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The Curvature of the Twilight Wedge

Updated: Feb 14, 2021

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In January 2010 I shot a 260-degree panorama at dawn from the summit of 14,265-foot Quandary Peak. Quandary Peak Panorama features a spectacular twilight wedge, the blue shadow of the Earth projected onto the western sky directly opposite the sun just before sunrise. Above the band of blue lies a swath of pink. The pink band occurs because light from the rising sun, which is still just barely below the horizon, takes a tremendously long path through the atmosphere, during which Rayleigh scattering causes the blue light to scatter out of the beam. The pink light that remains is finally scattered in its turn and returns to your eye. The shadow is blue because no direct light is reaching that part of the atmosphere. The only light you see coming from the direction of the shadow is the blue light scattered from the beam of direct sunlight reaching the atmosphere above.

As I examined the completed panorama, I noticed that the top of Earth's shadow was curved when compared to the straight horizon. Why? Could it be that I was actually seeing proof that the Earth was round? The shadow of the Earth, if projected onto a hypothetical flat “screen” positioned perpendicular to my line of sight, would appear circular. Could it be I was seeing just the edge of the circular shadow of the Earth rising above the straight horizon? I decided to find out.

In my initial reasoning, it seemed that the only way that the upper edge of Earth's shadow could appear curved, while the physical horizon appeared straight, would be if the light from the shadow was coming to my eyes from a much greater distance than the horizon. Any spherical object will appear to have a more pronounced curvature if viewed from a greater distance. The horizon is still curved when seen from a Kansas cornfield, but the deviation from a straight line is absolutely imperceptible. Seen from Earth orbit, however, the curve of the horizon is unmistakable. After much head-scratching and trigonometry, I concluded that the "screen" on which the shadow was falling was indeed much further away than the physical horizon. Granted, there’s no screen out there on which the shadow falls. There’s only air. Nonetheless, there has to be some average distance to the molecules which had scattered the light back to my eyes. If the “screen” was much farther than the physical horizon, that must mean that I had seen the curvature of the Earth in the form of Earth’s shadow. I was ecstatic.

I was also wrong. Or, to be more precise, I was right, but I am now convinced that my initial explanation was mostly wrong. Here's my best explanation now: the curvature of the top of the twilight wedge is indeed evidence that Earth is a sphere, but not primarily for the reasons I supposed. Imagine that you are on top of a mast on a sailing ship on a calm day in the middle of the ocean. The distance to your horizon is the same in every direction. Tha