Walls, windows, amplitudes and newspapers

The wall opposite my favourite corner chair, the chair in which I sit to read the morning newspaper, has one of those long windows in the shape of a letterbox. Shallow, but wide, it traverses the wall and provides a wide angle view of the eastern horizon. It is a rough measuring guide to the passing of the summer.

In midsummer the Sun is at its furthest point south (in the southern hemisphere) rising in the south east, passing to the north at local apparent noon and setting in the southwest. Just how far south of east it rises and how far south of west it sets is called the amplitude*. The amplitude depends on the declination of the Sun and the latitude of the observer. For example, in my latitude of 38 degrees South, today the Sun’s amplitude is 21 degrees. It rises at a bearing of 111 and sets at 249.

It reaches its greatest southerly amplitude on the summer solstice (on or about 21st December each year) when it rises at 120 and sets at 240.

During the approximate 6 weeks either side of the summer solstice, the rising Sun is shining directly through my transverse window into my corner chair. As the summer recedes, it rises later and further north until it is barely brushing by as I finish my coffee. For the rest of the year, it does not dazzle me. I can see now it has nearly reached that point of missing the window, signalling the path towards the darkest quarter of the year, 6 weeks either side of June 21. At the winter solstice the Sun rises at a bearing of 060 at my home.

Meanwhile, Londoners in mid June would be enjoying the Sun rising in the northeast at 050, passing to the south and setting at 310.

If you want to calculate amplitude, you need to know your latitude and the Sun’s declination (available from any number of sources of astronomical data).

sin (ampl) = sin (decl)/cos(lat)

* Amplitude is either north of east or south of east (090) for the rising Sun, corresponding to northerly or southerly declination respectively. Likewise, it is either north or south of west (270) for the setting Sun.