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March 31, 2015

March 31, 2015

Posted by **Johnathon** on Wednesday, February 16, 2011 at 12:39am.

- physics uncertenty -
**drwls**, Wednesday, February 16, 2011 at 5:12amac = 4 pi^2*r/T^2

ln(ac) = ln(4 pi^2) + ln r - 2 lnT

Now take the differential.

d(ac)/ac = lnr/r - 2 dT/T

For the standard deviation of the relative error, error, this leads to:

[σ(ac)/ac]^2 = [σr/r]^2 + [2*σT/T]^2

The relative error in ac, squared, equals the sum of the square of the relative error of r and the square of twice the relative error in T.

This assumes that errors in T and r are uncorrelated. Sometimes this is called the RSS (Root of the Sum of the Squares) rule.

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