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    Stick shadows and sundial curves
    From: Frank Reed
    Date: 2021 May 29, 14:46 -0700

    Here's an astronomical geometry puzzle, related to something I was talking about yesterday...

    Suppose the star Vega goes supernova tonight. Let's imagine it now has an apparent magnitude of -18 (it wouldn't really, but play along), considerably brighter than the Full Moon. It casts sharp shadows, even in daylight, and turns the night into continuous twilight.

    You hammer a stick into the ground. The tip of the stick is one meter above flat ground. During a 24-hour day, the shadow of the tip of the stick traces out a path on the ground. What is the shape of that path on the ground for any latitude? Assume the declination of Vega is +38.80°. Start at the north pole where the answer is easy (it's a circle... what radius?). Then work south in ten degree steps. 

    Frank Reed

       
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