The book that tells you where the sky will be

A sextant tells you the Sun stands 63° 26′ above the horizon. That is a fact about the sky, not about you. To turn it into a position you need a second fact: where the Sun was supposed to be at that moment. Every method in this museum, from the noon sight to the lunar distance, ends with a lookup in a book of predictions. This interlude is about those books: who computed them, what they printed, and how long each one was the navigator’s word on the sky.

An almanac (or ephemeris, from the Greek for “daily”) is a timetable for the sky. Over two thousand years the timetable changed in three ways. Who did the arithmetic moved from the user to the publisher. What was tabulated moved from what astronomers needed to what a pilot on a pitching deck could use. And the theory and machinery behind the numbers improved beyond recognition, from tables good to a few minutes of arc to numerical ephemerides used to navigate spacecraft.

Tables you had to work yourself§

For most of history, astronomical tables did not give positions. They gave the ingredients: mean motions per day and per year, and corrections that depended on where a body was in its cycle. To find where the Moon would be on a given night, you added up the mean motions for the elapsed time, looked up the corrections, and converted the result into the coordinates you needed. It was skilled, slow work, done by astronomers and astrologers on land.

Ptolemy’s Handy Tables, compiled in the second century CE after the Almagest, took the great book’s tables and added instructions without the theory, “to facilitate practical computation”^[1]. They were used and copied for centuries. In the Islamic world, astronomers produced a long series of zījes, handbooks of tables with rules for using them. Al-Khwārizmī’s Zīj al-Sindhind drew on Indian rather than Ptolemaic models^[2]; al-Battānī, observing at ar-Raqqah between 877 and 918, measured the length of the year as 365 days 5 hours 46 minutes 24 seconds^[3]. documented

The Toledan Tables, completed around 1080 by adapting earlier Arabic tables to the meridian of Toledo, passed into Latin and survive in more than a hundred versions^[4]. They were superseded by the Alfonsine Tables, compiled at Toledo in the 1270s for Alfonso X, with an epoch of 1 June 1252. Their Latin Parisian version was first printed at Venice in 1483 and was the standard European reference into the sixteenth century; Copernicus used the 1492 edition^[5]. None of this was used at sea. Greek, Islamic and medieval European mathematical astronomy did not become a shipboard practice of position fixing; it was the raw material that later navigators’ tables were built from.

Printed predictions§

The printing press changed who did the arithmetic. In 1474 Regiomontanus printed, on his own press at Nuremberg, a book of Ephemerides for 1475 to 1506: the daily positions of the Sun, Moon and planets, already computed, with predicted eclipses^[6][7]. Instead of computing a position, a reader looked it up. The book even explained how the Moon might be used to find longitude^[8]. documented

Explorers carried such books. Amerigo Vespucci, around 1502, named his references as “King Don Alfonso in his Tables, Johannes Regiomontanus in his Almanac, and Blanchinus, and the Jewish rabbi Zacuto in his Almanac, which is perpetual”^[7]. The most famous use is Columbus’s, stranded on Jamaica in 1504: he used a printed prediction of the lunar eclipse of 29 February to impress the Taíno who were feeding his crew. Which book he used is disputed. Morison held it was Regiomontanus; an older account says Zacut’s almanac^[9][10]. contested The longitudes Columbus reported from eclipses were poor, and historians doubt them^[7].

A table for a pilot§

An ephemeris built for astronomers still asks a lot of a sailor. The decisive step for navigation was to cut the sky down to one question a pilot could answer at sea: what is the Sun’s declination today? With that and a noon altitude, latitude follows, as Chapter 1 shows.

The source for Portuguese navigators was Abraham Zacut’s Almanach perpetuum, printed at Leiria on 25 February 1496 in a Latin translation by José Vizinho^[11]. Its planetary positions were computed from the Alfonsine Tables^[12]. A sixteenth-century chronicler, Gaspar Correia, credited Zacut with “the quadrennial table of solar declination”, and the historian Luís de Albuquerque accepted it; until Pedro Nunes’s new tables of 1537, the solar tables prepared for navigation in Portugal were computed from Zacut’s almanac^[13]. documented That Vasco da Gama carried tables derived from it in 1497 is widely believed but unproven^[14]. contested

The pilot’s handbook was the Regimento do estrolabio e do quadrante, whose first known printing is probably from around 1509. It gave a Portuguese translation of Sacrobosco’s Sphere, two versions of the rule for latitude from the Sun’s meridian altitude, a table of solar declination, the Rule of the North Star with corrections for eight positions of the Guards, and a table of Polaris altitudes from Lisbon^[15]. It turned astronomy into a routine: measure, look up, add or subtract.

Why “four-year”? The Julian calendar repeats its leap-year pattern every four years, and the Sun returns to nearly the same declination on the same calendar date four years later. So a table for four consecutive years could be reused indefinitely, in principle. In practice, the Julian year of 365.25 days is about 11 minutes longer than the year of the seasons, so the table slips a little against the Sun every cycle.

The drift is small for decades, a few minutes of arc after twenty years, which is a few miles of latitude. The calendar reform of 1582 was a different matter: the new calendar dropped ten days, and a table read by the new date without adjustment is out by up to three and a half degrees near the equinoxes. Errors in tables went straight into latitudes. Edward Wright, whose Certaine Errors in Navigation corrected many of them from his own observations, printed new declination tables and “Ephemerides of the Sun for five yeeres” with rules to continue them^[16]. documented

Computing the sky for longitude§

Latitude needs the Sun’s declination to a few minutes of arc, and it changes slowly. Longitude by the Moon needs the Moon’s position to seconds of arc, and the Moon moves fast and irregularly. That was a different scale of problem.

The French Connaissance des temps began with a volume for 1679, its calculations by Jean Picard; it has been published without interruption ever since, making it the oldest astronomical ephemeris still in print^[17]. It started at one page per month and precision of one arcminute, and grew as astronomy did. documented

The breakthrough for navigation came from Göttingen. Tobias Mayer’s lunar tables, built on Newton’s theory in Euler’s analytic form, were sent to London in 1755 and were good enough to give longitude to about half a degree^[18]. Nevil Maskelyne tested lunar distances on a voyage to St Helena^[19] and in 1763 published The British Mariner’s Guide, promising longitude “always within about a degree, and generally within half a degree”. In its preface he wished that the long computations “were made previously at land by capable persons, and published”^[20].

That wish became The Nautical Almanac and Astronomical Ephemeris, the volume “for the year 1767”, its title page dated 1766^[21]. Each month filled 12 pages: the Sun’s longitude, right ascension, declination and equation of time; the Moon’s position, semidiameter and horizontal parallax at noon and midnight; eclipses and Jupiter’s satellites; and, the heart of it, the distance of the Moon’s centre from the Sun and from selected bright stars for every third hour, all for the meridian of Greenwich^[21]. The Sun and Moon came from Mayer’s last manuscript tables, the planets from Halley’s. The navigator was relieved “from the Necessity of calculating the Moon’s Place from the Tables, and afterwards computing the Distance to Seconds by Logarithms”, leaving only the clearing of the observed distance and the time^[21]. Chapter 3 shows that procedure. documented

The numbers were computed by people. The 1767 preface says every article was “computed by Two separate Persons, and examined by a Third”^[21]. The computers worked at home, across the country; Maskelyne paired them so that no two worked together twice in a year and sent both copies to a comparer who checked them against each other^[22]. Some served for decades: Henry Andrews computed from 1768 to 1815, and the Reverend Malachy Hitchins was comparer from 1767 to 1809^[23]. A companion book, the Tables Requisite, carried the fixed tables a navigator needed to clear a lunar: refraction, parallax, dip, a star catalogue and proportional logarithms^[24].

The Americans followed. Congress created a Nautical Almanac Office in 1849, and the first American Ephemeris and Nautical Almanac, for 1855, appeared in 1852^[25].

Lunar distances lasted as long as the chronometer was expensive and unreliable. When chronometers and then radio time signals took over, the tables went: the British almanac last printed them in its volume for 1906^[23][26], the French dropped them from the volume for 1905^[7], and the American volumes omitted them from 1911 or 1912, the Navy judging them “of little practical use to navigators”^[27][28]. Sources differ by a year on each of these; the timeline gives the best-supported dates.

Better theory, then machines§

Behind the printed pages, the theory kept improving. Simon Newcomb, superintendent of the American office from 1877 to 1897, developed new theories of the Sun and planets^[25]. An international conference in Paris in 1896 settled the fundamental constants that, with Newcomb’s tables, served most almanacs for the next eight decades^[29]. The Moon, always the hardest body, got E. W. Brown’s Tables of the Motion of the Moon, published in 1919 and used in national ephemerides from 1923^[30].

Brown’s tables had over 1,400 periodic terms in 180 tables covering 660 pages; using them by hand kept two skilled computers busy full time. At the British Nautical Almanac Office, L. J. Comrie put the work onto Hollerith punched-card machines, which, he reported in 1932, “increased tenfold the speed” and cut the cost to a quarter^[31]. documented In 1984 the analytic theories gave way to numerical integration: the Jet Propulsion Laboratory’s DE200 ephemeris, followed by DE405 from 2003 and DE430 from 2015^[29][32]. Today’s almanac is computed from the same kind of ephemeris that navigates spacecraft.

The navigator’s almanac today§

The format changed as much as the theory. Navigators wanted fewer steps, so in 1934 the American almanac began tabulating Greenwich hour angle for the Sun, Moon and planets and sidereal hour angle for the stars^[28]: no more converting right ascension and time. The British seamen’s edition, separate since 1914, switched to GHA in 1952^[26]. Aviators got The Air Almanac, experimental in the US for 1933, British from 1937 and joint from 1953, with values every ten minutes^[33]. From the 1958 edition the British and American nautical almanacs became one book^[28], and in 1981 the two astronomical ephemerides were merged as The Astronomical Almanac^[32].

Open a modern Nautical Almanac and you find three days per opening. The left page gives, for every hour, the GHA of Aries and the GHA and declination of Venus, Mars, Jupiter and Saturn, with the SHA and declination of 57 navigational stars. The right page gives the hourly GHA and declination of the Sun and Moon, the Moon’s horizontal parallax and its v and d values, and sunrise, sunset and twilight times. Values are tabulated to 0.1′. At the back are the increments and corrections tables for the minutes and seconds between the hours, altitude corrections and Polaris tables^[34]. Ships are still required to carry it, on paper or in digital form^[35], and electronic almanacs such as the US Naval Observatory’s MICA have existed since 1993^[25].

Outside Europe§

Navigators outside Europe watched the stars as closely as anyone. Indian Ocean pilots measured star altitudes in iṣbaʿ, “fingers”, and Chinese sailing diagrams of the Zheng He era gave star altitudes in comparable finger units^[15]. But we have found no evidence that any of these traditions used a printed or tabulated ephemeris at sea. Their star knowledge was largely fixed, because the stars barely change from year to year, and it was held in rutters, texts and memory. Chapter 2 describes these traditions on their own terms. The almanac, a yearly timetable of a moving Sun and Moon, is a particular solution to a particular problem: finding position by measuring bodies whose places change.

Every almanac on the timeline is an answer to the same request: tell me where the sky will be, so I can work out where I am. What changed is who did the arithmetic, and how well they knew the sky.