Significant Digits as Related to Cosmology

Dec 14, 2021
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Suppose the mass of a particular star is observed to be 4.585 ×10^35 kilograms.
Now, suppose the mass of the same star at a higher level of precision is determined to be 4.584810034567×10^35 kilograms, and you use this discrete finite quantity as part of your broader calculations of how gravity behaves in this particular solar system, as well as the observable universe at large.
But on closer examination, it turns out the mass of your star is actually closer to 4.584810034567100999921235019044451678208472973056296937396592720478307307037504730640370270163047303740368103740264057402749026940275047395740572047593601720474947×10^35 kilograms.
The newly significant digits may not have much affect on your calculations of gravity's behavior over the short term, but wouldn't their significance add up over the long term?
The margin of error in your measurement of this one particular star may not have much bearing on your calculations of gravity in the observable Universe at large...
But wouldn't the missing significant digits from your earliest measurements, add up to something significant over the broader scale of the Cosmos?
In other words, if all stars are measured in terms of mass to the nearest whole kilogram, you will expect gravity to behave a certain way, and on relatively smaller scales your expectations will be met by observation.
But on relatively larger scales, you will need a higher level of precision in order for observation to match your calculations.
So if the mass of all observable objects is measured to the nearest 1×10^-999,999,999,999,999,999 nanogram with relative accuracy,
And the speed of light is measured to the nearest 1×10^-999,999,999,999,999,999 nanometer per 1×10^-999,999,999,999,999,999 nanosecond with relative accuracy (which would be much easier using, say... Base 10,000 math) gravity on large scales can now be predicted with a much higher degree of accuracy.
 

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