## Accuracy (Google Earth and sundials)

A colleague draws a short line at the edge of the whiteboard recording the image of the window frame when the Sun shines in the classroom window and then carries on. As he is an enthusiastic and engaging teacher, the students’ attention is drawn away from the mark. The students are always amazed at how far the image of the window has moved 10 or 20 minutes later. He reminds them that we, the desks and chairs, and the building are on the surface of a planet that rotates once each 24 hours. In the short silence that follows, you can hear the reference frames shift.

The sundial was showing a few minutes before XII (the shadow of the gnomon was thick enough to cover 8 minutes worth of the scale) at 1304 BST. Worcester is about 2 and a quarter degrees West, so it should be about 8 minutes early compared to UT, and we are on British Summer Time at present, so that explains the hour. Not bad for a small metal plate and a simple gnomon. If my watch stays set correctly, I can estimate my latitude to a fraction of a degree or so by looking at a sundial (360 degrees in 24 hours, so 15 degrees in one hour, if a sundial is 4 minutes early it is one degree West).

Google Earth gives the latitude and longitude of the red spot (on the tree, but as photographed by the satellites in April 2007) as 52° 11’ 18.34” North and 2° 13’ 16.37” West. As the cloister garden is a couple of seconds or so of latitude across, and as the Google Earth images appear to be projected onto a slanting plane, I’m somewhat dubious about the last few decimal places!

A simple sum: circumference of the Earth is about 24000 miles, so each degree of latitude is about 67 miles (66 and two thirds by cancelling), so one minute of arc is about a mile and tenth. So a second of arc is about (1760 + 176) ÷ 60 or 32 yards. Google Earth is claiming 2 decimal places of arc second, a change of one digit in the last decimal place represents a distance of about 12 inches!

It is difficult for us now to understand the symbols that surrounded people in the decades after 1000 AD. The ‘great chain of being’ that provided meaning for them is explained in the history books but we can’t think like they did. Are we changing again? Will the Web and the services built on top of the ubiquitous network change the meaning of our streets and buildings?