How do you find a circumference if given altitude of sun and equinox?

Answer 1

The formula is 2#pi# X (Sun-Earth distance) X (cos (latitude) #-# sin (latitude) X tan (altitude))

At equinox instant, Sun S is overhead at equinox Q of the Earth's equator. At the same instant, it is noon at Q's longitude, at all latitudes. L is one with latitude #theta#, The Sun's altitude from L, at noon, is #alpha#. Using that sides are proportional to opposite angles in the #triangle# SEL, E being the Earth's center ans S Sun's, the formula for Earth's radius EL is EL = ES ( cos #theta# #-# sin#theta# tan #alpha#). I thank the questioner for making me think on this handy formula. .

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Answer 2

Ian Aitchison

To find the circumference of the Earth given the altitude of the sun and the equinox, you can use the method of Eratosthenes. Measure the angle of the sun's shadow at two locations on Earth separated by a known distance. Use trigonometry to calculate the Earth's circumference using the formula: Circumference = Distance / (Angle Difference / 360 degrees).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.