A Triple Reflection
for Stardust, April 2020
"What is that glow?" asked Ross.
Figure 1 - Annotated crop from Ross Sinclair's timelapse https://youtu.be/enciugLM0cU
With so much happening in the moments approaching sunset, I needed Ross to point out to me the whereabouts of this unexpected patch of light. I quickly discounted an internal lens reflection, the source of most UFO accounts: those always form along the diagonal from a bright source through the center of the image.
My working hypothesis was a triple reflection of the setting Sun since that glow was too weak to be directly lit. Many of Edmonton's buildings are oriented within a few degrees of north-south, and sport east and west facing glass facades. Being less than 2 weeks from equinox, the Sun sets close to due west, putting us in an analogous situation to a hall of mirrors, where you see reflections heading out to infinity. Flat mirror math is simple: angle of incidence equals angle of reflection. The setup here is light comes from behind, reflects off a downtown building, comes back westward, bounces off an east face to land as the glow. It's just a matter of tracking it backward.
First step was identifying the building, which is straightforward thanks to GoogleMap's 3D functionality.
Figure 2 - GoogleMaps' view from above Ross' apartment. It wouldn't quite me get to a low enough angle to replicate the sight line from Ross' balcony. G is the position of the glow.
Next, one identifies which building face is well-placed to be causing the final glow.
Figure 3 - Westward view from above the target building, at lower right. Courtesy GoogleMaps.
Well, one tower stands out like a sore thumb <grin>. Other building faces are possible, but it is wise to start with the obvious choice. The Pearl has multiple facets, but the majority face due east and west, as near to 90/270 as I can measure.
Figure 4 - The Pearl tower (at right) from a February 2016 sunrise, showing how bright a direct (first order) reflection is at a distance of roughly 4 km.
Going with that presumption, what is the angle of incidence on the Pearl? The Photographer's Ephemeris (TPE) has a handy tool to measure azimuths, putting it at 266 from the glow, or 4 degrees from due west. This means that from the Pearl's perspective, the sunlight must arrive from 4 degrees south of due east, an azimuth of 94. Placing TPE's home pin on the Pearl and placing the secondary pin at Az 94 just past downtown, all I have to do is look along the gray line until I come across a building that is tall enough to catch the Sun's rays from the Pearl's perspective.
Figure 5 - the sight line crossing Chateau Lacombe. Courtesy The Photographer's Ephemeris/Google.
Chateau Lacombe gets a hit! Uh-oh, the setting Sun was at an azimuth of 262. That's 8 degrees off due west which would then reflect sunlight 8 degrees to the north, missing the Pearl by 4 degrees! However when mirrors are tilted away from "up-down", the path of a ray is changed by double the angle of the tilt.
Figure 6 - a ray hitting a 45 degree angle mirror comes out at 90. From http://smurfslight.blogspot.com
Chateau Lacombe has many facets at a series of angles. A couple of years ago I noted that there are 18 "ribs" around the 360 degree circle, each one sporting windows square to that rib. I carefully measured the angles ending with a value of -2 degrees for the E and W faces. Doubling that means a light ray will change by -4 degrees from its angle of incidence. The 8 degrees becomes 4, which means that the Chateau Lacombe windows reflect the setting Sun exactly onto the Pearl, which redirects that perfectly onto the side of that building, which then reflects it back to Ross.
The sequence took place on the superbly clear Monday evening March 9, 2020. A lot of people across the province and around the world took pictures of the near full Moon, in our case 7 hours after. Sadly many of those posted are gross misrepresentations, being wildly photoshopped into monstrous overly-coloured composites.