Why is my approach to the equation of time off by a constant?
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The Equation of Time
The Equation of Time takes the above 2 factors into consideration and can tell us how far ahead or behind the sun will be relative to the stars.
An explicit function that is a good approximation to the Equation of Time is as follows, where d is the day of the year and the resulting value is in terms of minutes of variation):
Time variation = -7.655 sin d + 9.873 sin(2d + 3.588)
This is made up of 2 components:
Variation due to Earth's tilt = -7.655 sin d
This contributes 7.655 minutes to the Equation of Time, and the period is 1 year (365.25 days).
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The "equation" of time historically was an indication of the difference between what a sundial said the time was, and what the actual time should be, considering Earth's axis title.
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