How big is the moon?

July 01, 2016  •  Leave a Comment

Photoshop lovers play games with the moon.  It's easy to do, but if you post it as real, it's a lie.

With a little analysis, it's actually pretty easy to spot the lie. Here are two images I made, one real and one with a photoshopped huge moon behind the Hotel Del Coronado in San Diego - not particularly great images, but good enough to show why the second one is fake.

The critical point is that we know how big the moon is - it covers about half a degree of the night sky.  So in this picture, we can estimate how many degrees the rest of the items in the image cover.  The flagpole, for example, is 542 pixels high; the moon is 1084 pixels high, or twice the flagpole.  (I built it that way.)  If the moon covers half a degree, the flagpole covers an angle of one-fourth of a degree.

Trigonometry tells us that the height of the flagpole divided by the distance from the camera to the flagpole is the tangent of that angle, which you can look up - it's 0.00436.  If I estimate the height of the flagpole to be 30 feet, then the distance from the camera is 30/0.00436 = 6881 feet, so if this image is real, I made this photo from over a mile and a quarter away - well out in the ocean!

It's also possible to deduce the focal length of the lens that I would have used, if the size of the image sensor is known.  The ratio of the size of the image sensor to the focal length of the lens is the tangent of the angle covered by the picture.  I was using a full-frame camera for this picture, so the image sensor size is 24mm wide by 36mm tall. The height of the picture is 4256 pixels, or about 3.5 times the width of the moon, so the angle covered by the entire image vertically in the altered photo would be about 1.75 degrees.  Do the math, and you find that the focal length of the lens I would have had to use if the phony picture were real is 1178 mm - way bigger than anything I own, or could afford!  Of course the picture might have been cropped, which would reduce the effective size of the sensor.  That would reduce the calculated focal length accordingly.  Or it might have been shot using a camera with a smaller sensor, although the focal length of lenses with such cameras is usually compensated for that. Because of this possibility, calculating the focal length of the lens is a less certain sign of photoshoppery than calculating the distance from which the picture was taken; but it can give you a very good reason to be suspicious.

So here's a general rule for judging whether a photo of the moon is real.  If the moon is the same apparent size as an object larger than about 50 feet in width or height, the picture must have been made from more than a mile away. Unless that seems reasonable, the picture is probably not real. If the moon occupies more than 7% of the picture's long dimension, the focal length was more than 300mm unless the picture was cropped.  Unless that seems reasonable, be suspicious.

 



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