## Info

3. The distribution of the Moon's perigee and apogee distances

The following text was first published in the Belgian journal Heelal of September 1984, where the distribution of the Moon's perigee and apogee distances was given for the period 1924-2005. We now have performed a new calculation for the years 1960-2040, based on the lunar theory ELP of Michelle Chapront-Touzi and Jean Chapront; the climatological data for Uccle have been updated.

In a given population the mean height of the adult men is 163 centimeters. It is evident that the height of most men of this group will not differ much from this mean value: for instance, there will be very few dwarfs of 120 cm or giants of 205 cm. The lengths are so-called 'normally' distributed; the distribution of the lengths present a single maximum near the middle: the mean length is the most frequent one (Figure 3.a).

Other examples of distributions with one maximum can be found, for instance, in meteorology. For the month of October, the mean air temperature at the Royal Meteorological Institute at Uccle (near Brussels, Belgium) is 10.5 °C. For the years 1901 -1994 the October means are distributed as shown in Table 3. A and illustrated in Figure 3.b. Another example: the annual amount of precipitation (rain, snow, etc.) at Uccle; see Table 3.B and Figure 3.c.

However, other types of distributions are possible. As we have seen in Chapter 2, the mean perigee and apogee distances of the Moon are 363296 and 405504 kilometers, respectively. And, as we know, the motion of the Moon is strongly perturbed mainly due to the gravitational attraction of the Sun. For this reason, the perigee as well as the apogee distances will vary greatly. But it is not true that the mean perigee (or apogee) distances are the most frequent. Prof. Dr. E. Hantzsche, of Berlin, Germany, drew my attention on the fact that each of these distributions has two maxima.

For the years 1960 - 2040 the distributions of the pengee and apogee distances of the Moon are given in Table 3.C, and illustrated in Figures 3.d and 'i.e. It appears that the extreme (smallest and largest) perigee and apogee distances are the most frequent. At first sight this is a most peculiar phenomenon. The explanation was given by C. Steyaert [now president of the Belgian astronomical society 'Vereniging voor Sterrenkunde'].

Fig. 3. a

TABLE 3.A TABLE 3.B

Distribution of the mean Distribution of the annual air temperature in October amount of precipitation at Uccle, 1901 to 1994 at Uccle, 1901 to 1994

Temperature

Number

in °C

of cases

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