• Semidiameter of the Moon

    Let D be the distance between the centre of the Earth and the centre of the Moon in kilometers, p the Moon's Equatorial Horizontal Parallax, s the geocentric semidiameter and k (equal to 0.272481) the ratio between the Moon's mean radius and the Moon's equatorial radius.

    So, we have:

sinp = 6378.14/D

sins = ksinp

    However, in the most of the calculations it will be sufficient to use the following formula:

s = 358473400/D (in arcseconds)

    Who originates an error less than 0.0005 arcseconds when we compare the results obtain with the previous formulas.

    The Moon's semidiameter calculated by this way it's a geocentric semidiameter, i. e., it's applied to an observer that are in the centre of the Earth! So we need the semidiameter that we observer, i. e., the topocentric one. This new semidiameter will be a little larger than the geocentric due to the fact of the observer are more close to the Moon (except when the Moon are in the horizon).

Fig. 01: Geocentric and Topocentric Semidiameter Observation Scheme.

    With a sufficient accuracy, the topocentric semidiameter can be obtain by multiplying the geocentric result s by (1+sinhsinp), where h is the Moon's altitude above the observer horizon line.

    This increase will be zero when the Moon are at the horizon and maximum (between 14'' and 18'') when the Moon is at the Zenith.