The day number that every ephemeris agrees on

Calendars are bad at subtraction. Months have different lengths. Most years have 365 days and some have 366. Countries switched from the old calendar to the new one in different decades, and several struck out ten or eleven dates when they did it.

So astronomers stopped counting in months and years. They number the days instead, straight through from a fixed starting point. That number is the Julian Day, and it sits in the left-hand column of every table of computed sky positions.

Two rules come with it. The count changes at noon, not midnight, because an astronomer working through a night wanted the whole night inside one number. So midnight lands on a half: 2455034.5. And day zero is noon on 1 January 4713 BCE, far enough back that every date anyone writes down gets a positive number. The name confuses people: the Julian calendar is a calendar, with a leap year every four years. The Julian Day is not a calendar at all. It is a count.

The essay takes one real date, 22 July 2009, the morning the moon's shadow crossed India, and works it both ways.

Forward: count January and February as part of the previous year, so the leap day sits at the end. Count 365 days for each finished year, then add one day for every four years, take one away for every hundred, put one back for every four hundred. Add the days from 1 March to your date. Add one fixed number, which the essay pins down using a value the US Naval Observatory publishes. The answer, 2,455,034.5, is what NASA's own ephemeris service prints for that midnight.

Backward is long division. Subtract the fixed number, then divide by 146,097 (the days in 400 years), by 36,524 (a century), by 1,461 (four years), by 365 (a year), and count the months off. The date comes back out.

Two things the count cannot guess: which calendar the date was written in, and which of the two time scales the clock was keeping.