Time of Day

The first image 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 .

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 »Æ´óÏɸßÊÖÂÛ̳ 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 »Æ´óÏɸßÊÖÂÛ̳ 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 second image features a twelve hour clock, which 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.

Day of the Week

The concept of a week that repeats indefinitely, and upon which the rhythm of human activity is based was first used by the Jews and probably goes back to the time of Moses. As it is independent of any astronomical phenomenon, it has the advantage of simplicity over the day, month, and year, all of which vary in length to some extent in order to synchronize. The Jewish days had no names other than numbers (with our Sunday as the first day of the week). Like the oblique references to the sun and moon in the description of creation in Genesis 1 (where they are described simply as "a greater light" and "a lesser light"), the philosophical implication of the Jewish week was to demythologize the natural world. In ancient times, the names of the sun, moon, and planets were inextricably tied to names of deities. Numbered days and weekly patterns that ignored the cycles of these deities expressed the contrary view that these objects were inanimate.

Much later, and independently, an astrological week of seven days was constructed beginning with Saturn's day (our Saturday). This likely originated in hellenistic Alexandria in the second century BC. Seven days matched the number of planets by the ancient definition: something that wandered against the backdrop of stars (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon). Horoscopes were written based on the planet associated with the hour of the day and the day of the week. Interest in astrology spread this week throughout Europe in the early centuries of the Roman empire. Hence the English day names all come from planet names directly (Sunday, Monday and Saturday) or indirectly (e.g., Friia was the Nordic god of marriage and fertility, so Venus-day became Friday).

In other parts of the world the week spread with the spread of Christianity and of Islam. In these places day names are generally based on numbers or more explicit Christian references (e.g. "the Lord's day" for Sunday). As both systems have seven days, it long ago became impossible to cleanly distinguish between the importance of each for later use of the week (e.g., German has two day names related to the Jewish numbering and five related to planet deities).