Fotheringham’s 1920 Accelerations of the Sun and Moon Revisited

Abstract

One hundred years ago, J.K. Fotheringham famously derived the “accelerations” of the Sun and Moon from the reports of 11 classical solar eclipses. We review critically the reliability of these eclipse reports and rework his diagrammatic method, treating the deceleration of the Earth’s rotation as an unknown, rather than the “acceleration” of the Sun. There is some serendipity in his choice of the critical eclipses, which opportunely facilitated his derivation of seemingly accurate results for the accelerations.

Keywords

Astronomy eclipses Earth rotation Fotheringham

Introduction

The Oxford scholar John Knight Fotheringham in 1920 published a seminal paper¹ in which he derived what were then termed the “accelerations of the Sun and Moon.” It had been known for some time that without tidal interactions the purely point-to-point gravitational theories of the geocentric motions of the Sun and Moon could not account for their apparent long-term positions. In particular, both longitudes required extra accelerations in order to reconcile reports of the places of ancient eclipses with the calculated tracks of totality or annularity. Fotheringham’s result for these accelerations from a consideration of 11 records of ancient solar eclipses formed the cornerstone of the subject for many years, and attracted much attention among geophysicists, notably in the influential discussion of the Earth’s rotation in the monograph by Munk and MacDonald.²

Fotheringham’s method entailed finding a linear combination of the unknown solar and lunar accelerations such that the computed resultant range of the paths of total or annular eclipses satisfied the geographical constraints imposed by the historical records. By way of illustrating his method, we consider one of the historical eclipses that Fotheringham analysed. The total solar eclipse of $- 762$ June 15, which we discuss in detail later in this paper, is recorded in an Assyrian chronicle: the Eponym canon. While the date is certain, it is not clear where in Assyria the eclipse was witnessed. Because this is the only record of an eclipse in the entire Assyrian chronicle, Fotheringham assumed that the eclipse was total somewhere in the most populous region of Assyria, and he adopted two limiting geographical positions in Assyria: 34°.18 N, 45°.15 E; 37°.40 N, 42°.19 E. He then calculated the linear combination of the unknown accelerations in the longitudes of the Sun ( $L'$ ) and Moon (L) that produced tracks of totality that satisfied the geographical constraints imposed by these limiting positions. Figure 1 shows one of the northernmost tracks with its southern edge passing over the north geographical limit, and the corresponding southernmost track with its northern edge passing over the southern limit. In Figure 2, Fotheringham plotted the linear combinations of $L'$ and L that produced bands of totality such as those plotted in Figure 1. The area between these lines in Figure 2 defines the boundaries of the solution space ( $L'$ , L) in which the accelerations must lie in order to produce a total eclipse or annular eclipse in the geographical area under consideration.

Figure 1.

Two limiting tracks of totality for the eclipse of –762 June 15 that was recorded as occurring somewhere in Assyria, which Fotheringham assumed lay between the N. and S. limits shown in the diagram.

Figure 2.

Reproduction of Fotheringham’s diagram showing his solutions for the solar and lunar accelerations derived from classical eclipses. The letter “F” marks his adopted solution.

Figure 2 shows the linear solutions for the 10 classical eclipses that Fotheringham analysed in the period $- 1062$ to $+ 71$ . Only the northernmost limit for $- 762$ produced a linear combination lying within the scope of the diagram, and the wide solution space resulting from this eclipse extends to the right of the line labelled ‘ $- 762$ ’. The eclipses of $- 128$ , $+ 29$ , and $+ 71$ produce relatively narrow corridors of solution space, as a result of their tighter geographical constraints than those obtaining for $- 762$ . The region common to these four eclipses defines the triangular area shown shaded in Figure 2. Fotheringham’s preferred solution for the “accelerations” lay in this triangular area

L (Moon) = + 10.8 ″ / {cy}^{2}

L' (Sun) = + 1.5 ″ / {cy}^{2}

By “acceleration” he meant the coefficient of $T^{2}$ in the expressions for the mean solar and lunar longitudes, where $T$ is measured in Julian centuries of Universal Time (UT).

Fotheringham’s result for the “acceleration” of the Sun is now regarded as purely apparent, and the consequence of the deceleration of the Earth’s rate of rotation produced principally by the tidal torques exerted by the Moon and Sun. This deceleration causes the UT scale, based on the period of the Earth’s rotation, to depart from the uniform time-scale Terrestrial Time (TT) by an amount ∆T, measured in seconds of time. The parabolic behaviour of ∆T over the historical period is measured in units of seconds of time per century per century (s/cy²).

In our recent discussion of many eclipses garnered from Babylon, China, ancient Greece, the Arab Dominions and medieval Europe (Stephenson et al.³), we found the average parabolic correction to the UT scale to be $Δ T = + 32^{s} . 5 T^{2}$ for the period $- 700$ to the present. For the shorter period covered by Fotheringham’s diagram (c. $- 1000$ to $+ 70$ ), a correction of $+ 31^{s} . 4 T^{2}$ is a better approximation, once centennial fluctuations about the average parabolic trend are taken into account. This correction to UT with respect to TT introduces an apparent acceleration in the motion of the Sun inversely proportional to its mean motion ( $1 / 0.04107 ″ / s$ ). Therefore, Fotheringham’s result of $+ 1 ″ . 5 T^{2}$ for the apparent acceleration of the Sun in longitude is the consequence of a correction to the UT scale given by, $Δ T = + 1 ″ . 5 / 0.04107 ″ / s T^{2} = + 36^{s} . 5 T^{2}$ . However, there is not an exact equivalence of a change in the Sun’s longitude, measured in the plane of the ecliptic, and a change in the Earth’s rotation, measured in the equator. Therefore, his result of $+ 1 ″ . 5 T^{2}$ cannot be equated exactly to the quadratic correction $+ 36^{s} . 5 T^{2}$ to the UT scale.

Fotheringham’s result for the Moon’s longitude includes the gravitational term $+ 6 ″ . 1 T^{2}$ . Subtracting this term from his result of $+ 10 ″ . 8 T^{2}$ , we obtain $+ 4 ″ . 7 T^{2}$ for the tidal contribution in the Moon’s longitude measured on the UT scale. Our correction of $+ 31^{s} . 4 T^{2}$ to the UT scale produces an apparent term in the Moon’s observed longitude of $31^{s} . 4 \times 0.548 (″ / s) T^{2} = + 17 ″ . 2 T^{2}$ , where $0.548 (″ / s)$ is the Moon’s mean motion. Subtracting this from Fotheringham’s result of $+ 4 ″ . 7 T^{2}$ on the UT scale, gives a value for the tidal contribution of $- 12 ″ . 5 T^{2}$ on the TT scale.

These amended results are quite close to those that are obtained today. For the tidal acceleration of the Moon in longitude, the Jet Propulsion Laboratory (JPL) (Folkner et al.⁴) gives us $- 12 ″ . 9 T^{2}$ (compared with Fotheringham’s⁵ $- 12 ″ . 5 T^{2}$ ), and Stephenson et al.⁶ gives us $+ 31^{s} . 4 T^{2}$ (Fotheringham $+ 36^{s} . 5 T^{2}$ ) for ∆T covering the period of Fotheringham’s investigation.

On this – the centenary of the publication of his paper – we thought it would be interesting to look again at the reliability of the classical eclipses he used, and what degree of serendipity underlies his result.

Fotheringham’s eclipses

Total or near-total solar eclipses are memorable events and many eyewitness reports of them have survived in the extant records of ancient civilisations. The 10 classical eclipses analysed by Fotheringham are listed in Table 1 with his attribute.

Table 1.

The 10 classical eclipses analysed by Fotheringham.

No.	Attribute	Proposed date
1	Babylon	–1062	July 31
2	Eponym canon	–762	June 15
3	Archilochus	–647	April 6
4	Thales	–584	May 28
5	Pindar	–462	April 30
6	Thucydides	–430	August 3
7	Agathocles	–309	August 15
8	Hipparchus	–128	November 20
9	Phlegon	+29	November 24
10	Plutarch	+71	March 20

Fotheringham also analysed an 11th eclipse – the so-called eclipse of Theon, identified as that of $+ 364$ June 16. This record consisted of timings of the eclipse, rather than a sighting from some place or region. Fotheringham’s resultant solution for the accelerations for this eclipse lay outside his diagram, and did not influence his solution. We shall not consider this eclipse further.

The reliability of Fotheringham’s result is dependent on the correct identification of the eclipses in question, and whether they were total or annular in the regions mentioned in the historical reports. Partial eclipses cover too wide a geographical area to be of use in his method of analysis.

We consider each of the eclipses he used in the light of more recent research. In computing the tracks of totality or annularity, the values of ∆T are taken from Morrison et al.⁷ It should be noted that these values are derived from a consideration of a wide range of eclipses reported from various civilisations, and, therefore, they are virtually independent of the eclipses under consideration here.

We begin with a detailed investigation of the two earliest eclipses in Fotheringham’s list, which we have not considered in our previous publications, namely; $- 1062$ July 31 (Babylon) and $- 762$ June 15 (Eponym canon).

—1062 July 31? (Babylon)

In his two-volume book, Chronicles concerning Early Babylonian Kings, King⁸ edited the Babylonian tablet BM 35968. Volume I, pp. 70–86 has a report of a putative eclipse in column 1 line 14. In volume II, chapter IX (pp. 232–240), he includes some comments on the possible identification of the eclipse from Cowell,⁹ who dated the eclipse to –1062 July 31. The tablet has been re-edited in Grayson.¹⁰ The relevant line is translated on page 135:

On the twenty-sixth day of the month Siwan, in the seventh year, day turned to night and [there was] a fire in the sky.

He italicises there was, because the relevant signs cannot be read and this is just his suggestion. The text of the tablet is very incomplete, but the part with this report seems to deal with a king who reigned for at least 17, or maybe 18 years. If the text follows any sequence at all, then the date falls between Nabu-Sumu-libur ( $- 1031$ to $- 1024$ ) and Nabu-mukin-apli ( $- 977$ to $- 942$ ), according to Brinkman’s chronological tables in Ancient Mesopotamia.¹¹

Thus, the conjectured eclipse would have occurred in the period $- 1024$ to $- 977$ . Consultation of von Oppolzer’s Canon of Eclipses¹² shows that there was not a total eclipse at Babylon in that period. However, in the period in question we compute that two total eclipses occurred in Babylonia, rather than the city of Babylon itself.

The eclipse of $- 1011$ May 9 reached a magnitude of $0.90$ (i.e. the fraction of the Sun’s diameter covered by the Moon) at Babylon, but the Sun set before the central shadow reached Babylon (see Figure 3). This would have seemed as a premature occurrence of twilight rather than “day turned to night.” The eclipse of $- 983$ April 30 passed to the north of Babylon and reached a magnitude of 0.75 at sunset. Both are disqualified on the grounds of magnitude. The fact that the reported month of April is not in Siwan (May/June) further disqualifies $- 983$ April 30. This latter disqualification also applies to the eclipse of $- 1062$ July 31, as July is a month late for Siwan. A further disqualification is that an eclipse could not have occurred on the 26th day of the lunar month. While this second objection might be attributed to a scribal error – recording 26 instead of the similar representation of 28 – the first objection seems insurmountable.

Figure 3.

The total eclipse of –1011 May 9, showing that the Sun set before reaching Babylon.

These two objections, combined with the fact that $- 1062$ lies outside the relevant period $- 1024$ to $- 977$ , lead us to conclude unequivocally that this record is not an account of an eclipse at or near Babylon. Perhaps the phenomenon described is of meteorological origin, as has been suggested by investigators in the past such as Kugler.¹³

Although Fotheringham did seem to regard this as a reliable and datable observation of a solar eclipse, we discount this eclipse as contributing any useful limits in his diagram.

–762 June 15 (Eponym canon eclipse)

The record of the solar eclipse of $- 762$ June 15 is to be found in the Assyrian Chronicle. Several damaged copies of this Chronicle are preserved in the British Museum. For a discussion, see Stephenson.¹⁴

The Chronicle, which covers a period of more than 250 years (from $- 909$ to $- 648$ ), has been transliterated by Millard.¹⁵ For the whole of the interval covered by the Chronicle, the text is mainly devoted to a list of the annual “limmu” – senior officials after whom each year was named. The Greek equivalent of limmu is “epony,” and this name is usually preferred by translators.

References to natural events in the Assyrian Chronicle are very rare, and – apart from the isolated reference to the solar eclipse – no astronomical phenomena are cited. Millard¹⁶ translates the brief account as follows:

[Eponym of] Bur-Saggile of Guzana. Revolt in the citadel; in (the month) Siwan, the Sun had an eclipse (in-a simani samas attalu istakan).

Points of specific importance are as follows: (1) the magnitude of the eclipse and the place of observation and (2) the year and the month of occurrence. We shall consider each of these issues in turn.

Although the Chronicle makes no mention of the magnitude of the eclipse, its inclusion suggests that it was a fairly striking event. It is the only reference to an eclipse in the entire annals, and occurred when Bur-Saggile was eponym. Fotheringham suggested that the uniqueness of the record implied that the eclipse was total. However, this is no more than speculation. Unfortunately, the precise place of observation of the eclipse is not reported. The capital of Assyria at this period was Assur, but in principle the observation might have been made anywhere in Assyria.

Millard¹⁷ gives a complete list of the names of the Assyrian eponyms and their year of office from $- 909$ to $- 648$ . Many of these eponyms were kings of Assyria, and Millard based his adopted chronology on various detailed studies of the preserved Assyrian king list and the recorded length of each reign. As a result, the year in which Bur-Saggile was eponym can be confidently deduced as $- 762$ . The month in which the eclipse occurred, Siwan, was the third month of the year. It is well established that this corresponded to May-June. Hence, the most likely date of the eclipse is some time in May or June in $- 762$ .

This date is remarkably close to that of the large solar eclipse of $- 762$ June 15, which our computation reveals was total somewhere in Assyria for a wide range of the acceleration parameters $L^{'}$ and L (see Figure 1). Further investigation reveals that the only other eclipse that could have been large in Assyria between $- 776$ and $- 744$ was that of $- 764$ February 10. This reached a magnitude of no more than 0.82 at Assur and was only total much to the north-west of Assyria. Furthermore, the eclipse of $- 764$ February 10 occurred some 3 months before Siwan, whereas that of $- 762$ June 15 took place within Siwan itself.

In summary, we confirm the date of the eclipse is $- 762$ June 15, both in regard to the excellent accord with the historically derived date of the event as recorded in the Assyrian Chronicle and in its impressive magnitude at Assur and throughout Assyria. This is the earliest reliable report in history of a solar eclipse known to us.

Following the inference by Fotheringham, we assume that the eclipse was total somewhere in the most populous region of Assyria, and we adopt his two boundary geographical positions for Assyria at the epoch of the eclipse (see Figure 1): $34^{°} . 18$ N, $45^{°} . 15$ E; $37^{°} . 40$ N, $42^{°} . 19$ E.

The next five eclipses in Fotheringham’s list were investigated in our recent paper Astronomical Dating of Seven Classical Greek Eclipses.¹⁸ We summarise in Table 2 our conclusions in that paper for the dating and area of observation of each eclipse.

Table 2.

A summary of the dating and area of observation for eclipses 3 to 7 of Fotheringham’s list.

No.	Attribute	Date		Remarks on the likelihood of the identification
3	Archilochus	–647	April 6	Highly likely; observed from Thasos or perhaps Paros.
4	Thales	–584	May 28	Definite; the battle associated with the eclipse took place somewhere in Asia Minor.
5	Pindar	–462	April 20	Very likely; observed from Thebes or possibly just to the north of Thebes.
6	Thucydides	–430	August 3	Definite; could have been observed from Athens, but anywhere in Greece is possible.
7	Agathocles	–309	August 15	Definite; observed at sea shortly after leaving Syracuse.

These remarks and conclusions are taken from Stephenson et al.¹⁹

The dates are all correct, but the lack of precision in the historical accounts as to where the eclipses were seen, produce a wide range of solutions which either do not fall within the bounds of Fotheringham’s diagram, or at best appear only marginally (Figure 2). They have no affect on his final solution, and we do not consider them further.

–128 November 20 (Hipparchus)

This eclipse was discussed extensively in our paper On the Eclipse of Hipparchus.²⁰ We concluded that the eclipse that Hipparchus used to calculate the distance of the Moon, was more likely to have been that of $- 189$ March 14. However, some doubts still linger, and we investigate the outcome for Fotheringham’s diagram of adopting both these options. In the first instance, we assume that Fotheringham’s identification of $- 128$ November 20 is correct, but adopt slightly wider geographical constraints than he did for the Hellespont region, where the eclipse was reported as being total: $39^{°} . 8$ N, $26^{°} . 1$ E; $40^{°} . 4$ N, $26^{°} . 6$ E. The eclipse tracks are plotted in Figure 4.

Figure 4.

Calculated eclipse tracks for (a) –128 November 20 and (b) –189 March 14.

+29 November 24 (Phlegon)

Eusebius, the fourth century theologian and historian, preserves a record of a very large solar eclipse which occurred early in the first century. Eusebius’ source for this record is an extant fragment from the Olympiads, originally a major work by the second century ad writer Phlegon of Tralles. Regrettably most of Phlegon’s works are lost, but Eusebius in his Chronicon cites a preserved fragment of Phlegon’s Olympiads (fragment 17). Fotheringham²¹ translates the Greek text as follows:

And Phlegon who also compiled the “Olympiads” writes about the same things in his 13th book in the following words: ‘In the fourth year of the 202nd “Olympiad” (AD 32-33), an eclipse of the Sun took place greater than any previously known, and night came on at the sixth hour of the day, so that stars actually appeared in the sky; and a great earthquake took place in Bithynia and overthrew the greater part of Nicaea.

Whereas Phlegon only gives brief details about the earthquake, he gives a fairly detailed account of the eclipse, including the time of day and remarks that stars were seen, which is one of the hallmarks of a total eclipse. There can be no doubt that at the place of observation, the eclipse was either total or virtually so. However, there are two main problems with this record. First, there is the question of the date of the eclipse. The only large solar eclipse visible in the eastern Mediterranean for many years around the recorded year (equivalent to $+ 32$ / $+ 33$ ) occurred on $+ 29$ November 24. This date first identified by Kepler, was confirmed by Fotheringham. However, as Fotheringham pointed out, this eclipse took place in the first year of the 202nd Olympiad, rather than the fourth year. A scribal error, whether by Eusebius, Phlegon or his source, may well have been responsible. However, we confirm that the only possible date for the eclipse is indeed $+ 29$ November 24.

A more serious difficulty relates to the place where the eclipse was actually observed. The track of totality is plotted in Figure 5 with a value of 10,250 seconds for ∆T taken from Morrison el al.²² As Phlegon asserts, the earthquake which took place around the same time as the eclipse, took place in Bithynia and caused great damage at Nicaea. Fotheringham presumed that Nicaea was the place where the eclipse was seen. However, he felt that this was the weakest presumption in his paper.

Figure 5.

The total eclipse of +29 November 24 passing very close to Nicaea in Bithynia.

We assume that the report of totality emanated from somewhere in Bithynia, and adopt the boundary positions of $39^{°} . 0$ N, $28^{°} . 0$ E; $41^{°} . 0$ N, $32^{°} . 0$ E.

+71 March 20 (Plutarch)

The last eclipse in his list is discussed in Astronomical Dating of Seven Classical Greek Eclipses,²³ where we conclude that the date is definitely correct and it was observed somewhere in Greece, between Athens and Delphi. Fotheringham adopted a smaller region, stretching from Chaeronea to Delphi. Their positions are listed in Table 3. In Figure 6, we show the track of totality using our best estimate of 9803 seconds for ∆T, taken from Morrison et al.²⁴

Table 3.

List of critical Greek locations in Figure 6.

Location	Latitude	Longitude
Athens	37 °. 98 N	23 °. 72 E
Chaeronea	38 °. 52 N	22 °. 85 E
Delphi	38 °. 48 N	22 °. 52 E

Figure 6.

The eclipse of +71 March 20, passing over Athens.

Analysis of the eclipses

We repeat Fotheringham’s analysis, but instead of his “acceleration of the Sun” we consider a change of the deceleration of the rotation of the Earth as expressed by the quadratic expression for the correction ∆T to the UT scale. For the tidal acceleration in the Moon’s longitude, we first subtract the latest value of $- 12 ″ . 9 T^{2}$ from the longitude taken from the JPL’s long-term ephemerides DE 431.²⁵ Using our eclipse predictor, we calculate the range of coefficients of the quadratic expression in ∆T and the tidal term in the Moon’s longitude which produce southern and northern boundaries for totality passing over the geographical extremities of the areas given by the historical accounts. The results are plotted in Figure 7(a), with the common area of overlap shaded for the four critical eclipses: $- 762$ , $- 128$ , $+ 29$ and $+ 71$ .

Figure 7.

Two alternative versions of Fotheringham’s diagram, with the parabolic correction to UT due to the Earth’s deceleration in rotation plotted against the tidal acceleration in the longitude of the Moon. The common area of overlap is shown in black. The “Hipparchus” eclipse is identified as: (a) –128 and (b) –189.

In Figure 7(a), the modern solution ( $+ 31^{s} . 4 T^{2}$ ; $- 12 ″ . 9 T^{2}$ ) for the quadratic corrections to the UT scale and the lunar tidal acceleration falls near the centroid of the black triangular area, which is common to the four eclipses. This is not unexpected because the modern solution is used in our eclipse programme to calculate the tracks plotted in Figures 1, 4 to 6, and the positions of these tracks all fall within, or close to, Fotheringham’s adopted boundary conditions. Therefore, all the solution spaces for these eclipses in Figure 7(a) necessarily contain the modern solution. We emphasise that any circularity in our reasoning is largely broken by the fact that the eclipses of $- 762$ , $- 128$ and $+ 29$ were not used by us in determining the values of ∆T utilised in our eclipse prediction programme. However, the eclipse of $+ 71$ was used in determining ∆T,²⁶ but it did not have much impact on the final solution.

The black triangular area in Figure 7(a) is dependent on the identification of the Hipparchus eclipse with that of the year $- 128$ , whereas there is a strong possibility²⁷ that it was in fact the eclipse of $- 189$ . Unlike $- 128$ , we calculate that the eclipse of $- 189$ was probably not total in the narrow region of the Hellespont itself, but somewhat to the south of it (see Figure 4(b)). We repeat our calculation with this assumption, and plot the resultant solution space in Figure 7(b). Instead of an enclosed triangle defining the common area of overlap, there is an extensive open-ended rhombic figure. The solution space is no longer reasonably well defined.

Conclusion

Fotheringham’s remarkable result was serendipitous on two counts:

He identified the Hipparchus eclipse as that of $- 128$ , rather than the more viable $- 189$ . He did not even consider $- 189$ , probably because the atlas of eclipses by von Oppolzer²⁸ showed the track of $- 189$ passed about 10° west of the Hellespont, and Fotheringham discounted it for that reason. Our modern solution for the Earth’s rotation, which is not dependent on the Hipparchus eclipse, shows that the track of $- 128$ probably passed directly over the Hellespont, thus fortuitously satisfying the constraint placed on it by Fotheringham.

It was also fortunate that he correctly identified the Eponym canon eclipse as that of $- 762$ , because this produced the vital limitation on the triangular area in his diagram (see Figure 2). This limitation arises from the upper track in Figure 1 passing over the N limit. The circumstances of this eclipse are such that the N limit is close to the crest of the eclipse track on the Earth’s surface, which results in the reversal of the slope for solutions of the Earth’s acceleration greater than $+ 27.5$ in Figure 7. Fotheringham necessarily made computational approximations, which resulted in his linear solution for $- 762$ in Figure 2. If he had not had possession of this vital observation, he would have had to rely on the limitation provided by the “Babylon” eclipse, which he identified as that of $- 1062$ . We now know that this identification is extremely doubtful.

Serendipity apart, Fotheringham’s method had the potential to produce good results from the material available to him in 1920.

[… fama semper vivat!….]

Footnotes

Acknowledgements

We thank Christopher Walker, formerly of the British Museum, for providing the possible date span for the putative eclipse of –1062 on Babylonian tablet BM 35968. We also acknowledge HM Nautical Almanac Office and the International Astronomical Union’s Standards Of Fundamental.

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.

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 astronomical records to reconstruct the history of Earth’s rotation, as exemplified in his book Historical Eclipses and Earth’s Rotation.

Catherine Y. Hohenkerk worked at the Royal Greenwich Observatory from 1971 and in the late 1970’s transferred to H.M. Nautical Almanac Office (HMNAO), where she worked on the Nautical and Astronomical Almanacs. She retired from the UK 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.