Those apps aren't even based on RET. They are based on regular patterns that occur in the sky. Prediction in astronomy is based on patterns. They are equations that predict future occurrences of an event or trend based on historic tables.
There is a book called Astronomical Algorithms which describes how things are predicted in astronomy. I am writing about it here:
https://wiki.tfes.org/NOAA_Solar_Calculator
Your analysis of the NOAA calculator shows an egregious lack of understanding of basic astronomy.
First you say:
See Column O with the title "Sun Rad Vector (AUs)"
The worksheet default is 1.000001018.
AU is short for 'Astronomical Unit', the distance between the sun and the earth in the Heliocentric Round Earth Theory, and Rad is short for 'Radius'.
Put 0 into that column 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. Looking closer at the equations for this field, the AU field appears to be an output variable, not an input variable. The data of the sun's position in the sky and the simple trending seen in the formulas is not being created from this element. The data is deriving slight adjustments to the default 1.000001018.
1.000001018 is not a 'default' - it is the actual semi-major axis distance of the earth's orbit about the sun. Why is it not 1.000000000? Because the formula they are using to predict the 'Sun Rad Vector' requires the length of the semi-major axis and not the average distance (1 AU). Further, column 'O' (Sun Rad Vector) is a prediction
and is not used as and not required as an input to the other predicted values. So, no, changing the value of the semi-major axis of the earths orbit is not going affect any other other predicted amounts - and one (an educated one, that is) would not expect it to. The very fact that you do is quite telling and it tells me you don't have much knowledge about this. You really should take that page down.
You further go on to say:
Other elements such as Right Ascension, Declination, Azimuth, and Altitude are merely terms coined by astronomers to describe where things are in the sky.
Merely? No, your not quite telling the whole story, are you? Altitude and Azimuth are rather arbitrary and depend heavily on time and where you are on the surface of the earth, and would even be useful in an FE model (although the values would not be the same as predicted by the NOAA tool). However, right ascension and declination are part of a complex system of astronomical coordinates called the Equatorial Coordinate System that is fully dependent on a rotating spherical earth with an tilt of precisely 23.439281° and an angular velocity of exactly 7.2921159 x 10^-5 Radians/second. They would not work otherwise, and ... they do work.
Wikipedea has a simplistic explanation of right ascension and declination, but pleas don't stop there. Get yourself a good textbook on celestial mechanics to further help you understand.
https://en.wikipedia.org/wiki/Right_ascensionhttps://en.wikipedia.org/wiki/Declinationhttps://en.wikipedia.org/wiki/Equatorial_coordinate_systemThen, repeating yourself somewhat you say:
However, as we can even delete the AU column entirely from the previously mentioned NOAA Solar Calculator Excel worksheet, and see that the worksheet still gives the same results for the sun, even when the year and day is changed to a future date after the column is removed, shows us that the element is useless in prediction of the sun's location.
Rhetorically, I have to ask, why would expect any of the other values in that calculator to depend so heavily on the distance from the earth to the sun? Are you expecting that value to change drastically? So, I am guessing you'd like the authors to work out everything from first principles. Is that it? I'm further supposing you think that, even though using the unvarying measurement of the semi-major axis of the earths orbit provides more than sufficient accuracy for the purposes of this calculator, it would be reasonable to employ general relativity calculations in every cell of that spreadsheet, or in the on-line calculator where such values could be determined that way. I'm looking for a palm plant emoticon, but I can't find one. You do realize scientists don't work everything out from first principles every time, don't you? I mean, after we do the calculations a few thousand times and keep getting the same value, we just tend to use the value knowing we can always go back and do the math if we want to. You do get that, don't you?
Most of the rest of your presentation is just basically complaining that you think the authors should have used some more rigorous methods. Like I said, this is not how things are done. Not everything is worked out from first principles every time. Your not getting that is again very telling, and again it tells me you don't understand what you a writing about.
Then, the hilarious icing on the cake ... you write:
The sun positions given by the NOAA calculator cannot be used to triangulate the distance or position of the sun in the Heliocentric system.
And you present this ... video:
https://www.youtube.com/watch?v=9puRZH0i6Sc in support of your claim.
You know, I was drinking my morning coffee when I viewed that video. It is so hilarious I ended up spitting coffee all over my keyboard! Wow, you could not pick a worse method of triangulating the distance to the sun if you asked a chipmunk for advice. Where is that palm plant emoticon when you need it
That calculator is not designed to provide information that can be used to calculate the distance to the sun. Just as a can opener is not designed to provide information on the volume of the can.
Here is good method if you want to use geometry:
http://curious.astro.cornell.edu/about-us/41-our-solar-system/the-earth/orbit/87-how-do-you-measure-the-distance-between-earth-and-the-sun-intermediateHowever, if you want to use first principles of heliocentric celestial mechanics, you would not use geometry at all, you would use the period of the earth's orbit.
Where:
a= semi-major axis of earth's orbit
GM = standard gravitational parameter
T = earth's orbital period (in seconds)