Suppose I want to calculate the diameter of the crater. I apply the small angle formula $$diameter=\frac{\theta_{diameter}}{206265''}\times D$$ where $\theta_{diameter}$ is the angular size of the crater, in arcseconds, and $D$ is the average surface-to-surface distance from the Earth to the Moon, which is around $375,900$ km. We know that the moon is about $\frac12$ degree, which is $1860$ arcseconds. But how do we estimate the angular size of the crater without using lens, with only eyes? I was thinking using ruler and applying scale but that way, I think, is inaccurate because the Moon has a round surface.
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Most lunar craters are too small to resolve with the naked eye; I would measure a published photograph. A crater near the limb appears as an ellipse whose minor axis is foreshortened but whose major axis measures about the same as if the crater were centrally located. Surface curvature has little effect on this measurement because most craters are small compared to the lunar radius.
