The Equation of Time

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.

Equation of time = Local Solar Time - Standard Time     or      Standard Time = Local Solar Time - Equation of Time

There is a difference because the orbit of the Sun is not 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.

Longitude correction
The time at which the Sun is at its highest point, i.e. the local solar time is noon, depends also on your longitude. The further East you are the sooner the Sun culminates. For every degree East you are of the Greenwich meridian you need to subtract 4 minutes from your solar time to calculate standard time. For every degree west you are you need to add 4 minutes.

Examples

1. Max lives in Cornwall, 5 degrees West of Greenwich. On a particular day the equation of time is +10 minutes. At what time will his shadow stick tell him it is noon?

Standard time = Local solar time - equation of time +/- longitude correction

Standard time = 12:00 -10 + (5 x 4) = 12:10 p.m.

2. A sailor in the North Sea finds that the Sun is at its highest at 12:04 on a day when the equation of time = -12 minutes. What is his longitude?

Standard time = Local solar time - equation of time +/- longitude correction

12:04 = 12:00 + 12 + longitude correction         notice     - (-12) = +12

so the longitude correction is -8 minutes meaning he is 2 degrees East.

Imagine you work for a company that makes and installs sundials all over the UK. Describe how you would go about setting up a sundial in someone's garden. What information would you need. What advice would you give to the owner?