Lunar Distance (navigation) - Method - in Practice

In Practice

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

Step One – Preliminaries

Almanac tables predict lunar distances between the centre of the Moon and the other body (see any nautical almanac from 1767 to c.1900). However, the observer cannot accurately find the centre of the Moon (and Sun, which was the most frequently used second object). Instead, lunar distances are always measured to the sharply lit, outer edge ("limb") of the Moon and from the sharply defined limb of the Sun. The first correction to the lunar distance is the distance between the limb of the Moon and its center. Since the Moon's apparent size varies with its varying distance from the Earth, almanacs give the Moon's and Sun's semidiameter for each day (see any nautical almanac from the period). Additionally the observed altitudes are cleared of dip and semidiameter.

Step Two – Clearing

Clearing the lunar distance means correcting for the effects of parallax and atmospheric refraction on the observation. The almanac gives lunar distances as they would appear if the observer were at the center of a transparent Earth. Because the Moon is so much closer to the Earth than the stars are, the position of the observer on the surface of the Earth shifts the relative position of the Moon by up to an entire degree. The clearing correction for parallax and refraction is a relatively simple trigonometric function of the observed lunar distance and the altitudes of the two bodies. Navigators used collections of mathematical tables to work these calculations by any of dozens of distinct clearing methods.

Step Three – Finding the Time

The navigator, having cleared the lunar distance, now consults a prepared table of lunar distances and the times at which they will occur in order to determine the Greenwich time of the observation.

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