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Sometimes it is easy to figure out the position of the sun from the shadows in a photograph, and sometimes it is more difficult. Home page of the Great Circle Studio’s solar ephemeris set up to calculate the ToD and the DoY for the Sheboygan Dead Horse photo. Usually, you must supply an ephemeris with the ToD and the DoY for which you would like to calculate the position of the sun. In the image, the shadows in the picture fall directly to the east across Griffith St, implying that the sun is directly in the west at an azimuth of 270 degrees. Finding the elevation of the sun is also easy using the triangle outlined in red in this image. The adjacent is the side next to the angle being used in the questionWhenever you have a trigonometry question you need to find the two sides involved and pick the formula that is correct.

Note: These only work for right angled triangles!A useful way of remembering these equations is SOH CAH TOA.
Example: A person 100 meters from the base of a tree observes that the angle between the ground and the top of the tree is 18 degrees. It depends on whether the camera was directly facing the object that was casting the shadow, and whether the object was on the same level as the camera. Having the sun in the west and the camera facing north and aimed directly at the man on the horse means we don’t have to correct the length of the shadows for perspective. Estimate the height h of the tree to the nearest tenth of a meter.So here we have the adjacent side and we need to find the opposite. If the solar positions that are output do not match the ones you have calculated from your photograph, you can adjust the input to the calculator and run it again.

You can continue adjusting your input ToD and DoY until you obtain a solar position that comes close to the one you want. Assuming that either you have a shadow that does not need correction for perspective, or that has already been corrected, you will need an ephemeris to find the ToD and DoY based on that shadow. We repeated inputting new dates and times based on our previous results until we pinned down August 10 as a date when the sun came close to our position of THETAa = 270 deg, and THETAe = 22.85 deg. Since the sun traces the same path every year to within a small error, we don’t have to worry about the year.

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