Why Tithi Duration Varies

A tithi is completed when the Moon gains 12 degrees of elongation over the Sun. The time this takes depends entirely on how fast the Moon is moving relative to the Sun at that moment. The Moon's speed is not constant — it follows Kepler's second law, sweeping out equal areas in equal times along its elliptical orbit. Near perigee (closest to Earth, about 356,500 km), the Moon races at roughly 15.4 degrees per day. Near apogee (farthest, about 406,700 km), it crawls at roughly 11.8 degrees per day. Meanwhile, the Sun's apparent motion is approximately 0.9 to 1.0 degrees per day.

The net relative speed (Moon minus Sun) thus ranges from about 10.8 to 14.5 degrees per day. A tithi at maximum speed takes 12 / 14.5 = approximately 19.9 hours. A tithi at minimum speed takes 12 / 10.8 = approximately 26.7 hours. This is why no two consecutive tithis are identical in length, and why the Panchang must be computed fresh for every day and location rather than simply following a fixed schedule.

Tithi at Sunrise

The Hindu calendar day (divasa) is reckoned from one sunrise to the next. The tithi prevailing at the moment of local sunrise determines that day's official tithi. In the most common scenario, a tithi starts after one sunrise and ends before the next — that tithi is present at the first sunrise but not the second, and the day bears its name. When a tithi spans two sunrises (is present at both), we have a Vriddhi situation. When a tithi fits entirely between two sunrises (present at neither), we have a Kshaya situation.