The Original Error -- Cumulative Systematic-Error in Constants of The Rydberg Equation

The error is about 0.000054 out of 1.  However, this is with the corrected from -4% error from the 0.87fm to the 0.84fm proton radius.

A check: plug in values of constants from the GPS system and compare to error with CODATA values

Therefore, for the original starting error, we will examine it with both values of the proton radius - 0.87fm & 0.84fm.

Then, after that, the first iteration error will be calculated using the corrected proton radius leaving the original -4% error behind.

1. Error from unity (1) with original incomplete Rydberg formula/equation.
2. Error from unity (1) with $r_p=0.87...fm$
3. Error from unity (1) with $r_p=0.84...fm$
4. Error from unity (1) with first full set of iterated values
5. ...continue...

A -4% error is unacceptable for real science.

9/12/2023 updates & comments:

It's worth looking at the error with the original Rydberg equation because it becomes apparent that the constants are FINE TUNED to make the error very small, less than 10^-10, even though there was a HUGE -4% error with the proton radius, and when CODATA/NIST updated the proton radius to 0.84fm THEY DID NOT UPDATE THE OTHER CONSTANTS! The error in some of them are so huge that they are likely only good to 3-4 decimal places from the ideal.

The Surfer, OM-IV

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