In Indian astronomy, a karaá¹Âa is a half of a tithi. It is the duration of time in which the difference of the longitudes of the Sun and the Moon is increased by 6 degrees. A lunar month has 30 tithi-s and so the number of karaá¹Âa-s in a lunar month is 60. These sixty karaá¹Âa-s are not individually named. Instead, the originators of the concept have chosen 11 names to be associated with the karaá¹Âa-s which means several karaá¹Âa-s will be associated with the same name. Of these 11 names, four are fixed or immovables (or sthira-s) in the sense that they are associated with four unique karaá¹Âa-s in a lunar month. These constant names are à Âakuni, Catuá¹£pÃÂda, NÃÂga and Kimstughna. The remaining seven names are variable or movable (or, cara-s) in the sense that there are several karaá¹Âa-s associated with each of them. These names are Bava, BÃÂlava, Kaulava, Taitila, Gara, Vaá¹Âij and Vá¹Âá¹£á¹Âi.
The four fixed names are assigned as follows:
The fifty-six half tithi-s starting from à Âukla paká¹£a pratipad second half to Ká¹Âá¹£á¹Âa paká¹£a caturdasi first half are given the variable names Bava, BÃÂlava, Kaulava, Taitila, Gara, Vaá¹Âij and Vá¹Âá¹£á¹Âi in a cyclical order. These names are repeated in the same order eight times so that the same name is assigned to eight different half tithi-s.
The fixed and variable names are assigned as in the following table.
The name of the karaá¹Âa at a particular moment on any given day can be determined by the following algorithm.
In the Malayalam astronomical literature, the eleven karaá¹Âas are assigned names which are words for various animals. The English equivalents of the animal words representing the various karaá¹Âas are given below.
Most probably the concept of karaá¹Âa arose almost simultaneously with the concept of tithi. Tithi-s are related to lunar-days and lunar-days are similar in concept to solar days or sÃÂvana days. A sÃÂvana day is the duration of time from one sunrise to the next sunrise. Roughly one half of a sÃÂvana day is the duration of time from sunrise to the next sunset and the other half is the duration of time from sunset to the next sunrise. Before the introduction of the modern concept of tithi, the concept of a lunar day was in vogue. It was the duration of time from one moon-rise to the next moon-rise. Similar to the division of a sÃÂvana day, the lunar-day can also be divided into two halves: One half being the duration of time from moon-rise to the next moon-set (the lunar day time) and the other half being the duration of time from moon-set to the next moon-rise (lunar night time). The concept of karaá¹Âa has originated in this division of the lunar day. Later, when the concept of tithi got established, the concepts of the lunar day time and lunar night time got replaced by the modern artificial concept of half-tithi-s. The works of the VedÃÂá¹ ga period - Atharva Jyotiá¹£a and á¹Âk-parià Âiá¹£á¹Âa mention the karaá¹Âa-s. So the origination of the concept of karaá¹Âa-s can be traced to as early as the period of VedÃÂá¹ ga Jyotiá¹£a, that is, around 500 BCE.