longitude without time? celestial navigation

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Longitude without Time? This article describes a 400 year old enigma that keeps being rediscovered. A flawed method to find longitude that occasionally fooled kings, cardinals, scientists, navigators, and astronomers. Tony Crowley

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This article describes a 400 year old enigma that keeps being rediscovered. A flawed method to find longitude that occasionally fooled kings, cardinals, scientists, navigators, and astronomers.

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Page 1: Longitude without Time? Celestial Navigation

Longitude without Time?

This article describes a 400 year old enigma that keeps being rediscovered. A flawed method to find longitude

that occasionally fooled kings, cardinals, scientists, navigators, and astronomers.

Tony Crowley

Page 2: Longitude without Time? Celestial Navigation

Here is a navigational enigma which those who are interested in traditional navigation techniques may like to ponder. It concerns a way of finding one’s longitude without a clock and its recorded origins go right back to 1634 when the French astrologer, Jean Baptiste Morin, presented it to Cardinal Richelieu. Later, the idea was stolen by another Frenchman, St. Pierre, who presented it to King Charles 11 as a solution to the longitude problem. The King assembled an advisory committee including Sir Christopher Wren and John Flamsteed to investigate the claim, but the experts gave it the thumbs down. It required far more accurate astronomical tables than were available at the time but it also had a fundamental flaw. It is doubtful that the committee admitted that the procedure was suspect, for they used it to convince the King of the need for an observatory from which more accurate measurements of the moon and stars could be made. Accordingly, funds were made available which hastened the construction of the Royal Observatory at Greenwich.

In 1714, the Board of Longitude was established in order to consider solutions to the longitude problem, and received numerous proposals based on the method.

Page 3: Longitude without Time? Celestial Navigation

Like the earlier committee, however, the Board had identified its shortcomings and filed these proposals away under Crackpot Solutions which included such gems as ‘Ships should carry dogs which have been trained to bark exactly at 1200.’ In fact, a further twenty associated proposals were submitted by the time the Board was finally wound up in 1828.

The method is closely related to the lunar distances approach which was practised by mariners throughout the 18th century, but it is much easier to grasp and doesn’t require special tables beyond those normally used in celestial navigation. The fascinating thing about this procedure is that it is constantly being rediscovered. It reappeared in the USA around 1900, and when Sir Francis Chichester published his version in 1966, David Sadler of the Nautical Almanac Office commented on its novelty and elegance. One writer observed that many ships and thousands of lives could have been saved if only someone had thought of it 300 years earlier! Later, David Sadler spotted the flaw and wrote an authoritative if rather complex rebuttal of the procedure, but variations of the method continue to surface in books and on internet sites. Here is an example of the procedure. See what you can make of it.

Page 4: Longitude without Time? Celestial Navigation

How it works.Imagine that an observer sees the moon and a nearby star descending in the west. Sights of the two objects are taken and the two position lines are plotted to cut the observer’s known latitude. If the timing, observations and calculations are accurate, the two position lines will coincide with the observer’s latitude as shown in the centre of the diagram below.

If, however, the time is in error, the two position lines will not intersect on the latitude. This is because, in their apparent movement westwards, the moon and stars do so at different rates. The stars move westward at 15° 02’ per hour, whereas the moon moves an

Page 5: Longitude without Time? Celestial Navigation

average of 14° 29’ per hour - a difference of 33’. So, if the chronometer is one hour fast, the data obtained from the almanac will put the star’s position line 33’ ahead of that from the moon. If the chronometer is one hour slow, the star’s position line will be 33’ behind that of the moon. (See the diagram)

To find longitude by this method, the observer calculates and plots the two position lines for one hour ahead and for one hour behind the estimated time. Then, by comparing the two discrepancies and applying some simple calculations, he or she can work out where the position lines would coincide, and discover the correct time and the place of the observation.

For example, if an estimated time of 1900 hrs puts the star’s position line 8’ east of the moon’s and an estimated time of 2000 hrs puts its position line 24’ west of the moon’s, the total discrepancy is 32’. As 8’ is a quarter of 32’, the time of the observation would be approximately 1915 hrs. By the same reasoning, the observer’s position is one quarter of the distance between the star’s east and west position lines.

Page 6: Longitude without Time? Celestial Navigation

Looking back at the figure, you may see another solution. Note that the two inaccurate fixes lie either side of the latitude. A line drawn between them will cut the known latitude at the observer’s longitude.

It all sounds very plausible but there is a weakness and it’s a severe one. For the procedure to work with any accuracy, the altitudes of the moon and the star must be measured to a level of perfection that is rarely attainable and there is no margin for errors in the associated data and calculations. Normally, an altitude error of a few minutes of arc is of no great consequence. In this approach, however, a small altitude error will disturb the exacting relationship between the two sets of fixes and produce an inaccurate longitude and estimate of the time. For example, a altitude error of just 1’ can sometimes cause a longitude error of 30’

To achieve an accurate result, the observer must be aware of any sextant errors, find a millpond with a razor sharp horizon, and somehow allow for varying amounts of atmospheric refraction which may be present and which may be considerable. It is a tall

Page 7: Longitude without Time? Celestial Navigation

order and, according toMurphy’s Law of the Sea, any errors will rarely, if ever, cancel each other out.

Despite its shortcomings, it’s always worth a try. Where the observer is unsure of the latitude, the moon may be observed in combination with two stars - the latitude being where the stars’ position lines coincide. Armed with a reliable sextant and an artificial horizon, you may find the results from your backyard, garden or country estate quite encouraging. At sea, with the horizon often doubtful, be prepared for disappointment. Perhaps the final word on the altitude method should go to Lt. Henry Raper who in 1840 declared ‘Notwithstanding the occasional success of observations of this kind, it cannot be prudent to depend upon the result as nearer than 3/4 of a degree.’

The final word? Not if history is anything to go by.