloux	0.977	Sun eclipsed – stars
Zwiefalten (?)	0.984	Dark as night – Sun clearly without light (place in doubt)
Liege	0.986	Sun eclipsed – great darkness – stars shining brightly
Brauweiler	0.992	Sun obscured – stars
Disibodenberg	0.994	Sun obscured – darkness – stars
Kloosterrade*	1.000	As night – stars – birds roosted – dew formed
Augsburg (?)	1.000	Sun eclipsed – as night – stars in almost whole sky
Freising	1.000	Darkness – stars
Salzburg	1.000	Sun disappeared – darkness – stars
Heilsbronn	1.000	Sun black as pitch – many stars – as night
Egmond	1.000	Sun eclipsed – day turned to night – stars
Würzburg	1.000	As middle of night – stars
Admont	1.000	Sun eclipsed – darkness – stars
Reichersberg*	1.000	Eclipse of Sun – entirely concealed – many stars
Hirschau	1.000	Eclipse of Sun – stars clearly visible
Paderborn	1.000	Eclipse of Sun – stars
Melrose	1.000	Day turned into night
Corvei	1.000	Eclipse of Sun – almost like night – many stars
Jerusalem	1.000	Death of Sun – whole world darkened
Praha	0.981	Like a crescent Moon

The two asterisked reports were used in Morrison et al. (see Note 2).

Our objective is to deduce whether the reports are specific enough to fix the computed eclipse path in longitude, and hence the value of ∆T. We have adopted $Δ T = + 1108 s$ in our computations. If $Δ λ$ is the correction in longitude in Figures 1 and 2 required to bring the belt of totality, the phase boundary $0.986$ or $0.888$ – whichever is applicable – over the place of observation, then the corrected value of ∆T is

+ 1108 + 240 Δ λ,

where ∆λ measured in degrees is positive if the required shift is to the east, and negative to the west. We have rounded the results to the nearest 5 seconds.

The paper by Morrison et al.¹¹ was restricted to the consideration of reports of totality. The two most explicit reports of totality were used to constrain ∆T. The upper boundary of the computed belt of totality in Figure 1 can not be moved further west than $2^{\circ} . 33$ , otherwise the eclipse would not have been total at Reichersburg (Re). This sets a lower limit of $+ 530 s$ for ∆T. The lower boundary of the computed belt of totality can not be moved further east than $0^{\circ} . 001$ , otherwise the eclipse would not have been total at Kloosterrade (Kl). This sets an upper limit of $+ 1110$ seconds for ∆T. Thus, the constraints on ∆T from these two observations alone are $+ 530 < Δ T < + 1110$ seconds.

In the present paper we expand on our derivation of the limits on ∆T by analysing reports of the eclipse from the penumbra as well as the umbra.

Discussion of individual reports

As a working hypothesis, we adopt the criteria that if a few bright stars are seen at a place, it is positioned somewhere between the $0.888$ and $0.986$ boundaries. If many stars are reported, and it is not clear whether or not the eclipse was total, the phase can be anywhere between the upper and lower $0.986$ contours. However, it is usually evident whether it is the upper or lower which is relevant in the discussion of the constraint on ∆T.

We begin with the discussion of the report from Monte Cassino (see Figure 2), which is furthest to the west of the computed path and proceed eastwards across the path of totality, ending with the easternmost report from Praha.

Monte Cassino (Figure 2)

The eclipse is definitely not total here. No sighting of stars is reported, which means that not even Venus was seen. This implies that Monte Cassino was either outside the phase boundary $0.888$ or just within it. This degree of uncertainty does not permit a useful constraint on ∆T.

Malmesbury (Ma, Figure 1)

William of Malmesbury was librarian at the monastery of Malmesbury, England at that time. He does not state that the eclipse was total, but reports seeing stars around the Sun. This implies that at least Venus and Mercury were visible, and therefore Malmesbury was somewhere in the zone between $0.888$ and the boundary of totality. This is a comparatively wide zone of longitude and therefore does not produce useful constraints on ∆T.

Cambrai (Ca, Figure 1)

This report states that the Sun was suddenly obscured and there was darkness over all the Earth. Contrary to Malmesbury, no sighting of stars is reported, even though it has a slightly greater maximum phase. If Venus and Mercury were visible at Malmesbury, they should have been visible at Cambrai. The next report from Dover, with virtually the same greatest phase, does remark on the sighting of stars. This apparent inconsistency highlights the problem of variations in reporting, possibly due to differences in the local transparency of the atmosphere. As with Malmesbury, this observation does not produce useful constraints on ∆T.

Dover (probably) (Do, Figure 1)

The chronicle of John of Worcester records that the King and his army were assembled on the south coast of England in preparation to cross the channel to the continent. The likelihood is that they were at or near Dover, which is the nearest crossing point to the continent. The report states explicitly that the eclipse was not total, but that at greatest phase the Sun appeared like a new moon and many stars were seen. In that case, Dover would have to lie within the $0.986$ boundary, and the computed longitude of the eclipse path moved west by 3°.00. This requires that ∆T is less than

+ 1108 - 240 \times 3.00 = + 390 s .

On the other hand, the Anglo-Saxon Chronicle reports that the Sun was like a 3-day old moon with stars about it. For a 3-day old moon, the eclipse magnitude would be about $0.88$ . At this phase, only Venus would have been visible. This disagrees with the statement that more than one star was seen, and we cannot usefully constrain the range of ∆T.

Bourbourg (Bo, Figure 1)

With a greatest phase similar to Cambrai and Dover, the report from Bourbourg concurs with Dover in seeing some stars, again, probably Venus, Mercury and Sirius. This does not usefully constrain ∆T.

Fosse, Floreffe, Gembloux (Fo, Fl, Ge, Figure 1)

None of this geographically close group of places asserts unequivocally that the eclipse was total. They are all consistent in sighting [some] stars; but as distinct from the first of the two reports for Dover, they do not assert that many stars were seen. The ‘stars’ could have been Venus, Mercury, Sirius, and possibly a few of the very brightest stars. So, we cannot be sure that these places were positioned inside or close to the $0.986$ boundary. Again, this does not usefully constrain ∆T.

Liege (Li, Figure 1)

The report states that there was great darkness and stars were shining brightly. This suggests that Liege was within the 0.986 boundary, but not definitely total. To be within the $0.986$ boundary, ∆T must be less than

+ 1108 - 240 \times 0.08 = + 1090 s .

The lower boundary $(- 20 s)$ is outside the area of interest.

Zwiefalten (Zw, Figure 1)

The report from Zwiefalten Monastery states that it darkened into night and the Sun was clearly without light. This definitely means that the eclipse was total. However, Liege, with nearly the identical greatest phase stops short of stating that the eclipse was total there. The problem with the report from Zweifalten is that its provenance is in doubt. The account may have been borrowed from another lost source. If the provenance were secure, totality would be possible if ∆T were less than $+ 805 s$ .

Brauweiler and Disibodenberg (Br, Di, Figure 1)

These two places are close to one another, and both state that the Sun was obscured and stars were seen, but this is not qualified by ‘many’. Therefore, we cannot be certain that they lay within the $0.986$ contour, and ∆T cannot be usefully constrained.

Kloosterrade (Kerkrade) (Kl, Figure 1)

The report from Klooserrade supplies the supplementary information that the birds roosted and dew formed. This definitely indicates totality, and sets an upper limit of $+ 1110 s$ on ∆T. The lower limit $(- 220 s)$ is redundant.

Augsburg (Au, Figure 1)

The entry in the chronicle is definitely an account of totality. The Final sentence states: At length the Sun emerging from the darkness appeared in the manner of a star, then in the form of a new moon. The manner of a star is probably the appearance of a Baily’s bead, which is followed by a crescent shaped Sun. The only reservation with this report is its provenance. The exact place of observation is unknown. Our computation with $Δ T = + 1108 s$ , which relies on the definite report of totality at Kloosterrade, puts Augsburg just within the belt of totality. This suggests that the report could indeed have emanated from Augsburg, but we cannot use this as an independent corroboration of the result from Kloosterrade.

Freising, Salzburg, Heilsbroon, Egmond, Würzburg, Admont and Reichersberg (Fr, Sa, He, Eg, Wu, Ad, Re, Figure 1)

Apart from Freising and Admont, all these places either definitely describe totality or at least strongly suggest it. Salzburg (Sun disappeared; darkness; stars), Heilsbroon (Sun black as pitch; many stars), Egmond (Sun eclipsed; day turned to night; stars), Würzburg (as middle of night; stars), Reichersberg (Sun entirely concealed; many stars). These places, which strongly indicate totality, set the following lower and upper limits on ∆T:

Place	Lower ΔT (seconds)	Upper ΔT (seconds)
Salzburg	+265	+1440
Heilsbroon	+280	+1520
Egmond	+255	+1730
Würzburg	+390	+1610
Reichersberg	+530	+1725

Freising and Admont (darkness and stars) were probably within the $0.986$ contours. These produce the following limits:

Place	Lower ΔT (seconds)	Upper ΔT (seconds)
Freising	(−80)	+1605
Admont	+295	+1935

The value in brackets is outside the range of interest for ∆T

Hirschau, Paderborn, Corvei and Melrose (Hi, Pa, Co, Me, Figure 1)

None of these places states that the Sun was completely covered. On the other hand, they are explicit enough to put them inside the $0.986$ contours. This sets the following limits on ∆T:

Place	Lower ΔT (seconds)	Upper ΔT (seconds)
Hirschau	+405	(+2170)
Paderborn	+525	(+2485)
Corvei	+720	(+2685)
Melrose	+445	(+3385)

Jerusalem (Figure 2)

The chronicle of St Andrew of Cambrai contains the following report:

After a long time it has been told much after returning home from Jerusalem, on that very day and that hour of darkness four hundred soldiers of the temple except five were killed by the Saracens on the other side of the river. And no wonder because of the killing of his members God had pleasure to introduce darkness to the world, and in this death of the Sun also the whole world was certainly darkened.

This is an intriguing report relayed from Jerusalem. It cannot be used to constrain ∆T because it does not say precisely where the eclipse was witnessed nor whether or not it was total. However, it is noteworthy that the computed northern limit of totality passes over the River Jordan close to Jerusalem. So, we could surmise that the report emanated from the east of the Jordan, looking towards Jerusalem, where the eclipse was either total or very nearly so.

Collected results

We collect together the dependable constraints on ∆T discussed in the previous section. These are plotted in Figure 4. The two dashed lines show the solution space for ∆T common to all these results.

Figure 4.

Constraints on ∆T from discussion of places with reliable reports.

The results constrained by the $0.986$ contours are intrinsically less accurate uncertain than those from the belt of totality, because they do not define such a sharp transition in the visibility of stars. For this reason, we prefer to retain the upper limit of $+ 1110 s$ from Kloosterrade over that from Liege $(+ 1090 s)$ . The relatively close agreement of these two results suggests that the uncertainty of the results from the $0.986$ boundaries is about $\pm 20 s$ .

Conclusion

We conclude that

+ 720 < Δ T < + 1110 s .

This is the tightest constraint on ∆T from consideration of all 27 reports, and thereby constitutes a moderate tightening over our previous result of

+ 530 < Δ T < + 1110 s

for the solution space for ∆T at the epoch $+ 1133$ .

We note that ∆T has to be greater than $+ 980 s$ to satisfy the definite report of totality at Novgorod for the contemporaneous eclipse of $+ 1124$ (see Stephenson et al.¹²) Although this falls within the constraints above, it is not possible to corroborate from the observations discussed here that ∆T does lie within the narrow limits $+ 980 < Δ T < + 1110 s$ .

Supplemental Material

sj-pdf-1-jha-10.1177_00218286231209030 – Supplemental material for Total solar eclipse of AD 1133 and ΔT

Supplemental material, sj-pdf-1-jha-10.1177_00218286231209030 for Total solar eclipse of AD 1133 and ΔT by Leslie V. Morrison, Catherine Y. Hohenkerk, Marek Zawilski and F. Richard Stephenson in Journal for the History of Astronomy

Footnotes

Acknowledgements

The authors acknowledge HM Nautical Almanac Office and the International Astronomical Union’s Standards of Fundamental Astronomy. We thank the two referees for their helpful criticisms and suggestions, which have led to an improvement in the presentation of this paper.

Supplemental material

Supplemental material for this article is available online.

Notes

Notes on Contributors

Leslie V. Morrison worked in the fields of astrometry and the Earth’s rotation at the Royal Greenwich Observatory, 1960–1998. He has collaborated with F. Richard Stephenson on several studies of the long-term variations in the Earth’s rotation, including, Measurement of the Earth’s rotation: 720 BC to AD 2015.

Catherine Y. Hohenkerk worked at the Royal Greenwich Observatory from 1971 and in the late 1970s transferred to HM Nautical Almanac Office (HMNAO), where she worked on the Nautical and Astronomical Almanacs. She retired from the U.K. Hydrographic Office, latterly HMNAO’s host organisation, at the end of January 2017. She is a fellow of the Royal Institute of Navigation and chair of the International Astronomical Union’s Standards of Fundamental Astronomy (SOFA) Board. She collaborated with Stephenson and Morrison in the paper Measurement of the Earth’s rotation: 720 BC to AD 2015.

Marek Zawilski worked 1972–2016 as a scientist at the University of Technology of Lodz, Poland, in the field of environmental engineering. He was a long-time observer of occultation phenomena, and in the years 1979–2004 he was the co-ordinator of the observation of these phenomena at the Polish Society of Amateur Astronomers, as part of the activities of IOTA (International Occultation Timing Association). Since 1990, he has been collecting information on historical observations made in medieval Europe and the Middle East of solar eclipses and occultations of stars by the Moon. These have been compiled into an archive. In 2022, he was honoured with the annual David E. Laird IOTA award for his activities.

F. Richard Stephenson is an Emeritus Professor at the University of Durham, in the Physics department. His research concentrates on historical aspects of astronomy, in particular analysing ancient and medieval astronomical records to reconstruct the history of Earth’s rotation, as exemplified in his book Historical Eclipses and Earth’s Rotation, Cambridge University Press.

Supplementary Material

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