This dial gives the time of sunrise, transit (when the sun is above the southern point of the horizon), and sunset. The inner circle gives "mean solar time", the time given by a clock that runs at a uniform rate. The outer circle gives "sun time", which is defined by the assumption that the sun transits at noon. Since the time from transit to transit is not uniform, the mean solar time of transit varies in an irregular way from 17 minutes before mean solar noon (in late October) to 14 minutes after (in early February). The difference (sun time minus mean solar time) is known as the equation of time. This annual variation is due both to the tilt of the earth's spin axis with respect to its orbital plane (23.5 degrees) and to the eccentricity of its orbit (1.7 percent). For a full description see the analemma web site.

Clocks in Grand Rapids (including the twelve hour clock on the planetarium) generally show the mean solar time at the center of the Eastern Standard time zone. Since Grand Rapids is in the extreme west of that zone, the clocks at Calvin College read 42 minutes later than the mean solar time of our longitude. (From April to October, they read 102 minutes later, adding 60 minutes extra for daylight savings time).

The length of the day (sunrise to sunset) at Calvin College varies from 9 hours exactly in December to 15 hours 22 minutes in June. Where Botjes lived in the Netherlands (10 degrees north of Grand Rapids), the day varies from 7 hours 32 minutes to 16 hours 57 minutes in length. The range is determined both by the observer's latitude and by the tilt of the earth's spin axis.

The twelve hour clock runs like any standard clock. The idea of dividing the day into 24 hours goes back to the Egyptians, who by 1300 BC recognized 10 hours of dark, 10 of light, bounded by 2 hours each of morning and evening twilight. Since sunrise and sunset divided the 12 nighttime hours from those of the day, a December daytime hour in the Netherlands might be only 38 minutes long while a nighttime hour lasted 82 minutes. With the spread of mechanical clocks in the fourteenth century, hours of uniform length were adopted. Hence the hours read from the twelve hour clock pictured here are labelled "o'clock" (of the clock), in distinction to "of the sun".

The word "minute" comes from a Latin phrase meaning "small part". The practice of dividing things into sixties (rather than, say, tens or hundreds as done in the metric system) goes back to the ancient Babylonians.

	The celestial sphere: diurnal motion of the stars
	Botjes planetarium home page
	Day of the week