Sunrise at sixty degrees north

The Indian calendar counts lunar days. A lunar day is called a tithi. It is one step in the moon's separation from the sun, and it does not line up with our dates: a tithi can begin on one afternoon and finish the next evening.

So the almanac needs a rule for deciding which date gets which tithi's name. Look at the minute the sun comes up. Whichever tithi is running then names the whole day, and fasts and festivals hang on that name.

The rule asks for one instant, not a stretch of time, which is why it travels well. In Kochi the sun rises at 6.06 in late June and 6.36 in late December, so nobody there notices the rule. In Trondheim, in Norway, it gives 3.02 in the morning in June and 10.01 in December. It still works. It just picks an hour nobody is awake for.

Rules that need a length of day break sooner. Rahu kaal is one eighth of the daylight. In Kochi that is about an hour and a half whatever the month. In Trondheim it is 2 hours and 34 minutes in June and 34 minutes in December.

Go further north and the sunrise rule runs out of input. In Tromsø the sun does not set for about 10 weeks in summer and does not rise for about seven in winter. The almanac can still print when each tithi starts and ends, because those are facts about the solar system. What it cannot say is which date carries the name: the test needs a sunrise, and there is not one.

At that point arithmetic stops and people decide. Four answers are in use. Keep the hour of the last real sunrise. Borrow the times of the nearest town that still has ordinary ones. Fix a clock hour and hold it, as the mosque in Inuvik in Arctic Canada does with Mecca's times. Or keep the sunrise of the city you came from, so your fast starts when your mother's does. Each answer gives something up, and none of them is a mistake.