## Sundials and the Equation of Time

### Sundials

The development of the sundial appears to have gone thru several stages

- A
**Shadow Clock**can be formed from a stick stuck vertically in the ground, but this will only be accurate for one particular season at a time. The rate of shadow movement will vary with the declination of the Sun. - By orientating the pole or
*style*, to use its proper sundial nomenclature, to point at the pole star, this previous difficulty disappears. At a simple level, the dial can be equally graduated but needs to be placed perpendicular to the style. This unfortunately means that for half of the year, when the Sun is low down, its light will not shine across the dial. - To improve the sundial further, the dial needs to be horizontal. The graduations can no
longer be equally divided but the calibrations required are fairly easy to work out nowadays.
There are still problems
- It will show local time, not the recognized national time. For Britain, where Greenwich is in the East, western regions can be about 20 minutes behind Greenwich time
- Adjustments still need to be made for the Equation of Time (see below). In a nutshell, this adjustment is required because the Earth does not move along its orbit at a constant speed.

### Equation of Time

The Earth's orbit is an ellipse and the Earth moves at different
speeds along this ellipse, as explained under
Kepler's Laws.
There is an astronomical concept of a **mean Sun**, one that **does** move uniformly as though
the Earth's
orbit was circular. The real Sum will sometimes be in front of this mean Sun and
sometimes behind.

The time we use in everyday life is based on the behavior of this mean Sun, and variations between this 'mean Sun' time and the time measured by the real Sun can be as much as 16 minutes.

Stated as a formula

**
Equation of time = apparent solar time - mean solar time
**

Stated in another way

**
Equation of time = Sundial Time - Clock Time
**

### Analemma

If throughout the period of one year you were to plot the position of the Sun in the Sky at the same sidereal time, then you will produce a figure-of-eight figure - the Analemma.

### General Information (not part of the GCSE syllabus)

To find South, point the small hand of your watch towards the Sun, determine the bisector of the angle between this small hand and the direction of the number 12 on your watch, and this bisector will indicate the South. This knowledge is not specifically a part of the syllabus but what you will learn on the course will enable you to understand how it works. I am sure those with digital watches will still be able tio improvise the method without me having to state the details explicitly.

Alternatively, place a stick or pole in the ground vertically and mark off the top of its shadow with a stone. Wait for about quarter of an hour or so, at least, and again mark the top of the current shadow with a stone. Stand with your left foot on the first stone and your right on the second. You are now facing North.