Lunar Parallax

We use modern astronomy to determine the appearance of the sky in different parts of the world at different times in the past. The formulae we use are derived from mathematical models of the motions of the earth through space, as it orbits around the sun, spinning and wobbling under the gravitational influences of the sun and moon. One consequence of this is that when we use standard formulae to calculate the declination of a celestial body or event, we implicitly make the assumption that we are standing at the center of the earth. Although this sounds crazy, the distances of most celestial objects are so vast that it makes no practical difference to the ar-chaeoastronomer studying naked-eye observations of the skies in the past. Only in the case of the moon is the difference important.

The lunar parallax is the difference between the position of the moon in the sky as viewed (theoretically) from the center of the earth and (actually) from somewhere on the earth's surface. If we are interested in the possibility of lunar alignments of a precision much greater than the size of the moon (about thirty arc minutes across), then we must take parallax into account. There are two ways of doing this. The usual way, which is adequate in most cases, is to adjust the "target" declination values that correspond to various lunar events, such as the moonrise or moonset at the major standstill limits. However, if we are interested, as was Alexander Thom, in possible alignments of very high precisionâ€”precise to a just few minutes of arcâ€” then we must take account of the fact that the parallax correction varies slightly from place to place and from time to time. We can only do this by increasing by an appropriate amount, different in each case, the altitude of any given horizon point, and hence of the moon if it were rising or setting behind that point, in order to calculate where it would be seen in the sky, and hence what its declination would be if we were standing at the earth's center. The corrected declination, which can now be compared directly with the target declination, is known as the geocentric lunar declination.

Thom, Alexander (1894-1985).

Altitude; Declination; Moon, Motions of.