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For a very short answer, move to the last two paragraphs. If you need further explanation of how it actually works, read the rest.
The Hindu calendar is a lunar calendar, which means its days are based on the movement of the moon. This is unlike the calendar we are used to (Gregorian calendar), which is a solar calendar. So, the Gregorian/solar day has 24 hours, and it does not change ever, because the rotation of the earth about its axis is at a uniform rotation speed (15 degrees per hour).
Now try to imagine a lunar day. If the moon were to rise and set at the same intervals every day (i.e. a lunar day would always have the same length, like a solar day has), then it would be really easy, which it is not. The length of the lunar day VARIES every day, and it makes things complex.
One lunar day is the time taken when there is a 12 degree change in the angle subtended by sun (S) and the moon (M) on the earth (E), i.e. ∠SEM. So,
- When the ∠SEM is 0° (when sun, moon, and earth are collinear, with the moon in between), the tithi is poornima (full moon—we can see the whole round moon).
- On the next tithi, the moon has moved a little bit further in its orbit around earth, enough to make ∠SEM = 12°. The angle makes it slightly difficult for us to see the full face of the moon, as the moon does not have light of its own. The tithi is “ekam”, the paksha is krishna paksha (krishna = dark; as the moon is now losing its size, i.e. waning).
- The waning of the moon continues. Gradually, we reach a stage when ∠SEM = 180°, and the moon is nowhere between the sun and earth. The tithi is amavasya (new moon), when we can’t see the moon at all. Now begins the waxing of the moon (shukla paksha), and it approaches back towards the full moon stage. The whole cycle takes 30 days, a maas (month).
But what’s the problem, you ask. Get a pen and paper and draw the situation, and you’ll immediately understand it. The thing to be noted here is, the 12 degrees is the angle subtended at the earth by the moon and sun! Had it been the change in angular position of the moon in its orbit around the earth (i.e. ∠M¹EM², where M¹ is the position of moon on Day 1 and M² is the position of moon on Day 2), the length of a tithi would have been the same (because the moon would take the same time everyday to traverse 12° in its orbit (constant angular speed). However, it becomes very complex because
- the tithi changes upon a 12 degree change in the angle ∠SEM (with S fixed while E and M moving in their own independent speeds and orbits), and
- at every turn of the tithi, the earth is at a new position with respect to the sun, as the earth has also been rotating and revolving all the time!
For convenience, calendars show a solar date’s tithi as the tithi at the time of sunrise. So, 1) if a tithi begins after sunrise on a certain solar date and ends before sunrise on the next date, it is not shown on calendars, and you think that a day is missing. 2) And when a tithi begins before sunrise on a certain solar date and ends even after sunrise on the next date, the same tithi is shown for both dates in calendars, and you think a day has been repeated.