Building Angle Deriving

Ah, the unbounded possibilities of astronomical phenomena! Everywhere one looks, the apparently mundane isn't, providing us with a unlimited source of beauty as well as enjoyment that comes through personal discovery in simple situations.

My interest in reflections began by pure chance. My sole intent was to capture the full Moon setting behind the Alberta legislature when I was caught by surprise by the rising Sun bouncing back at me:

Using a road map of Edmonton (pre-Google!) I measured the angles of the buildings with a protractor. Using the simple Euclidean geometry rule that angle of incidence equals angle of reflection, I came up with the formula at the end of the article. All is fine until one encounters reality. At the appointed place and time for a full Moon reflecting off the TD building, I was only getting a few glints. A few minutes later it was central:

Back at home, I got the time of the image from the camera, plugged that into the planetarium program to get the azimuth of the Moon and stuffed the numbers through the formula to find that the building was actually 6.3 degrees from North instead of the 5 that I had got off the map.

It may come as a surprise, but it's not easy to get the Moon to cooperate. When its declination is near the equator, from night to night its rise point can change by 10 degrees. Throwing in the complications of weather and life means that a particular reflection event becomes uncommon. So you don't want to waste it on incorrect building angles. I realised that for several of these angles I had only the paper map and protractor values, not a real reflection to confirm them. Here's where the Sun comes in: its azimuth rise and set change only by a half degree a day or so, depending on the time of year (steepness of the ecliptic to the local horizon). On February 24th, I saw that the rising Sun would reflect off Scotia Bank as seen from the Capilano bridge. But it almost didn't. Thankfully I could move far enough north to get some of it. Given the northerly position and time, I revised the building orientation by a degree.

Next, I adjusted the angle for my observing site in Belvedere, at the river bank down from where Victoria Trail crosses the Yellowhead, and noticed that the Sun should reflect from Scotia Bank on the morning of March 11th. And did it ever!