The hour angle of a celestial body is the angle measured west along the celestial equator expressed in hours where one hour is fifteen degrees.

Unfortunately, these units are not consistent with the basic definition of time: time is defined to make motion look simple. The hour angle of the true sun is not regular due primarily to the ellipticity of the Earth's orbit and to the obliquity of the ecliptic. Moreover, the length of the day is gradually increasing due to tidal friction and the number of days in a month and in a year change with time.

Hence, a new unit of time, the atomic second defined as 9,192,631,770 periods of the hyperfine resonance line of cesium-133 (¹³³Cs) has replaced the solar second as a standard.

The metre, originally 1/10,000,000 the distance from equator to pole, is now defined to be 1/299792458 of the distance light travels in 1 atomic second (so the speed of light is defined to be 299792458 metres per second).

TROPICAL YEAR
The time that the sun crosses the celestial equator moving from south to north is very important to farmers. This is the vernal equinox the first day of spring, heralding the new planting season. The interval between vernal equinoxes is known as the tropical year and is about 365.242199… ephemeris days in length. The tropical year is what we base the calendar on. Do not confuse the tropical year with the sidereal year, 365.256366… ephemeris days.

JULIAN CALENDAR

Sosigenes of Alexandria suggested to Julius Caesar a new calendar having twelve months each of average duration 30½ days rather than the Republican 29½-day lunar calendar. So in 46 BC the Julian calendar which starts on 1 January 45BC was introduced. The new calendar approximated the tropical year by having three common years each 365 days in length and a leap year every fourth year (every year divisible by four). The transition from the Republican to the Julian calendar involved the intercalculation of three extra months to bring the date of the vernal equinox back to the traditional March 25 making the first Julian calendar year length to 445 days -- the year of confusion.

The dates of the observance of Easter were fixed by the order of the council of Nicea in 325AD. Easter falls on the first Sunday after the "fourteenth day of the Moon" (almost full moon) that occurs on or (usually) after March 21. Between 45 BC and 325 AD the vernal equinox slipped back from March 25 to March 21 because the Julian year is too long by about 11m 14s.

By 1582 the 11m 14s per year difference between the Julian 365.25 day year and the tropical year brought the vernal equinox back to March 11. This gradual regression prompted Pope Gregory XIII to institute a further calendar reform. Basically, Gregory shortened the Julian year length from 365.25 to 365.25-3/400 = 365.2425 by deleting any century leap year not divisible by 400, giving a calendar correct to one day in about 3300 years.

To put the vernal equinox back to March 21 (where it was in 325 AD) ten days had to be dropped from the calendar. So by proclamation, the day following 1582 October 4 became October 15. But the Eastern Church and most Protestant countries did not adopt the new calendar until much later.

England and her Empire did not make the change until 1752. By then an 11 day discrepancy had built up and by parliamentary decree 1752 September 2 was followed by September 14.

The Gregorian calendar has been modified since (before anything could go wrong) to bring the Gregorian 365.2425 down to 365.2422 by cutting out "leap centuries" that are divisible by 4000 thus giving an accuracy of about one day in 20,000 years.