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WORHP Kata of March 2023: Equation of time ⌚ 2023-03-01

A kata (in the context of programming) is a small training unit to practise coding. In this series of WORHP Katas we present standard problems of optimization which you can use to get familiar with optimization (and our optimization software WORHP).

Equation of time

Next to a sundial in the Rhododendron-Park Bremen, you can find this stony graph of the equation of time. The equation of time combines the effect of the orbit eccentricity (a sine wave with the period of one year) and the effect of the obliquity of the ecliptic (a sine wave with the period of a half year) and can be used to convert the time shown at the sundial to the mean solar time.

Kata: We want to reconstruct the function from the graph. For this, select a useful ansatz function with some unknown parameters, and determine the parameters using data points from the graph.

Hint: the ordinate values along the vertical lines can be read as:  3  13  13  4  -3  -2.5  3  6.5  0  -10  -16  -10  (3)

A solution will be provided with the next WORHP Kata.