Lunar distance (navigation)

In celestial navigation, lunar distance, also called a lunar, is the angular distance between the Moon and another celestial body. The lunar distances method uses this angle and a nautical almanac to calculate Greenwich time if so desired, or by extension any other time. That calculated time can be used in solving a spherical triangle. The theory was first published by Johannes Werner in 1524, before the necessary almanacs had been published. A fuller method was published in 1763 and used until about 1850 when it was superseded by the marine chronometer. A similar method uses the positions of the Galilean moons of Jupiter.

In celestial navigation, knowledge of the time at Greenwich (or another known place) and the measured positions of one or more celestial objects allows the navigator to calculate longitude. Reliable marine chronometers were unavailable until the late 18th century and not affordable until the 19th century. After the method was first published in 1763 by British Astronomer Royal Nevil Maskelyne, based on pioneering work by Tobias Mayer, for about a hundred years (until about 1850) mariners lacking a chronometer used the method of lunar distances to determine Greenwich time as a key step in determining longitude. Conversely, a mariner with a chronometer could check its accuracy using a lunar determination of Greenwich time. The method saw usage all the way up to the beginning of the 20th century on smaller vessels that could not afford a chronometer or had to rely on this technique for correction of the chronometer.

The method relies on the relatively quick movement of the moon across the background sky, completing a circuit of 360 degrees in 27.3 days (the sidereal month), or 13.2 degrees per day. In one hour it will move approximately half a degree, roughly its own angular diameter, with respect to the background stars and the Sun.

Using a sextant, the navigator precisely measures the angle between the moon and another body. That could be the Sun or one of a selected group of bright stars lying close to the Moon's path, near the ecliptic. At that moment, anyone on the surface of the earth who can see the same two bodies will, after correcting for parallax, observe the same angle. The navigator then consults a prepared table of lunar distances and the times at which they will occur. By comparing the corrected lunar distance with the tabulated values, the navigator finds the Greenwich time for that observation. Knowing Greenwich time and local time, the navigator can work out longitude.

Local time can be determined from a sextant observation of the altitude of the Sun or a star. Then the longitude (relative to Greenwich) is readily calculated from the difference between local time and Greenwich Time, at 15 degrees per hour of difference.

Having measured the lunar distance and the heights of the two bodies, the navigator can find Greenwich time in three steps:

Having found the (absolute) Greenwich time, the navigator either compares it with the observed local apparent time (a separate observation) to find his longitude, or compares it with the Greenwich time on a chronometer (if available) if one wants to check the chronometer.

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).