Sidereal Time and the Earth’s Orbit To fully appreciate the workings of the clock one needs a basic understanding of the motion of the earth sun and moon with respect to each other and to the stars. Whilst astronomy is a very complex subject the part that we need to know is thankfully quite straightforward. Although the universe is expanding, the stars are so far away that for practical purposes within our lifetime we can regard the stars that we see as being stationary. They can be imagined to be painted on the inside of a dome with the earth situated beneath and because the earth spins on its axis it appears to us that the stars rotate around us. Although the heavens seem very complicated with their strangely named stars and supposed figures such as the Great Bear and Mr. Orion, we actually see the same stars apparently circling around above us every day. Pick any star in the sky and twenty four hours later it will be in exactly the same position. (Well, very nearly 24 hours later - watch this space). The time taken for that star to return - i.e. the time it takes for the earth to make one revolution is called one Sidereal Day. The star called Polaris which is directly above the North pole never appears to move at all - which is very useful for travellers wishing to know which way is North. As well as spinning on it axis the earth orbits the sun. It might be thought that when the earth makes its way to the far side of the sun, our view of the stars would change; but it doesn’t, as the stars are so far away that moving a mere 180 million miles across space makes no visible difference (unless you are an astronomer). The Sidereal Day - the time taken for the earth to turn on its axis - is one definition of a day. But the way that we become aware that the earth has spun around is because we see the sun rise and set. Could we define a day as being the time from one sunrise to the next? This is not practical as due to seasonal variation the sun rises at a different time every day. We could however utilise the time from noon (defined as the moment that the sun is in its highest point in the sky) to the next noon. This is the definition of a day which we use. It is called a Solar Day, or more correctly a Mean Solar Day, for reasons to be explained later.
							While spinning on its own axis the earth also orbits the sun, taking one year to make one lap. In fig 1 it is noon for an observer at the point indicated by the red dot - the sun is directly in front. In figure 2 the earth has made one complete revolution and has progressed fractionally along its orbital path.
In this diagram it might appear that the sun is directly in front once more; i.e. that the next noon has been reached. However, if we consider situation in Fig 3 it is apparent that although the earth has made ninety complete revolutions it still needs to make a further ^1/4 turn until noon. This illustrates the fact that one revolution of the earth does not bring it to the next noon - it needs to rotate a fraction more. This takes approximately four minutes which means that a solar day is actually about four minutes longer than a Sidereal day. In one year these minutes add up about one day which is why there are 365^1/4 Solar days in a year but 366^1/4 Sidereal days. To summarise: In one year the earth makes one complete orbit of the sun. It rotates 366^1/4 times on its own axis so we see the stars appear to rotate 366^1/4 times and we experience 365^1/4 noons - i.e. 365^1/4 solar days. Solar days are what we use to measure time in our everyday lives and each solar day is divided into 24 hours, each of which contains sixty minutes etc. Certain factors exist which result in either an apparent or an actual variation in the speed at which the earth orbits the sun and consequently the rate at which the sun appears to go round the earth.
				Most people know that the earth’s axis is tilted with the result that in December we in Britain experience the fewest hours of daylight each day whereas in July we enjoy the greatest number. Another effect of the earth’s tilt is that in December the noonday sun is lower in the sky than it is in July. For timekeeping purposes however we are not interested in the actual height of the sun above the horizon - purely its progress around the earth in relation to those lines of longitude which we draw on our maps stretching from the North to the South Poles.
In the diagram below two vehicles are travelling along a straight road. Both are driving at 26mph, but because the leading vehicle is travelling downhill its horizontal progress reduces to 24mph. At the same time this vehicle descends vertically at a speed of 10 mph.
			From a helicopter directly overhead it would appear that the leading vehicle has slowed down, because the fact that the vehicle is descending is not perceptible. The vehicle’s speed has not changed - only its apparent speed.
We usually think of the earth’s orbit around the sun as being horizontal, with the earth’s axis inclined…
…but if we change our point of view by rotating the picture until the earth’s axis appears vertical we can appreciate how in each year the earth not only circumnavigates the sun, but also moves up and down, or North and South.
	The earth moves southward from December to July and northward back to December. Although the earth’s orbital speed does not vary, some of its motion is “wasted” simply moving up and down. The amount which is wasted varies from month to month.
	In December and July almost all of the earth’s motion propels it around the sun whereas in March a significant proportion of the earth’s motion is southward, so it makes slower progress around the sun.Between July and December the earth moves northwards, again making its circular progress slower. What is the result of this variation in apparent speed? Remember that each time the earth rotates once on its axis it then has to make a further fraction of a turn to the next noon. If the earth is travelling more slowly then it will not move quite so far around its orbit during one turn, and so the extra fraction of turn will be less. In other words the day will be shorter. Conversely, when the earth moves (apparently) faster, the days will be longer.
These days of differing lengths are not just conceptual. They have a real effect which is reflected in the fact that on most days of the year the noonday sun does not appear to be quite where we expect it. This is demonstrated by the fact that a sundial does not usually show the time that our watches show. Due to the effect described above, on December 21^st each year a sundial will read the correct time (if the sun can be seen), but each day after that the sundial will run slow, resulting in a cumulative error of 10 minutes at the start of February. As we head towards March the days start to shorten and so the sundial catches up, until on March 21^st the sundial is again correct. This process is repeated throughout the year, with the Sundial only being “correct” on the two dates above plus June 21^st and September21^st. So much for time variation due to perceived effect. Now (and finally) we come to a phenomenon which actually does cause the earth’s speed to vary. So far we have regarded the earth’s orbit of the sun to be circular. In fact the orbit is very slightly elliptical. The sun is not exactly at the centre of the ellipse, but at one of two foci, which are geometrical features of all ellipses. Because of this, the earth’s distance from the sun varies, being nearest on December 31^st and furthest away on July1^st.
			The laws of physics dictate that when the earth comes nearer to the sun its speed must increase as otherwise it would be drawn towards and eventually crash into the sun. On the other hand, when further from the sun the earth must slow down to prevent it from flying off into space. The result is faster motion (longer days) from April to October and slower motion (shorter days) from October to April.
These varying day lengths also affect the sundial and this is shown by the dark line in this chart which also shows - in purple - the effects due to the earth’s tilt. These charts courtesy of National Maritime Museum’s website www.nmm.ac.uk
		When the effects of these two phenomena are added together the result is a chart known as the Equation of Time. This shows the cumulative effects on the accuracy of a sundial. The time shown by a sundial, determined by the actual position of the sun in the sky is known as True Solar Time. If the lengths of all the True Solar Days in a year are added together and then divided by 365^1/4, the result would be the length of an average day, or Mean Solar Day as it is called.
The Mean Solar Day is what we base our modern clocks on - i.e. Mean Time. Taking the 0 degree meridian line as a reference gives rise to the term Greenwich Mean Time. For a further explanation of the Equation of Time visit http://www.nmm.ac.uk/server/show/conWebDoc.351 Although the reasons for this discrepancy between Mean Solar Time and True Solar Time were not known in the fourteenth century, the effects were well documented over hundreds of years. This allowed Richard to design his clock to model both Mean time - for the operation of the bell - and True time when displaying the position of the sun.