Systems for Measuring Time
The passage of time can be seen in the motion of the Sun across the sky during the day, and the stars at night. To make measurements easier, sundials were devised, which avoided the problem of looking directly at the Sun. The apparent motion of the Sun and the stars each day is due to the rotation of the Earth around its axis. As the Earth spins, the Sun 9 (or any star) appears to rise above the horizon to some maximum (zenith), and then gradually sinks to below the horizon. By dividing this apparent movement into equal arcs, a method of measurement may be devised. This is called sidereal time, that is, time based on the rotation of the Earth.
Since the Earth both rotates on its axis and revolves around the Sun, the length of the day varies, depending upon whether the Sun or the stars are used as the basis of measurement. If a suitably distant star is used (far enough to have no significant parallax over the course of a day), we can assume the star to be a fixed point in space relative to the Earth. However, the Sun is much closer, and during the course of a day, the Earth completes 1/365 of its orbit around the Sun (approximately 1 degree). Therefore, the Solar day is a bit longer than the sidereal day, because exactly one sidereal day after a given noon, the Earth has moved forward in its orbit around the Sun, and needs to rotate a bit more than a full circle to have the Sun at zenith again. The Solar day is about 4 minutes longer than a sidereal day. Check figure below (orbital motion exaggerated for effect).
Diagram showing the difference between the solar and sidereal day.
The figure above explains the difference between a solar and sidereal day. The blue circle is the Earth, the small yellow circle is the Sun. The star is not actually shown, since it's very far away. Because of this great distance, the rays of light coming from this star can be considered to be parallel, that is, there is no parallax over the course of two observations, taken 1 day apart. The rays of light from the star are shown, in orange. A sidereal day would be the time between two successive occasions when the star is directly above the local meridian. This period is approximately 23 hours and 56 minutes. If the Sun was as far as the star, the solar day would also be exactly the same length. However, the Sun is much nearer, and during the course of a day, the Earth has moved in its orbit by about 1/365 of a circle, or 1 degree. Therefore, at the end of the sidereal day, the Sun is still not directly over the local meridian; it is in fact, about 1 degree behind. The Earth's rotation will bring the Sun directly over the local meridian about 4 minutes later, which is the end of one solar day. The solar day is 24 hours, about 4 minutes longer than the sidereal day.
The relationship between a solar and sidereal day is easy to see intuitively. A year is 365 days long, meaning there are 365 solar days in it. In other words, 365 times during the year, the Sun is directly over the local meridian. But how many times has the earth rotated with respect to the stars? The answer is 365+1, with the extra 1 coming from the fact that during during a full circle in orbit, the earth has rotated 365 times plus the one time any non-rotating or tidally locked body would rotate with respect to the stars during a full orbit. In actual fact, the length of a solar year is 365.25 days, so the relationship between a sidereal and solar day is 365.25/366.25, or 23 hours, 56 minutes, 4.1 seconds.
Coordinated Universal Time
Obviously, sidereal time is different, depending upon where you are on the surface of the Earth. It varies with longitude. When your local meridian is directly under the Sun, it is locally noon. It would be midnight at the meridian directly opposite your local meridian, on the other side of the Earth. There is a need to have a standard or uniform time system across a region (for the purpose of scheduling activities such as work, transportation, etc.), while keeping this region small enough that no part of it has an obvious conflict with sidereal time (such as the clocks showing midnight when the sun is still overhead). I am using the words "sidereal time" instead of "solar time" but the two are close enough to be equivalent in this context.
Time zones are an answer to this problem of achieving a uniform time across regions, while still respecting celestial phenomena locally. However, there is still a need for some uniform time across the entire planet, to which these local time zones can be related. This universal time is based on an arbitrarily chosen meridian, which is the prime meridian passing through the Royal Observatory in Greenwich, England. This is UTC, or Universal Coordinated Time.
International Atomic Time
So how is time actually measured? Well, we use clocks, and the most accurate are the atomic clocks. Our clocks are actually more accurate than many celestial phenomena, such as the length of the solar day. We can actually measure the gradual slowing of the Earth's rotation, and the consequent lengthening of the solar day. They are so accurate that relativistic effects in the presence of a large mass such as the Earth can affect them. For this reason, there is no single clock that is used to measure time. International Atomic Time (TAI) is a weighted average of about 300 clocks, many of them cesium atomic clocks, across about 50 laboratories (and some satellites) spread across the globe. The time signals regularly broadcast by these clocks are later compared and analyzed, and any corrections applied. The results are then published. TAI is therefore retrospective, it tells you what the real time was back when clock number "x" broadcast its "n'th" time signal.
Now that we have an accurate time measurement from TAI, it can be used to define UTC. So UTC is the same as TAI, with occasional leap seconds added, to compensate for the slowing of the Earth's rotation. In effect, UTC translates TAI in terms of astronomical phenomena, specifically length of the solar day at the prime meridian. Since the solar day is lengthening as the Earth slows, UTC compensates by adding leap seconds.
With this definition of time in place (UTC), astronomers use a specific calendar to date events. Commonly, the Julian calendar is used. This is the same calendar we use today (introduced by Julius Caesar in 46 BC), but modified somewhat as follows:
- Julian days begin at noon, not midnight like our usual days. This goes back to Ptolemy. A recurring astronomical event was needed, and the local solar zenith was selected as being the most convenient. Midnight was tough back in the days of no electricity and water clocks.
- The Julian calendar initially used the meridian of Alexandria as prime, but this was later changed to Greenwich.
- The Julian calendar starts at noon UTC, on January 1, 4713 BC. This date was chosen for historical and astronomical reasons, in order to make calculations easier.
- There is a year zero. In our regular calendar, 1 AD is preceded by 1 BC, with no 0 in between. This is bad math.
Why Does the Epoch Begin on this Particular Date?
This goes back to Joseph Scaliger in 1583, at the time of the Gregorian calendar reform. Scaliger considered 3 cycles: the Indiction cycle, the Metonic cycle and the Solar cycle (which were in use at his time), and calculated when all 3 cycles would have been in their first year together. This happened in 4713 BC, which was a nice, ancient date, prior to recorded history, and therefore convenient.
Solar Cycle: a cycle of 28 years, based on leap years and days of the week. A leap year occurs every 4 years, and there are 7 days in the week, so a solar cycle is 4 x 7 = 28 years. In other words, the leap day falls on the same day of the week once every solar cycle.
Indiction Cycle: These were 15-year cycles used in medieval record keeping. Historically, they go back to 3rd century Roman Egypt, where a land tax was levied every 5 years. Eventually, they became 15 year cycles instead of 5. The 15-year first indiction cycle is dated to either the years 297-298 AD, or to the years 312-313 AD, depending on which historical source is used. Years were numbered within the cycles, such as first indiction, second indiction, eleventh indiction, etc. but the cycles themselves were not numbered. These cycles were still in use in Scaliger's time.
Metonic Cycle: This based on the ancient Greek astronomer, Meton of Athens, who noted that 19 tropical years almost exactly equal 235 synodic (lunar) months. A synodic month is 28 days, the time it takes for the Moon to circle the Earth once. A 'tropical" year actually has nothing to do with the tropics (tropos is the Greek word for "turn"). It is, in fact, the same as what we mean by a solar year, which is the time taken by the Sun to return to the same exact spot in the sky. Typically, this is measured at specific occasions, such as the spring or vernal equinox. The time between two vernal equinoxes would be a vernal equinox tropical year. Similarly, one can measure an autumn equinox tropical year, or a year based on either of the two solstices. All of these differ from each other by a minute or two, so often an average known as the mean tropical year is used instead. This tropical year differs from the sidereal year, which is star-based. A sidereal year is the time taken by the Earth to complete one full orbit around the Sun, that is, to return to exactly the same position relative to the backdrop of stars. The difference is due to the precession of equinoxes.
The Earth's axis precesses, that is, rotates in a circle every 25765 years. This is why Polaris is the pole star now, but was not so in the past. This precession was noticed by Hipparchus about 127 BC, as a westward movement of the equinoxes along the ecliptic plane, against the backdrop of stars. A tropical year is based on the measurement of equinoxes, which are directly a result of the Earth's axial tilt. Assume that the Earth is in a certain position in its orbit at the time of an equinox (meaning that you the observer standing on the northern hemisphere are as close to the Sun as the tilt will allow). About a year later, you are again at equinox, but the Earth hasn't quite reached the same point in its orbit as it was at the last equinox. This is because the Earth's axial tilt has changed, due to precession, and the equinox has come sooner than expected. The difference between the tropical and sidereal year is about 20 minutes (1/25765 of a year). After 25765 years, the equinox will again happen at the exact same place in orbit.
Meton was trying to reconcile solar and lunar years, and he noticed that 19 solar or tropical years were almost exactly the same as 235 lunar or synodic months (only 2 hours difference between the two). He used this 19 year cycle to calculate when to add extra months in the year to bring the months back in line with the solar year.
Since there is a year zero in astronomical calculations, Scaliger's calculated date of epoch of January 1, 4713 BC is actually January 1, -4712 (BC is expressed simply in negative numbers, the numerical value is 1 less because of the introduction of year 0 between years -1 and 1). This is the first Julian day.
Calculating Julian Dates
Astronomers like Julian days because astronomical events can be directly compared. For example, two events which happened on Julian day 27000 and Julian day 23000 are exactly 4000 days apart. This would be hard to calculate if conventional dates were used, for example to compare two events in the years 523 AD and 1634 AD. In order to calculate these, we would need to know:
- were there any intervening leap years?
- were any other corrections applied?
- are those dates even on the same calendars, since calendars have been changed/reformed many times.
Julian dates bypass all these problems. They are therefore very useful for calculations, and for converting dates from one calendar system to another. Julian dates are expressed as decimals, with the integer portion (before the decimal) representing the number of days since the start of the Julian epoch, and the decimal portion representing the time of the day. For example, a Julian date of 2454115.05486 would mean:
2454115 days since the start of the Julian epoch, plus 0.05486 of a day, which is 1 hour, 18 minutes, 59.904 seconds. Since the Julian day starts at noon, adding an hour would bring it to 13 hours 18 minutes and 59.904 seconds UTC. Calculation of the day is slightly more complicated, and done as follows.
First, 3 coefficients are calculated: a, y and m.
a = (14 - month) / 12 [where month is from 1 to 12, January being 1 and December being 12]
y = year + 4800 - a
m = month + 12a - 3
Next, these coefficients are plugged into a formula. For calculating Julian days from a Gregorian calendar (which we use today), the formula is:
Julian Day = day + ((153m + 2)/5) + 365y + (y/4) - (y/100) + (y/400) - 32045
The formula for calculating Julian day from the Julian calendar is:
Julian Day = day + ((153m + 2)/5) + 365y + (y/4) - 32045
If you divide the Julian Day by 7, then the remainder indicates the day of the week, with Monday = 0 and Sunday = 6.
As an example, let's calculate the Julian Day for 7:34 p.m. on the evening of August 15, 2006. Solution here.