Lunar Distance (navigation) - Errors

Errors

Effect of Lunar Distance Errors on calculated Longitude

A lunar distance changes with time at a rate of roughly half a degree, or 30 arc-minutes, in an hour. Therefore, an error of half an arc-minute will give rise to an error of about 1 minute in Greenwich Time, which (owing to the Earth rotating at 15 degrees per hour) is the same as one quarter degree in longitude (about 15 nmi (28 km) at the equator).

Almanac error

In the early days of lunars, predictions of the Moon's position were good to approximately half an arc-minute, a source of error of up to approximately 1 minute in Greenwich time, or one quarter degree of longitude. By 1810, the errors in the almanac predictions had been reduced to about one-quarter of a minute of arc. By about 1860 (after lunar distance observations had mostly faded into history), the almanac errors were finally reduced to less than the error margin of a sextant in ideal conditions (one-tenth of a minute of arc).

Lunar distance observation

The best sextants at the very beginning of the lunar distance era could indicate angle to one-sixth of a minute and later sextants (after c. 1800) measure angles with a precision of 0.1 minutes of arc, after the use of the nonius or vernier was popularized by its description in English in the book Navigatio Britannica published in 1750 by John Barrow, the mathematician and historian. In practice at sea, actual errors were somewhat larger. Experienced observers can typically measure lunar distances to within one-quarter of a minute of arc under favourable conditions, introducing an error of up to one quarter degree in longitude. Needless to say, if the sky is cloudy or the Moon is "New" (hidden close to the glare of the Sun), lunar distance observations could not be performed.

Total Error

The two sources of error, combined, typically amount to about one-half arc-minute in Lunar distance, equivalent to one minute in Greenwich time, which corresponds to an error of as much as one-quarter of a degree of Longitude, or about 15 nautical miles (30 km) at the equator.