Equation of Time

Sundials have been used for thousands of years to measure

time

and are still widely seen in homes, parks, and other public spaces. Sundials measure solar

time

. Time is calculated based on the position of the sun in the sky, but interestingly they are not particularly good timekeepers on average. For an entire year, this time displayed by a sundial will be correct, assuming of course that it has been set correctly for the time zone and longitude, but on any given date it can be up to 50 minutes ahead or 50 minutes behind on the time you use for day to day activities the graph shows for greenwich the difference between solar time and gmt this variation extends between the sundial with 14 minutes and 15 seconds behind on february 12, so when it shows the time of 12 noon will be 12 14 and 15 seconds gmt the sundial accelerated 16 minutes 25 seconds on November 3, so when it shows the time of 12 noon it will be 11 43 and 35 seconds gmt on this video I am going to talk about the

equation

of time, that is the difference. between solar time measured by a sundial and mean solar time anywhere on the line of zero longitude, mean solar time is similar to greenwich mean time gmt elsewhere mean solar time will depend on its longitude, as I will explain the reason below.

For the

equation

of time, the length of a solar day is not always 24 hours, but varies throughout the year, said to be the shortest in mid-September and the longest just before Christmas Day. If we look at this graph, the y-axis shows the difference in seconds between the length of the solar day and 24 hours, so for example, 10 means 24 hours 10 seconds 20 24 hours 20 seconds minus 10 23 hours 59 minutes 50 seconds, the variation in the length of the solar day is not due to the change in the speed of the Earth's rotation, although very recently, the effects are small and unpredictable, while the variation in the length of the solar day is large and predictable , there are actually two different causes of this variation: firstly, the Earth moves in an elliptical orbit around the sun and secondly the earth is tilted on its axis now I will talk about each of these effects in turn the earth It takes 23 hours and 56 minutes to make a complete rotation on its axis, however, one soul per day is on average 24 hours long.

This is because during the time it has made a rotation the earth has moved a little around the sun. in its orbit for example if we take the point in time where the sun is at its highest point in the sky marked with a purple dot then, one rotation later, because the Earth has moved in its orbit, the Sun is not overhead at this point, it takes the Earth an additional four minutes to rotate a little more to reach the point where the Sun is once again at its highest point. the sky and that is why a day lasts on average 24 hours because the earth's orbit is elliptical its distance from the sun varies throughout the year it is closest in early January furthest in early July when the earth is closest to the sun It moves more quickly in its orbit and when it is further away it moves more slowly.

In January when the Earth is moving at its maximum speed in its orbit, it probably takes more than one rotation plus four minutes for the sun to reach its highest point in the sky. on the next day, so this means that the solar day is a little longer than 24 hours in early July, when the Earth is moving at its slowest speed in its orbit, it takes a little less time than a rotation plus four minutes for the sun to bite the highest point in the sky the next day, so this means the solar day is slightly shorter than 24 hours.

The graph here shows the variation in the length of the solar day if the eccentricity of the Earth's orbit were the only factor. The second factor that affects the duration. of the solar day is the tilt of the Earth's axis, many, if not most, people know that it is this tilt that causes the seasons, but at first glance it is not immediately clear why the tilt should also cause the longitude of solar data varies and many people find it difficult to visualize this, so I will talk about this below and hope my explanation is easy to follow.

Astronomers use a system called celestial coordinates where all celestial objects, including the sun, planets, and stars, are given a position on an imaginary sphere. known as the celestial sphere surrounding the earth, latitude is known as declination and longitude is right ascension, the sun moves on the path shown on the celestial sphere, the zero right ascension line shown as the green line is the position of the sun at the March equinox. What you can see in the diagram is at the March and September equinoxes, the sun moves quite sharply in declination and because of this its daily change in right ascension is slightly less than at other times of the year at the June and December solstices the sun's declination does not change much it remains at a declination of 23.4 north or south for the few days around the solstice its change in right ascension is slightly greater than At other times of the year you look at the image in two dimensions from a point directly above the north pole, then the sun's apparent orbit is not circular at all, but is flattened due to its inclination.

If you observe the sun as it rotates around this apparent orbit, the sun's right ascension changes faster at the solstices and more slowly at the equinoxes. Astronomers actually measure right ascension in hours and there are 24 hours in a circle, so one hour of right ascension is equal to 15 degrees, but I've decided to stick with degrees for this video around the time of the solstices in June and December, when the sun's right ascension changes most rapidly in its apparent orbit, it takes a little more than one rotation plus four minutes for the sun to be at the highest point in the sky the next day, so this means that the sun's day lasts a little more than 24 hours around the time of the equinoxes in March and September, when the Sun's right ascension slowly changes its apparent orbit, it probably takes less than one rotation plus four minutes for the Sun to be at its highest point. in the sky the next day, so this means that the solar day is slightly shorter than 24 hours.

This graph shows the variation in the length of the solar day if the Earth's axial tilts were the only factor, as you can see you will be longest on the June and December solstices around 24 hours 20 seconds and the shortest 23 hours 59 minutes 40 seconds at the two equinoxes the combination of the two effects is shown as the black line in the graph below, as I mentioned near the beginning of the talk, the longest solar day is around December 23 and the longest short around September 17, although these dates vary a little from year to year. The other interesting thing is that although a day is often thought to be 24 hours long, there are actually only four days in a day. year in which the calendar day measured by the movement of the sun in the sky is 24 hours and even then it is not exactly equal to 24 hours to the nearest millisecond, so, first, let's put everything together to recapitulate the equation of time that shown in the graph and which we have known before is the difference between solar time or natural time shown by a sundial and mean solar time, assuming that all days are 24 hours long and is caused by the variation in the length of the solar day throughout the year, so if we start in the region a solar day has more than 24 hours, which means that the half of the day where the sun is at its highest point in the sky will get progressively later each day, so a sundial will get progressively later behind mean solar time at this time. continues until February 12, when Sundale will be 14 minutes and 15 seconds slower now in region b our solar day is now shorter than 24 hours, meaning the half of the day where the sun is highest in the sky will set progressively earlier each time. day this continues until May 15 when the sundial will now be four minutes faster we move to region c a solar day is again longer than 24 hours meaning the middle of the day when the sun is highest in The sky once again arrives later each day, this continues until July 26, when a sundial is six and a half minutes from its lowest point and finally, in region D, a solar day again has less than 24 hours, so the middle of the day changes earlier and this continues until November. on the 3rd when the sundial will be ahead 16 and a half minutes foreign