Pollux Delta Sagittarii and the period of 183 years

As was mentioned at the end of the preceding chapter, stars with a celestial latitude larger than 6°36' cannot be occulted by the Moon. The latitude of Pollux (0 Geminorum) is +6°4l'. So this star is just outside this limit and hence cannot be occulted for observers on the Earth's surface. However, due to the star's proper motion and the rotation of the ecliptic, the latitude of Pollux is presently increasing at the rate of +26" per century. Near the year -400, the latitude of the star was +6°30', so in B.C. years occultations of Pollux were indeed possible.

We calculated all occultations of Pollux taking place between the years —600 and +2100. Fifteen cases were found, which are listed in Table 20.B. So, the very last occultation of /3 Gem took place on -116 September 30. It was a very short, almost grazing occultation, visible from a very small part of the southeastern Pacific Ocean, near longitude 90° W, latitude 55° S. See Figure 20.e.

TABLE 20.B The occultations of Pollux since the year —600

-599 March 24

-469 September 6

-320 March 28

-506 March 16

-469 October 4

-302 September 18

-488 October 2

-450 February 27

-283 September 18

-487 March 16

-450 March 26

-264 March 11

-469 March 26

-432 September 16

-116 September 30

The 18.6-year period of revolution of the nodes of the lunar orbit is clearly visible from the dates mentioned in Table 20.B. For instance, there was an occultation of Pollux in the year -506, then two others in -488 and -487, followed by three in —469, two in -450, and one in —432.

Moreover, we see that the occultations of Pollux took place in 'groups'. For instance, one group of nine occultations lasted from -506 to -432. After a gap of more than one century, we have a smaller group of four occultations, from -320 to -264; and, Finally, there is a 'group' of one isolated occultation in the year -116.

These groups occur at intervals of 183 years. The reason for this is as follows. One sidereal revolution of the lunar nodes has a duration of 6793.477 days, or 18.59953 Julian years. During this time interval, the motion of the Moon's perigee with respect to the stars is 756.55745 degrees, or 720° + 36.55745 degrees. For a star lying near the above-mentioned latitude limit of 6°36', occultations are possible only when, at the time of its conjunction with such a star, the Moon is near its greatest celestial latitude and near its perigee, because

Fig. 20.e : The last occultation of Pollux by the Moon, it took place on September 30 of the year —116. The drawing shows the Moon (the smaller circle) passing in front of the Earth as seen from Pollux.

in this last case the sum it + st mentioned in the previous chapter, has its maximum value. If a conjunction of the Moon with, say, Pollux takes place with the Moon at its maximum northern latitude, and simultaneously with the Moon in perigee, this situation will repeat after

360 x 18.59953 -36.55745 = 183 yearS

Another interesting case is that of 6 Sagittarii. This star is presently at celestial latitude j8 = —6°28', and hence is just inside of the limit 6°36'. It is, however, receding from the ecliptic, and hence its occultations by the Moon will be less and less frecfbent in future years, and finally come to an end.

Table 20.C lists all occultations of 5 Sgr from A.D. 1900 to 3000. For this star, too, we find 'groups' at intervals of 183 years. One group begins on 1913 March 29 (this was the first occultation of 5 Sgr since that of 1857 March 19); it will end with the occultation of 2024 October 9. This group contains 18 events. After a gap of almost one century, there will be a group of 10 events, from 2117 to 2192. Finally, there will be a group of two grazing occultations, in 2322 and 2359. That of 2359 October 1 will be the last occultation of 5 Sgr before many centuries!

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