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The Relativity Page also treats some questions dealing with time.

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## 1. Time and Astronomy

Some astronomical things occur at regular or accurately predictable times, so that you can use those astronomical things to tell the time. Some basic units of time are tied to astronomical things, such as the rotation period of the Earth (the day), the synodical orbital period of the Moon (the lunar month), and the orbital period of the Earth (the year).

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## 2. Units of Time and Angle

The sexagesimal (base-60) divisions of units of angles (one circle = 6×60 degrees, 1 degree = 60 minutes of arc, 1 minute of arc = 60 seconds of arc) and time (1 hour = 60 minutes, 1 minute = 60 seconds) are ultimately based on practices of the ancient Babylonians, who used base 60 for all of their calculations. Their divisions of time and angle were copied by the ancient Greeks, and theirs by the Romans, and we inherited them from the Romans. The 24 hours of a day come from the ancient Egyptians, who divided both the day and the night into 12 equal parts.

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## 3. Time and Gravity

Gravity influences how fast time flows, but the gravity of the Earth is far too weak to have great influence on the flow of time. At the surface of the Earth, time runs slower than deep in space by one part in about three thousand million. If you have an atomic clock, then you need to pay attention to the effects of gravity, but for ordinary clocks it is not important.

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## 4. Daylight Savings Time and Standard Time

In many countries outside of the tropics, time on the clock is moved forward by one hour in the summer and is moved back by one hour again in the winter. The time that is used during the summer is called Daylight Savings Time and the time that is used during the winter is called Standard Time. In the tropics there is little interest for Daylight Savings Time because there the Sun rises around the same time each day and sets around the same time each day (see question 100).

Daylight Savings Time (DST) was started to save energy. The Sun sets one hour later on the clock when DST is in effect, so then it's one hour later on the clock when you have to turn on the lights because it is getting dark. On the other hand, the Sun then rises one hour later on the clock, too, so if you need to get up at a very early fixed time according to the clock, then you may need to keep the lights on longer. Apparently there are more people who like later sunsets in the summer than people who dislike later sunrises in the summer.

In winter we return to Standard Time because the days are short then and otherwise there would be too great of a difference between the number of hours of daylight before noon (on the clock) and after noon. Here in the Netherlands and Belgium, the sun would rise only at about 10 a.m. DST in the middle of winter and would set at about 5:30 p.m. With Standard Time, the Sun rises "already" around 9 a.m. in the middle of winter (and sets already at 4:30 p.m.).

You can find a diagram of the times of sunrise and sunset with Daylight Savings Time and Standard Time in the Netherlands and Belgium on the page about the position of the Sun. For other places you can refer to the tables on the appropriate tables page.

In Europe, Daylight Savings Time begins in the night from Saturday to Sunday in the last weekend of March, and lasts until the night from Saturday to Sunday in the last weekend of October.

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The history of the use of Daylight Savings Time in the Netherlands is described, in Dutch, at //www.phys.uu.nl/~vgent/wettijd/wettijd.htm.

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The intention of official clock time is that each second lasts equally long. This has nothing to do with Daylight Savings Time or Standard Time, because those differ by a fixed amount.

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## 5. The Length of a Year

There is no finish line in the orbit of the Earth around the Sun that shows when the Earth has completed another lap (year), so we have to invent our own rule for detecting when another year is past. Many rules can be invented, which all give a different length for the year. To the nearest minute, we have:

Table 1: Year Lengths

days hours minutes name rule
365 5 48 the northern solstice
365 5 49 calendar year the average of the Gregorian calendar
365 5 49 the average of the seasons
365 5 49 tropical year the ascending equinox
365 5 49 the descending equinox
365 5 50 the southern solstice
365 6 14 anomalistical year the perigee of the Sun

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## 6. The Length of a Day

The rotation of the Earth is very slowly slowing down, mostly because of the gravity from the Moon, so the length of the solar day is very slowly increasing. We want our clocks to follow the changes in the length of the solar day (so that "12 o'clock noon" won't slowly drift into the nighttime). There are two ways to do that: adjust the length of the seconds (and hence also of the minutes and hours) in pace with that of the solar day so that you can keep the same number (86400) of seconds to a day, or else keep the seconds equally long but insert or omit seconds from specific days as needed to keep pace with the solar day. The first method was used until 1972, and the second method is used since then.

So, in current official timekeeping, almost all calendar days have a length of exactly 24 hours of each exactly 60 minutes of each exactly 60 seconds, for a total of 86400 seconds, with those seconds being equal-length SI seconds as measured by atomic clocks. The only exceptions are the days when a leap second is inserted, which makes such days 1 second longer than the regular days, or 86401 seconds. It is possible in theory that seconds must be skipped instead of inserted, or that more than one extra second must be added to a given year, but those cases haven't happened yet until now (2006).

Leap seconds are inserted when the need arises, which is irregularly, because the slowing down of the Earth does not have a regular pace. For example, a leap second was inserted 6 times between the beginning of 1992 and the end of 1998, but after that none were needed until the end of 2005. See //en.wikipedia.org/wiki/Leap_second for more information about leap seconds.

There are other time scales besides the official clock time, and those can continue to use days that are all 24×60×60 seconds long, but then those time scales must either slowly run out of step with the Sun (such as for the TAI = International Atomic Time scale), or else have seconds that are not all equally long (such as for Solar Time).

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## 7. LunarTime

There is no official lunar time, but you can define a lunar time similar to solar time. It's 12:00 solar time when the Sun is highest in the sky (or the least far below the horizon), and 0:00 (or 24:00) solar time if the Sun is lowest in the sky (or the furthest below the horizon). In the same way, we can define that it is 12:00 lunar time when the Moon is highest in the sky, and 0:00 (or 24:00) lunar time when the Moon is lowest in the sky.

Because the Moon returns to about the same location relative to the Sun after a synodical month (about 29.5 days), there is one fewer lunar day than solar days in such a synodical month. One lunar day is therefore on average about 50 minutes and 28 seconds longer than a solar day.

Lunar time and solar time run are the same when it is New Moon. At First Quarter (about a week later), lunar time is 6 hours behind solar time. At Full Moon (after about two weeks) lunar time is 12 hours behind solar time. At Last Quarter the difference is 18 hours, and at the next New Moon it is 24 hours, so then the lunar clock and solar clock show the same time again.

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## 8. How Often Does The Earth Revolve Around the Sun?

How many times the Earth revolves around the Sun depends on how much time you give the Earth to revolve, and on how you figure out that the Earth has completed yet another revolution around the Sun.

The Earth moves around the Sun through empty space, so there are no convenient mile markers to show where the Earth is in its orbit, and there is no finish line to indicate when the Earth has finished yet another orbit. You can only look where the Earth is relative to something else, and there are several "something elses" that you can use, which unfortunately all move relative to one another (though slowly).

That's why each different kind of "something else" leads to a slightly different kind of year, and so to a slightly different number of revolutions completed in any fixed amount of time.

For example, there's the sidereal year (measured relative to the stars), the tropical year (measured relative to the seasons), the anomalistic year (measured relative to the annual closest approach to the Sun), and various kinds of calendar years. The first three of these differ in length from one another by at most about half an hour, which makes a difference of about one part in eight thousand in the number of revolutions completed during a given amount of time. Calendar years may be as short as 354 days, or as long as 384 days (depending on the used calendar).

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## 9. Past Stars

You see a thing as it was when the light coming from that thing started on its journey to your eye. If the trip takes a long time, then you see the thing as it was a while ago: then you look into the past. You can compare this to an instant picture of yourself that you immediately put in a letter to a friend. Your letter is delivered to your friend a few days later, so when he takes out your picture and looks at it, he sees what you looked like a few days ago. The delay in the arrival of light is therefore not a special characteristic of light, but shows up for any kind of transmission of information. Because light travels very much faster than mail, the travel time of light is not noticeable in your day-to-day life.

So, you see any thing as it was a while ago. This holds for a very distant star, but also for a nearby planet or for a tree next to your house. The travel time of light is very short if the thing is nearby, and is very long if the thing is very far away. The travel time of the light indicates how far you look into the past if you look at the thing.

For example, there is light from just after the Big Bang that came from so far away that it reaches us only now. That light shows us what the Universe looked like just after the Big Bang.

We can look back in time, but we cannot choose what we get to see from bygone times. We cannot see what our neighbor galaxy the Andromeda Nebula looked like just after the Big Bang, because the Andromeda Nebula is so close to us that the light that came from there just after the Big Bang (assuming that the Andromeda Nebula already existed then) has travelled past us a very long time ago.

Light travels very fast indeed, at almost 300,000 kilometers per second (186,000 miles per second), so you don't notice the travel time of light as you go about your daily business. If your sister sits opposite you at the table (at 1.5 meters distance), then the light travelling from your sister to you (and hence the image of your sister that you see) takes only one 200 millionths of a second.

The Moon is on average at about 380,000 kilometers distance, which takes light 1.3 seconds to travel, so we see the Moon as it was 1.3 seconds ago. Astronomers say that the distance to the Moon is about 1.3 lightseconds. Radio waves travel at the speed of light as well, so if you want to talk to an astronaut on the Moon, then you have to wait at least 2.6 seconds for every reply (1.3 seconds for the journey of your question to the Moon, and 1.3 seconds for the journey of the response back to Earth).

The Sun is on average about 8 lightminutes away, so we see the Sun as it was 8 minutes ago. If the Sun were to turn blue right now (which is very unlikely), then we would not see that until 8 minutes later.

The planet Saturn is on average about 75 lightminutes away from Earth. If astronomers send a command to an unmanned space probe at Saturn (like Cassini), then that command reaches Cassini 75 minutes later. If the command is to take a picture and send it back to Earth over the radio waves, then it takes at least 150 minutes (2.5 hours) before the astronomers receive a reply to the command that they sent, and every picture of Saturn that reaches Earth is at least 75 minutes old, even if it was sent as soon as possible.

The farthest planet is at about 4 lighthours from Earth. The closest star (Proxima Centauri, a dim member of the multiple star system Alpha Centauri) is at about 4 lightyears distance. Light from that star therefore takes 4 years to reach Earth, and we see that star as it was 4 years ago.

The stars that you can see at night are not all at the same distance from us, and they are not all equally bright, either. A star can appear bright because it is very close (for a star), or because it emits lots of light (i.e., is intrinsically bright). An intrinsically dim star that is close by can appear brighter in our sky as an intrinsically bright star that is far away, just like a small candle that is very close by can appear as bright as the headlights of a car at great distance.

For example, Sirius (in the constellation of the Great Dog) is the brightest star in the sky, and appears three times as bright as Rigel (in the constellation of the Orion the Hunter), even though Rigel shines 2000 times brigher than Sirius. Because Rigel (at 800 lightyears distance) is 90 times further away than Sirius (at 9 lightyears), Rigel appears dimmer than Sirius in our sky. Of the 50 brighest stars in our sky, the furthest one is about 2000 lightyears away. The furthest thing you can just see without a telescope or binoculars, from a dark place, is the Andromeda Nebula. That nebula is a giant galaxy (like our own Milky Way Galaxy), at 2,200,000 lightyears distance. Because it is so far away, it appears as a small blurry smudge.

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This looking back in time works the same no matter where you are. The further that things are from where you are (wherever that is), the further you look into the past when you look at those things. An observer on an object that appears to be at the rim of the visible Universe as seen from Earth would consider himself to be in the center of the visible Universe, and us to be at or near the rim of the visible Universe. The Universe is probably much greater than the part of it that we can see.

This can be compared with the experiences of people in a dense fog. To an observer in a fog, nearby things are clearly visible, but the more distant that things get, the more difficult they are to see, and beyond a certain distance nothing can be seen. At that distance is the rim of the observer's sphere of visibility in the fog, similar to the edge of the visible Universe.

If Archie and Betty are both in the fog, and if they are at a distance from each other such that Archie can barely see Betty, so that Betty is at the rim of Archie's sphere of visibility, then Archie is likewise at the rim of Betty's sphere of visibility. The two spheres of visibility share a certain volume: Both Archie and Betty can see things that are located between them. Each sphere also includes a volume that is not inside the other one's sphere: Archie can see some things that are invisible to Betty, and vice versa. And the bank of fog can be vastly larger than the volumes that Archie and Betty can see.

As far as we can tell, Earth is not at a special location in the Universe, so the Universe appears roughly the same from here as it does from any other location. Of course, the individual stars and galaxies will not look quite the same from another location, but the large-scale structure and behaviour of the Universe do look the same no matter where you are.

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## 10. At the Same Time Old and New?

Someone on planet X at 5 million lightyears from Earth sees the Earth as it was 5 million years ago. At the same time, someone on Earth sees the Earth as it is right now. If you could travel from the Earth to X in a very short time, then the Earth would suddenly seen 5 million years younger to you.

The Earth then doesn't really go 5 million years back in time. "Information about Earth" is not the same as "the Earth itself". The things that arrive here at X are carriers (light light) of information about Earth, that happen to arrive just now. There are many other carriers of such information (with the same or greater age) but they are at different places and not (yet) at X. The information about Earth that arrives at X now is 5 million years old, because it took 5 million years for them to travel from Earth to X, but the Earth itself has experienced 5 million more years since that information was sent, just like X has. The Earth of 5 million years ago does not exist anymore, but information about the Earth of 5 million years ago does still exist.

It often helps to think of the similar case with letters. Suppose that A every day sends a letter to X, that says what has happened to A since the previous letter. A and X are far apart, and the letters from A taken 5 weeks to arrive at X. (We assume that there is no faster way for A and X to send things to each other.) At any given moment, X knows what the situation of A was 5 weeks ago. The letter that just arrived at X exists "now", just like A and X and all other letters that are still in transit, but the information from the letter that just arrived is 5 weeks old. If X were suddenly transported to A, then X wouldn't find the A of 5 weeks ago that wrote the letter that just arrived, but the A of now, who has experienced 5 more weeks than that letter described.

If X travels to A along the mail road, then along the way X sees the letters from A that are still on their way to the house of X. Those letters didn't have to travel as long (because X gets ever closer to A) so the news in those letters is ever less old. X then receives on average more than one letter a day from A, and thus each day receives the news from more than one day. It then seems to X as if time at A runs faster than at X, but that is only because X is travelling toward the sender of the letters. If Y starts sending X one letter a day from their home after X left to travel to A, then the letters from Y have to catch up with X, because X gets ever further from Y (and closer to A), so X receives on average fewer than one letter per day from Y, as if time goes slower at Y than at X.

These examples show that how often you receive a signal from a transmitter depends also on your speed relative to that transmitter. If you move toward the transmitter then you receive its signals at a higher frequency than the frequency at which the transmitter sends them, and if you move away from the tramsitter then you receive the signals at a lower frequency. This is the Doppler effect and it holds for all kinds of "signals", including light and sound and radar and letters.

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## 11. Ancient Time Measurement

It is not known for sure what the oldest method was of measuring time, but we can guess. The easiest way of measuring time is by looking at the height of the Sun above the horizon (or at the length of the shadow of a vertical stick). If the Sun is high, it must be around the middle of the day, and if the Sun is low, then it must be just after sunrise or just before sunset. This method is best when it is used to determine the time since sunrise or the time until sunset, but is not so good at determining the time in the middle of the day, because then the height of the Sun varies but slowly. Also, the greatest height that the Sun reaches during the day depends on the season, so you have to take that into account as well.

A slightly more difficult method of measuring time is to look at the direction of the Sun compared to the direction due South. That works well even in the middle of the day, because the Sun then moves quickest (as measured along the horizon). This method is more difficult than the previous one because you need to know where South is.

If you take into account both the height and the direction of the Sun, then you can do even better. You can do that, for example, with a well-adjusted sundial. With such a device, you can determine not just the local solar time, but also the season (the distance to midsummer and midwinter, but not whether it is spring or autumn).

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## 12. SolarTime

Solar time is the time measured according to the position of the Sun. At 12 o'clock noon solar time, the Sun is highest in the sky (or the least far below the horizon), and at 12 o'clock midnight solar time, the Sun is lowest in the sky (or the furthest below the horizon). At 12 o'clock noon solar time, the Sun stands straight over a point on the same meridian where you are. At 12 o'clock midnight solar time the Sun is straight over a point on the same meridian as the point at the exact opposite side of the Earth from where you are.

In the half of the Earth that is turned towards the Sun at a given moment, the Sun is above the horizon and it is day. In the half of the Earth that is turned away from the Sun, the Sun is below the horizon and it is night. This is exactly the same as when you shine a light on a small sphere (such as a ball or an apple) when it is dark: half of the sphere is in light, and the other half is in darkness.

If everbody wants to use a clock that indicates 12 o'clock noon when the Sun is highest in the sky, then it cannot be the same time on that clock everywhere on Earth, because when it is midday here, then it is midnight on the exact opposite side of the Earth.

A clock that shows when the Sun is highest in the sky (because it is then about 12 o'clock noon) shows solar time. Three different kinds of solar time are relevant:

• The true solar time is a time scale in which the Sun is highest in the sky at exactly 12:00:00 hours each day, but not every day needs be equally long (as measured using something that does not care about the position of the Sun in the sky, such as an atomic clock or planetary phenomena in the sky). You can read true solar time from a well-adjusted sundial.
• The mean solar time is a time scale that runs in step with true solar time on average but in which all days are equally long. Averaged over many planet days and planet years, the Sun is highest in the sky at 12:00:00 mean solar time. You can read mean solar time from a well-adjusted clock or watch. This time is often referred to as "Local Time" in these pages.
• The official clock time that you use in daily life is the mean solar time of a certain meridian that belongs to your time zone. The difference between official clock time and the mean solar time of a location depends only on the difference between the geographical longitude of that place and the longitude of the meridian that the official clock time is based on.

The difference between the mean solar time and the true solar time is called the Equation of Time. This indicates how much earlier or later than average the Sun is highest in the sky each day. The following table shows the solar transit times in mean solar time for the beginning of every month. You find the Equation of Time by subtracting 12:00.

 Month 01 02 03 04 05 06 07 08 09 10 11 12 Transit 12:03 12:14 12:12 12:04 11:57 11:58 12:04 12:06 12:00 11:50 11:46 11:49

The characteristic points are as follows:

• latest around 11 February, at about 12:14:15 mean solar time
• at local noon mean solar time around 16 April
• earliest around 14 May, at about 11:56:18 mean solar time
• at local noon mean solar time around 13 June
• latest around 26 July, at about 12:06:29 mean solar time
• at local noon mean solar time around 1 September
• earliest around 3 November, at about 11:43:35 mean solar time

The Equation of Time has a contribution from the eccentricity of the orbit of the Earth and a contribution from the obliquity of the ecliptic compared to the equator of the Earth, and those contributions are roughly equal in size. The position of the Earth relative to its perihelion is important for the first contribution, and the seasons are important for the second contribution. The Earth is in its perihelion around 3 January, which is not at the beginning of any season, so the Equation of Time is not symmetrical compared to the seasons or compared to the perihelion.

For calculations on the Equation of Time, go to the Calculation Page on the Position of the Sun.

All places on the same meridian, which have the same geographical longitude, also have the same true solar time and mean solar time. The solar time shifts by 24 hours over 360°, which means 4 minutes per degree. A place that is 10 degrees further to the east has its solar time 40 minutes later. At the latitude of the Netherlands (about 52°), this corresponds with about one minute for each 17 kilometers in the east-west direction.

The extent of the Netherlands in geographical longitude is about 3.86 degrees, which corresponds to a solar time difference of about 15 and a half minutes: The Sun is highest in the sky about a quarter hour earlier at the eastermost point of the Netherlands than at the westernmost point.

It would be rather inconvenient in these modern times if each city observed its own (solar) time. Then, if friends in different towns agreed to call each other at some set time, then they'd have to very carefully specify who's clock everyone should watch to see if the time to call had arrived. Otherwise the friend in The Hague (on The Hague Solar Time) would call about 6 minutes later than the friend in Arnhem (on Arnhem Solar Time) expected. Times in the tv guide or the railway timetable would not match everybody's clock anymore, either. That's why everybody in the Netherlands uses the same official time, Central European Time (CET), which is also used by many other west-European countries.

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## 13. SiderealTime

Solar time is the time as measured by the position of the Sun in the sky. Sidereal time is the time as measured by the position of the stars in the sky. When the same sidereal time comes around again, the stars are back in the same positions in the sky (as seen from the same location). You can find maps of the stars for 50° north latitude for different sidereal times through the Starry Sky Page.

Because the Earth goes around the Sun in a year, it seems as seen from Earth as if the Sun goes between the stars along the ecliptic in a year. Therefore, the Sun moves a bit further between the stars every day, and if you look at the stars at the same time (according to the Sun) each night, then you'll see that all of the stars together shift a bit from day to day.

When the Sun has passed through the sky 365 times and a bit (i.e., when a full year has passed), then the stars have made an extra circuit and so have gone around 366 times and a bit. A sidereal day (day of the stars) therefore lasts about 365/366 times as long as a solar day, or about 4 minutes shorter than a solar day.

Officially, the sidereal time at a given moment is equal to the right ascension that passes through the celestial meridian at that time. The right ascension is measured relative to the vernal equinox, so when the vernal equinox is highest in the sky, then it is 0 hours sidereal time. The vernal equinox is the point between the stars where the Sun is at the beginning of spring in the northern hemisphere and autumn in the southern hemisphere, so it is around 21 March. When it is 12 o'clock (noon) solar time on that day, then it is 0 hours sidereal time (because on that day the Sun is in the vernal equinox and at that hour the Sun goes through the celestial meridian, so then the vernal equinox goes through the celestial meridian and it must be 0 hours sidereal time). The difference between sidereal time and solar time is then 12 hours.

At the beginning of the northern autumn and southern spring, around 23 September, solar time and sidereal time are the same. For each month later, sidereal time runs about 2 hours fast compared to solar time. For each additional month, sidereal time gains about another 4 minutes on solar time. You can calculate the sidereal time at 0 hours solar time on 15 December as follows: 0 hours on 23 September, add eight times 4 minutes to get to 1 October, then twice 2 hours to get to 1 December, and fourteen times 4 minutes to get to 15 December. The total is 5 hours 28 minutes. Another method: 0 hours on 23 September, add three times 2 hours to get to 23 December, and then subtract eight times 4 minutes to go back to 15 December. This also adds up to 5 hours 28 minutes. So, on 15 December at midnight solar time it is about 5 hours 28 minutes sidereal time. That diffence remains the whole day, except that you should add another minute for each 6 hours. At 18:00 hours (6 p.m) solar time, for example, the sidereal time is 18 hours + 5 hours 28 minutes + 3 minutes = 23 hours 31 minutes (= 11:31 pm) sidereal time.

To go from solar time to the standard time of the official time zone you must apply a correction that depends on your distance from the meridian on which the time zone is based. For each degree of longitude that you are west of the meridian of your time zone, you must add 4 minutes to the solar time to get the clock time (and subtract 4 minutes for each degree of longitude to the east). In the Netherlands and Belgium we use Central European Time (CET) in the winter, and this time is based on the meridian of 15 degrees east. Someone in our area at 5 degrees east longitude should therefore add ten (= 15 - 5) times 4 minutes or 40 minutes to solar time to get clock time (CET). The Sun reaches its highest point at on average 12:40 hours here.

For convenience, I provide a table that shows sidereal times at midnight local (mean) solar time, and at midnight CET for 5 degrees east longitude (a reasonable fit for the Netherlands and Belgium) for various dates (day - month) of the year 2002. The times for the same days in other years can differ by up to 3 minutes in either direction.

date local CET, 5° east
01 - 01 06:38 05:58
02 - 01 06:00
07 - 01 07:00
17 - 01 07:00
22 - 01 08:00
01 - 02 08:40 08:00
07 - 02 09:00
17 - 02 09:00
22 - 02 10:00
01 - 03 10:31 09:51
04 - 03 10:00
09 - 03 11:00
19 - 03 11:00
24 - 03 12:00
01 - 04 12:33 11:53
03 - 04 12:00
08 - 04 13:00
19 - 04 13:00
24 - 04 14:00
01 - 05 14:31 13:51
04 - 05 14:00
09 - 05 15:00
19 - 05 15:00
24 - 05 16:00
01 - 06 16:33 15:53
03 - 06 16:00
08 - 06 17:00
18 - 06 17:00
23 - 06 18:00
01 - 07 18:32 17:52
04 - 07 18:00
09 - 07 19:00
19 - 07 19:00
24 - 07 20:00
01 - 08 20:34 19:54
03 - 08 20:00
08 - 08 21:00
18 - 08 21:00
23 - 08 22:00
01 - 09 22:36 21:56
03 - 09 22:00
08 - 09 23:00
18 - 09 23:00
23 - 09 00:00
01 - 10 00:34 23:54
03 - 10 00:00
08 - 10 01:00
18 - 10 01:00
23 - 10 02:00
01 - 11 02:37 01:57
02 - 11 02:00
07 - 11 03:00
18 - 11 03:00
23 - 11 04:00
01 - 12 04:35 03:55
03 - 12 04:00
08 - 12 05:00
18 - 12 05:00
23 - 12 06:00

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## 14. Time Zones

A time zone (such as the Central European time zone) is an area in which everone uses the same official time. The advantage of a time zone is that everyone agrees when any specific time has arrived, like a quarter past three in the afternoon. This makes it easier to make appointments. If you want to arrange something with someone in another time zone, then you have to keep calculating what time that would be in the other time zone. For example, when it is four o'clock in the Netherlands, it is only three o'clock in England, but already six o'clock in Moscow, because England and Moscow are in different time zones than the Netherlands. Most time zones on Earth differe a whole number of hours from each other.

The Sun rises in the east and sets in the west. If you travel around the Earth in an easterly direction, then you travel towards where the Sun rises, and you'll experience sunrise, noon, and sunset sooner than your friends and relatives back home. If you want to keep your travel clock on local solar time (so that the Sun is always highest in the sky when it is 12 o'clock noon in your location at that time), then you'll have to advance the time on your travel clock as you travel more towards the east. When you finally reach your home again, you'll have seen the Sun rise one time more often than the people who stayed home, and your travel clock will have accumulated 24 hours of extra advancement, while the time on the clock at home hasn't had any extra advancement. Your travel clock is then exactly one day ahead of the clock at home.

This phenomenon was very important to the story Around the World in Eighty Days by Jules Verne. The travellers in that book went in an easterly direction but did not realize that they had, by the time they got back home, experienced one sunrise more than the people back home did. They thought their journey had taken too long, and that they had lost the bet. At the last minute, they realized their mistake, and could claim the winnings after all.

It can't be be two different dates at the same time in the same place on the same calendar, and the people who did not travel around the world aren't going to adjust their date just because you did travel around the world and saw the Sun rise one time more often than they did, so the clock at home is right and you have to hand the extra 24 hours on your travel clock back somewhere along the way. This happens at the international date line.

If you travel around the world in a westerly direction, then you go in the same direction as the Sun appears to do, and then you'll experience sunrise, noon, and sunset later than the people back home, and then you'll have to move your travel clock back a bit whenever you go a bit further towards the west. When you get back home, you'll have set your travel clock back by exactly 24 hours, and you'll have seen one fewer sunrise than the people back home. Here, too, the people back home won't adjust their calendar to your count of sunrises, so you must pick up an extra day somewhere along the way. This happens at the international date line.

The international date line is a line between the North Pole and the South Pole. Just to the east of this line, it is one day earlier than just to the west of this line. If you cross the date line going towards the east, then you must subtract a day from the date, and if you cross the date line going towards the west, then you must add a day to the date. If you take the date line into account properly, then you can travel around the world as many times as you like and yet agree about what date it is when you get back home.

The international date line roughly follows the meridian of 180 degrees (east or west, it is the same there), but with deviations to the east and the west. There is no official treaty or law that specifies this line. Every country can decide for itself which date it will have, and so on which side of the international date line the country is. Since 1995, the international date line runs furthest to the east at the eastern border of the country of Kiribati, by an official decision of that country. Kiribati (pronounce the ti as an s) comprises a number of islands in the Pacific Ocean, of which the easternmost use the earliest time zone, so a particular date (like New Year's Day) begins first, and at the same time, on all eastern islands of Kiribati (like Caroline Island) -- at least, if you let the day begin at midnight. For a description of a trip to Kiribati, see //web.mit.edu/jync/www/writing/xmas.html.

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## 15. Polar Days and Polar Nights

It is daytime for half of the world, and nighttime for the other half. However, the rotation axis of the Earth is not perpendicular to the plane of the orbit of the Earth around the Sun, so the North Pole sometimes points a bit towards the Sun (most in June), and sometimes a bit away from the Sun (most in December).

As long as the North Pole is tilted towards the Sun, the Sun does not set there. This lasts for half a year at the North Pole. As long as the North Pole is tilted away from the Sun, the Sun does not rise there. This lasts for half a year, too, at the North Pole. So, at the North Pole, you have a period of half a year when the Sun does not set (a "day" lasting half a year), and a period of half a year when the Sun does not rise (a "night" lasting half a year). At the South Pole things are the same, except that it is night at the South Pole when it is day at the North Pole, and the other way around. In other spots near the poles you also have such long days and nights, but not quite as long as at the poles.

A period in which the Sun does not set during at least 24 hours is a polar day, and a period in which the Sun does not rise for at least 24 hours is a polar night. Polar days and nights can only occur within the polar circles, at northerly or southerly latitudes of 67 degrees or higher.

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## 16. The Time at the Poles

Most people's activities depend on how high the Sun is in the sky: sleep or gaze at the stars when it is dark, work or lie on the beach when it is light. A clock is then the most useful if it (roughly) shows the position of the Sun, because then you can make appointments based on the clock time without first having to calculate if that time is in the middle of the night or in the middle of the day.

The closer you get to the geographic poles, the less the height of the Sun in the sky varies during the day, so the less the clock time (and the more the season) says about whether it is light or dark. You can then choose to use the clock time of a location outside of the polar regions where you have many contacts; then your clock says little about how high the Sun is in your sky (but no clock could do that much better there), but a lot about whether your chances are good to find your contacts outside of the polar regions awake.

Exactly at the poles the Sun is useless to determine the time (within the 24-hour period), because there the Sun sets only once a year, instead of once every 24-hour period as it does outside of the polar regions. That's why the usual definitions of solar time (and the clock time that is tied to it) break down at the poles.

Every solar time and time zone is tied to a particular meridian. The poles lie on all meridians, so there is no natural preference there for any particular solar time or time zone. If you want to know what time it is at a pole, then you'll have to import that time from somewhere else, for example through a radio signal or from your watch that shows the time at home.

Whether it is the same time on both poles depends on who you ask that question. However, it is clear what the deal is with night and day: If the Sun is above the horizon as seen from one pole (i.e., it is daytime there), then the Sun is below the horizon at the same moment as seen from the other pole (i.e., it is nighttime there) ― but that day and that night each last for 6 months.

Reputedly, the scientific stations in Antarctica use the time zone of the place where their supplies come from.

## 17. The Speed of Time

Everybody notice the passage of time. Sometimes time seems to go by very quickly (for example when you are doing something fun), but sometimes time seems to pass very slowly (when you are doing something boring). While you are doing something fun (your time goes quickly), someone else can be doing something boring (her time goes slowly), but still your clock and her clock run at the same speed. The time that you can measure using a clock goes equally fast for both of you, even though time seems to go much more slowly for one than for the other.

The only way that we know of to measure time directly is using a clock. If you build many clocks that all run equally fast in the factory, and then move each of those clocks to a different place, and after a while return the clocks to the factory, then you can check if they still show the same time as each other. If the clocks don't all show the same time, and if you have checked that they are not broken, then you know that time does not go equally fast everywhere all the time.

This kind of experiment has already been done, using atomic clocks that are really accurate and keep in step with each other very well when they are in the same place. It turns out that how fast the clocks run depends on how strong the force of gravity was in the places where the clock has been, and also on how much acceleration or deceleration the clock has had (for example in a speeding or braking or curve-taking car or airplane). In our daily life these time differences are very very small. See the page about the Theory of Relativity for formulas.

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If you want to express the speed of time in kilometers per hour, then that speed is equal to the speed of light, approximately 300,000 km/s or 1 thousand million kilometers per hour. Information about what happens somewhere at a certain moment travels through space at about that speed. A certain moment from a television programme that is broadcast from a transmitter travels through space at that speed.

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## 18. The Direction of Time

The laws of nature are symmetric with respect to the direction of time: they don't care whether time runs forward or backward. However, in daily life we can tell the difference between time running forward or backward. You can tell if a movie is shown from end to beginning rather than from beginning to end. If there are two pictures of something happening, then usually you can tell which picture was taken first and which was taken last. You often see chaos emerge from order, but not very often see order emerge from chaos. Time runs in the direction of order to chaos.

As time passes there is ever more chaos in the Universe, and ever less order. If you waited long enough (much longer than the current age of the Universe), then there would be no order left, and then you can't tell anymore which picture was taken first and which one last. You might say that time doesn't run anymore then.

At the moment there is enough order in the Universe to make the direction of time very clear. The real question is: Where did all of that order come from? It must have been put into the Universe at the beginning.

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Last updated: 2021-07-19