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The rules for adding the extra month in the Hindu calendar are complicated. A simplified version of the rule is explained here. A solar year is about 365.25 days long, while a lunar year is about 354 days long. The difference of 11 days amounts to a month in about 2.7 years. So, in about 3 years it becomes necessary to accommodate one extra month to keep lunar year in step with the solar year. Note that the average length of a solar month is 30 days and 10.5 hours. On the other hand, a lunar month is 29.3 days. Thus, it is possible that there will be solar months which will have two new moons. On such occasions, the two lunar months are given the same name. Of these two lunar months, the one which does not contain a Sankranti is called adhika ( अधिक , extra) month, or malamāsa. The year then consists of 13 months. During such a year, all the festivals occur about a month earlier. In the next two years, they drift back to later times in the year. Thus, the festivals oscillate and occur within a range of about one month. The problem of a festival occurring on two successive days has to do with another element of the Hindu calendar. This one is called astronomical tithi (थ), or just simply, tithi. A tithi is a lunar date and determined by the positions of the Sun and the moon at any given time. The duration of a tithi is determined by the angular separation between the Sun and the moon as seen from the earth. The next tithi begins when their separation changes by 12 degrees. There are in all 30 tithis. A tithi can change at any time during the day. The orbits of the Sun and the moon are elliptic. In an elliptic orbit, such as that of the moon around the earth, the orbital speed of an object is not uniform. Moreover, the motionoftheSunandthemoonmaysufferfromvariousother perturbations. Thus, the duration of tithis is not constant. Its duration can vary between 19 and 26 hours. Some tithis may be longer than the time from one sunrise to the next (a day according to the Hindu calendar) and some may be shorter than this interval. Since the tithis are of variable duration, quite often there is a change of tithi during a day. For example, according to a Pañcaṅga of 24 October 2017 for North India, the tithi at sunrise (6:27 AM) is fourth tithi, which could also be Pañcami and it will change to the fifth tithi, which could also - be Caturthi during the day. A school of astronomers believes that the tithi at sunrise on a particular day should be considered the tithi for the whole day even if it changes to the next during the day. Considering the above example, according to this school of thought, the tithi for the whole day would be fourth. Now Astronomy india 83 Reprint 2026-27