circumpolar is when the earth is at its greatest distance from the sun.
when the earth is at its greatest distance from the sun?
circumpolar
na
na
in the second book, hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the sun of 490 earth radii. this would correspond to a parallax of 7′, which is apparently the greatest parallax that hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2′; tycho brahe made naked eye observation with an accuracy down to 1′). in this case, the shadow of the earth is a cone rather than a cylinder as under the first assumption. hipparchus observed (at lunar eclipses) that at the mean distance of the moon, the diameter of the shadow cone is lunar diameters. that apparent diameter is, as he had observed, degrees. with these values and simple geometry, hipparchus could determine the mean distance; because it was computed for a minimum distance of the sun, it is the maximum mean distance possible for the moon. with his value for the eccentricity of the orbit, he could compute the least and greatest distances of the moon too. according to pappus, he found a least distance of 62, a mean of , and consequently a greatest distance of earth radii. with this method, as the parallax of the sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 earth radii – exactly the mean distance that ptolemy later derived.
hipparchus