The Equation of Time

demonstrate an understanding of the terms ‘apparent Sun’ and ‘mean Sun’
demonstrate an understanding of the term ‘equation of time’ (apparent solar time — mean solar time) and perform simple calculations

Gordon lives in Greenwich. He makes a shadow stick to record at what time the Sun is at its highest point. He finds that on some days it is at its highest before 12:00 and on some days after 12:00. He records the difference every day and plots a graph of how far ahead the sundial is.

The difference between the sundial time and standard time (clock time) is called the Equation of Time.

For someone living at Greenwich or after accounting for longitude

     Equation of time = Apparent Solar Time - Mean Solar Time

The reason for the difference is due to the orbit of the Sun is not being circular and because the Earth's axis of rotation is tilted.

All days throughout the year are not exactly 24 hours long. They can be up to 30s longer or shorter. Over a month or so the difference can add up to as much as 16 minutes. Over the course of a year however (actually 4 years) both times end up where they started from.

The equation of time can be positive or negative as you can see on the graph above.

• When solar time is ahead of standard time it is positive.

• When solar time is behind standard time it is negative.

Greenwich Mean Time is a system which assumes that every day is exactly 24 hours long. This is obviously for convenience. Before railways (and the need for accurate timetables) it didn't matter very much if the time in Manchester or Newcastle was slightly different to what it is in London or if noon varied slightly from day to day. Now it does very much.

The length of a day (i.e. from noon till noon) can vary quite a bit. Greenwich Mean Time is a system based on an imaginary sun that takes exactly 24 hours from noon till noon every day. It is called a mean sun.

Are you confused?

This is a tricky topic which takes a while to get your head around. It is worth the effort as there is nearly always a big question on this in the exam.

Study the data in this table. The last few are for you to complete.

I find it useful to remember the equation of time on a particular day is how far ahead your sundial is compared to your clock.