NOAA Solar Calculator
To find the positions of the sun the common method is to use the NOAA Solar Calculator. It is often alleged that the NOAA Solar Calculator is based on Round Earth Theory and Heliocentricism, and that because it can predict the position of the sun, and that it means that the Round Earth Theory must true.
Firstly, these claims are universally made without demonstration that the calculator is correct in all instances. A source for records of observations, comprehensive or not, is never given.
Secondly, the assumption that the calculator is based on Heliocentricism is seen to fall flat on cursory reading of the details. The calculations are simple equations that are based on the pattern of previous observations and occurrences, as all astronomical calculators are. By studying the repeating pattern of behavior of astronomical bodied over a period of time it is possible to create an equation that will predict when the next occurrence will occur or how it will behave in the future.
Online Calculator Link
Online Calculator Link: https://www.esrl.noaa.gov/gmd/grad/solcalc/
Excel Worksheet Version
Under the "Calculation Details" link The NOAA has provided an Excel spreadsheet version of their online calculator here:
https://www.esrl.noaa.gov/gmd/grad/solcalc/NOAA_Solar_Calculations_day.xls
Feel free to look at the formula sources in the spreadsheet above and try and find where the Round Earth Theory is expressed or where we see keplerian orbital mechanics. The calculations are simple equations that are based on the pattern of previous observations and occurrences, as all of the astronomical calculators are.
Heliocentric Elements
There does appear to be a Heliocentric element in the calculator.
See Column O with the title "Sun Rad Vector (AUs)"
The worksheet default is 1.000001018.
Put 0 in those boxes and see what happens. It doesn't affect the predictions at all. Also try 9.5 AUs. No effect. The same results are seen result whether the calculator is operating under the assumption of 0 Astronomical Units or 9.5 Astronomical Units.
Algorithms Based on a Book
The online NOAA Solar Calculator and the associated Excel worksheet version are based on equations from a book:
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A PDF of the above book is found here.
The following is found in the glossary:
This is interesting, as we can even delete the AU column entirely from the worksheet, and the worksheet still gave the same results, even when the year and day was changed after it is removed. In some areas of the book the author likes to pretend that he is using Heliocentric theory for his algorithms.
Reading closely, the book author admits that the algorithms are really just using statistical (pattern-based) methods:
