By K. Rupa
Department of Mathematics, Global Academy of Technology, Bangalore
Rohiṇῑ (Aldebaran) is the brightest star that the Moon can occult. Rohiṇῑ also known as Alpha-Tauri is located entirely within the constellation of Taurus. The name Rohiṇῑ translates as the "Reddish One"
Star Rohiṇῑ is given importance in Indian astronomy. The aspect of Rohiṇῑ coming very close to the Moon made an impact on ancient Indians. So when they came up with a list of the 27 “Nakshatras” (lunar mansions), they were thought as the daughters of Daksha Brahma, and wives of the Moon. And out of these 27 wives, Rohiṇῑ is said to be the most favorite among them to the Moon. This imagination comes since the Moon occults Rohiṇῑ quite regularly. In this paper we discuss about lunar occultation of Rohiṇῑ.
The celebrated Sanskrit poet Kalidasa, famous for similes (Upamā) in his magnum opus Abhijña Śākuntalam gives a very interesting and beautiful allusion to the conjunction in the following stanza.
"It is by a piece of good luck, my lovely darling, that you stand before me whose gloom of delusion has been broken by a return of memory." This has been, as it were, the star Rohiṇῑ has got conjoined with the moon at the end of a lunar eclipse.
An occultation occurs when one object passes in front of another as seen by the observer. In the course of its sidereal revolution of 27.32 days the Moon frequently passes in front of a star and when their longitudes are equal lunar occultation of that star occurs.
Occulations are not rare events, but occulations of bright stars is somewhat rare, as seen from a given place. For instance, an occultation stated to be visible in a continent is not necessarily visible for each point of this continent.
Successive occultations of a star by the Moon occur in series, which are separated by periods during which the Moon does not occult the star.
The circumstances leading to occultation can be calculated in the same manner as those for a solar eclipse. The lunar orbit has mean inclination of 5°8’which can go up to 6°21’. Thus the stars whose latitude lies in this limit are eligible for lunar occultation. Thus star Aldebaran (Rohiṇῑ) whose latitude is 5°28’ is eligible for occultation. The larger the latitude of the star the longer is the length of each series.
In a lunar occultation participating bodies are the Moon and the star. At the instant of conjunction (in longitude λ) of the Moon with the star, the angular semi diameter s, the horizontal parallax Π and the latitude (śara) β1 of the Moon are determined. The semi-diameter and the horizontal parallax of the star can be ignored since these are too small compared to those of the Moon. Let β2 be the latitude of the star. The condition for occultation is that the absolute difference in latitudes should be less than the sum of the Moon’s semi-diameter and parallax: i.e., | β1- β2|<Π+ s
The minimum values of Π and s are respectively about 3223''.5 and 878''.5 and the maximum values are 3672''.3 and 1000''.7. Accordingly, the minimum and the maximum values of (Π+s) are respectively 4102''.0 and 4673''.0 i.e., 1°8'22'' and 1°17'53''. Thus, we have:
The lunar occultation of a star of latitude β2 is certain if: | β1-β2|<1°8'22''
Occultation is not possible when | β1-β2|>1°17'53''
The phenomenon is doubtful if 1°8'22''<| β1-β2|<1°17'53''
We shall consider the case of the occultation of Aldebaran (Rohiṇῑ) whose magnitude is 0.85. The ecliptical co-ordinates of the star are respectively, tropical longitude λ = 69°47'20'' and latitude β2 = 5°28'12''.
A star whose latitude is less than 3°56' has two series of lunar occultation during the sidereal period of the Moon’s node. For a star whose latitude lies between 3°56' to 6°21' has only one series of lunar occultation, will have only one series of occultation whose length is 3.529 years in the sidereal period of the Moon’s node equal to 18.6 years.
In the preceding section we have discussed the condition for a lunar conjunction and occultation of Aldebaran (Rohiṇῑ).