The Julian day number
The Julian day number counts days continuously from a fixed starting point, so that dates can be subtracted and time differences found without calendar rules.
What it is
The Julian day of a moment is a number with a fraction for the time of day, starting at noon. The site's calculations convert the birth date and time to Julian day, and the J2000 epoch is Julian day 2451545.0.
How it is worked out or read
Calendar arithmetic, such as leap years, is handled once when the date is converted, so later steps work with a simple count of days. The Julian centuries used in the precession and obliquity formulas come from this count.
Where it appears on this site
The conversion is part of the method on the method page.
A continuous count of days
The Julian Day number is a continuous count of days used by astronomers, starting from noon on 1 January 4713 BCE in the proleptic Julian calendar. It ignores months, years, calendar reforms and leap-year rules, and simply numbers every day in sequence, with fractions for the time of day. For example, noon on 1 January 2000 is Julian Day 2451545.0, a moment astronomers call J2000.0 and use as a standard reference epoch.
The count begins at noon rather than midnight, a convention from the days when astronomers observed through the night and preferred not to change the date in the middle of their work.
Why calculations need it
Astronomical formulas need the time elapsed between two moments, and working that out across calendars, leap years and the Gregorian reform of 1582 is tedious and error-prone. Converting both moments to Julian Days turns the problem into a simple subtraction. Every planetary position on this site begins with this step: the local birth time is converted to Universal Time, then to a Julian Day, and the number of days since J2000.0 is fed into the equations for the Sun, Moon and planets.
Related counts
Several variants are in use. The Modified Julian Day subtracts 2400000.5, giving smaller numbers that begin at midnight. Astronomers also distinguish between Julian Days on Universal Time and on Terrestrial Time, a uniform scale used in the equations of motion; the difference between them, delta T, is about a minute at present and was much smaller or larger in past centuries, depending on the irregular rotation of the Earth.
The Indian equivalent
Indian astronomy had its own continuous day count, the ahargana, the number of days elapsed since the start of the Kali Yuga, which the siddhantas place in February 3102 BCE. Planetary positions were computed by multiplying the ahargana by each planet's daily mean motion. Karana texts, such as those of Brahmagupta and Bhaskara, chose a more recent epoch to keep the numbers small, much as modern astronomers use J2000.0 instead of counting from 4713 BCE.
A small exercise
The Julian Day for any date can be computed with a short formula found in astronomy textbooks, such as Jean Meeus's Astronomical Algorithms. Working through it once for one's own birth date is a good way to see that every chart, however traditional its reading, rests on simple, checkable arithmetic.