Abstract
Contemporary physicists and science experts include Eratosthenes’ measurement of the Earthʼs circumference as one of the most beautiful experiments ever performed in physics. Upon revisiting this famous event in the history of science, we find that some interesting generalizations are possible. On the basis of a rather simple model of the Earthʼs insolation, we have managed, using some advanced mathematics, to derive a new formula for determining the length of the year, generalized in such a way that it can be used for all planets with sufficiently small eccentricity of the orbit and for all locations with daily sunrises and sunsets. The practical technique that our formula offers is simple to perform, entirely Eratosthenian in spirit, and only requires the angle of the noonday sun to be found on successive days around an equinox. Our results show that this kind of approach to the problem of the Earthʼs insolation deserves to be included in university courses, especially those which cover astronomy and environmental physics.
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