Date And Time

Date and Time The positions of the Sun, Moon, planets, and stars change over the course of days, months, and years. Thus the units we use to mark the passage of time are intimately tied to astronomy. A day is (roughly) the length of time the Earth takes to turn on its axis, i.e. for the Sun to return to the same position in the sky. A month is (roughly) the time the Moon takes to orbit the Earth, i.e. to return to the same position relative to the Sun. A year is (roughly) the length of time the Earth takes to orbit the Sun, i.e. for the Sun to return to the same position among the stars.

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History of the Calendar

The first calendar to be based on the motion of the Sun was used by the ancient Egyptians. The Egyptian year had twelve months of thirty days each, plus an extra five days at the end of the year, given over to celebrations of the birthdays of the gods. Thus the Egyptian year was exactly 365 days long. But in fact, the amount of time the Earth takes to orbit the Sun is actually 365.24219… days. So the Egyptian calendar gradually fell out of step with the actual seasons, in a cycle that would take 1460 years to complete. To solve this problem, Julius Caesar introduced the concept of leap-years in 44 BC. Every fourth year, an extra day was added to the month of February, thus making the length of the year 365.25 days. The Julian calendar prevailed for more than 1500 years, and is the predecessor of the calendar system the Western world uses today. But 365.25 days is still not the correct length of the year, and by the 16th century the Julian calendar had gotten significantly out of sync with the seasons. The Gregorian calendar, with its more complicated leap-year rules - every 4th year, but not every 100th year, except for every 400th year - was introduced by Pope Gregory XIII. It officially replaced the Julian calendar on 10 October 1582 and has now come into universal use. However, the changeover from the Julian to the Gregorian calendar did not happen until 1752 in England and the American colonies, until 1873 in Japan, and until 1927 in Turkey.

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Julian Date

This calendar confusion presents some difficulties for astronomers - months have different lengths; different years have different numbers of days; and different calendar systems were used at different times in different parts of the world. To rectify this problem, the 18th-century English astronomer John Herschel introduced a simple, uniform time scale to use for astronomical calculations. This is the Julian Date (JD), and it is simply the total number of days elapsed since 12 noon at Greenwich on 1 January 4713 B.C. The start of the third millennium, i.e. Greenwich midnight on 1 January 2000, corresponds to JD 2451544.5. Julian dates always start at noon (not midnight) Greenwich time, and do not observe any time zones or daylight saving time changes. One advantage of the Julian date is that the time interval between two events is found by simple subtraction. Moreover, there are mathematical formulae to convert any Julian date to a Julian or Gregorian calendar date. If you reckon time using the Julian date, there is no Y2K problem. For all of these reasons, the Julian Date is still widely used by astronomers today.

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Universal Time and Time Zones

At any given time, half of the Earth is in sunlight and the other half is in darkness. If the Sun is overhead in Beijing, it is midnight in New York. In 1884 an international conference divided the Earth into 24 time zones. The meridian of Greenwich, England was set as the zero of longitude, and the time zones were measured in steps of 15 degrees from this location. The exact boundaries of each zone would vary depending on local politics and circumstance. Time zones of the world. Universal Coordinated Time (UTC) - also called simply Universal Time (UT), or Greenwich Mean Time (GMT) - is simply the local time in the time zone of Greenwich, England. UT is traditionally counted on a 24 hour clock, and is widely used by astronomers and navigators.

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The Equation of Time and the Analemma

Our activities are regulated by the cycle of day and night; it is natural to use the Sun as our time keeper. We could define a day as the period between successive passages of the Sun across the meridian. But this does not work well, since the length of the day varies continuously throughout the year. Due to the slight eccentricity of the Earth’s orbit and the tilt of the Earth’s axis, the Sun’s eastward motion against the background stars is not uniform. The Sun moves faster in the winter and slower in the summer. The 24 hour day would in some months be 10 minutes less, and in other months 15 minutes more. This is one reason that classic sundials provide very crude time keeping. To resolve this difficulty, astronomers defined a “fictitious sun” that moves at a uniform rate throughout the year. This is called the mean sun, and it gives us a uniform day. The mean solar day is the average length of the apparent solar day over the course of one year. Mean solar time is what we use in our daily lives. The difference between apparent solar time (using the real Sun) and mean solar time is the called the equation of time. Over one year, it can be as large as 16 minutes. The Equation of Time is commonly plotted on globes of the Earth, where it appears as a figure “8” curve. This figure is known as the analemma; it shows the Sun’s position at exactly 1-day intervals over an entire year. The Sun moves north and south across the celestial equator because of the inclination of Earth’s polar axis to its orbital plane (the Ecliptic). The Sun shifts in longitude because of the difference between the mean and apparent solar time.

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Solar and Sidereal Time

A sidereal day is the period of the Earth’s rotation in relation to the stars, rather than the Sun. A sidereal day is about 4 minutes shorter that a mean solar day. Over 24 hours, the Earth moves about 1/360 of its orbit. We see the Sun drifting eastward against the stars by 1/360 of a circle, which is 1 degree. In terms of the Earth’s rotation, this amounts to 4 minutes in 24 hours. If the Sun and a star are at the same position in the sky, after one rotation of the Earth, the Sun will have drifted eastward, and the star will pass overhead 4 minutes before the Sun. The sidereal day is approximately 1436 minutes, 4 minute less than 24 hours. The Sidereal Day. Sidereal time is “star time”. It is the elapsed time in hours, minutes, and seconds since the vernal equinox crossed the meridian. The right ascension that is currently on the zenith is the local sidereal time.

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Dynamic Time

Universal Time is necessary in civil life to set our clocks, and to make the trains run on time. UT is based on the rotation of the Earth. But the Earth’s rotation is uneven, and gradually slowing down - by about 1 second per year - so the average length of the day is increasing unevenly. This forces us to insert or remove leap seconds every so often to make UTC line up with where the Earth is actually pointing. Hence UTC is not a uniform time scale, and it is therefore not suitable for accurate astronomical calculations. Precise astronomical calculations require a dynamical time scale that is free of the irregularities caused by the Earth’s rotation. Terrestrial Dynamic Time (TDT) or simply Dynamic Time is based on atomic clocks, and it is the standard for precise time keeping in astronomy. The difference between UTC and TDT is known as Delta T (ΔT): ΔT = TDT - UTC The value of Delta T can only be deduced empirically, by observations of the Moon or extra-galactic radio sources. If the positions of the Sun and Moon are known to high accuracy at a specific dynamic time, the corresponding Universal Time (based on the irregular rotation of the Earth), and hence ΔT, can be calculated. It is currently about 70 seconds. Extrapolating backward, ΔT was as large as 4-1/2 hours around 500 B.C. - we know this value because of observations of eclipses that were recorded by the ancient Greeks.