Saturday, May 10, 2014

newtonian gravity - Watt (Kibble) balance and the kilogram - how does the dependence on $g$ get eliminated?


The standard ${kg}$ is now in the process of being redefined by the watt balance (rather than the lump of metal in Paris)


A watt balance is very simple, you measure the force needed to support a mass against gravity (by accurately measuring the current/voltage in an electromagnet).


But in order to translate this to mass you obviously need to know local $g$. This varies by a few 0.1% due to latitude and local geology so how do you measure mass to a few parts per billion without a method to calibrate out the local $g$?



The obvious point being that if you had a sufficiently accurate test mass to take around all the labs in the world to calibrate their balances - isn't that the standard mass?



Answer



You are quite correct that the determination of mass requires measuring the local value of the $g$. However this is routine these days with instruments like the FG5 gravimeter giving accuracy of $2$ $\mu$Gals which is getting on for $1$ part in $10^9$. The gravimeters measure freefall speed so they measure the acceleration directly and do not depend on a standard mass.


I can't find anything on the NIST web site saying which gravimeter they plan to use, but presumably it will be at least as good as if not better than commercial gravimeters like the FG5. There is a reference to the NIST gravimeters here but it is frustratingly vague.


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