# Measure the radius of the earth using the sun?

Can someone tell me why this would or would not work?

I have a sun spotter device that projects an image of the sun onto a piece of paper using a lens and some mirrors. When you use the device it’s quite clear that the sun moves across the image pretty quickly due to the earths rotation. This got me thinking: I can measure (on the paper) how many inches the sun shifts over some timescale, and divide that timescale by 24 hours. This should be the angle that the earth turned through. Then i can use s = r theta and solve for r, where s is the length that i measured and theta is the angle. Should this work?

I’m unsure because the earth rotates quite quickly, and the image of the sun only shifts slightly. Perhaps the lens makes things difficult

• It's not clear what your sun spotter is doing. A diagram would help. Is it like this? scientificsonline.com/product/sunspotter Apr 12 at 4:50
• "the earth rotates quite quickly" Indeed! At the equator, the rotation speed is ~465 m/s, and about half that at latitude 60°. Obviously, your sun spotter image, or shadows on a sundial, don't move at that speed. ;) Apr 12 at 4:54
• This seems like a very simple experiment to run. When you did it, what did you come up with? Did your answer make sense? Apr 12 at 16:12
• You've essentially made a sundial. You could, in theory, measure the angle the Sun moved and measure the distance the image moves, but doing so over a short distance is going to have a lot of error margin. It is essentially what Eratosthenes did, but over a much, much larger distance. Apr 12 at 16:29