English: Distribution of horae and vigiliae for the year AD 8 - GIF animation.

The surise and sunset times for this diagram are calculated for Forum Romanum 41°53′33″N 12°29′07″E / 41.892426°N 12.485167°E / 41.892426; 12.485167 AD 8 (the Julian calendar). Sunrise and sunset times are used as boundaries of day and night. Many sources however are ambiguous because of confusing terms sunrise with dusk and sunset with dawn. This is important, because times of dusk and dawn differ significantly from times of sunrise and sunset. The semidiameter of the sun and atmospheric refraction are taken into account. Equinoxes and solstices are computed too, not set by Romans.

Sunrise and sunset times were calculated using algorithms from:
Jean Meeus, Astronomical algorithms, Second English Edition, Willmann-Bell, Inc., Richmond, Virginia, 1998, With corrections as of August 10, 2009, ISBN 0-943396-61-1.
There is an online calculator also based on Astronomical Algorithms, by Jean Meeus, computing sunrise and sunset times, sun azimuths and elevations:
http://www.esrl.noaa.gov/gmd/grad/solcalc/ NOAA Solar Calculator
(Gregorian calendar)

however calculations for this image are based directly on this Meeus's book.