5

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?

Martin Beckett
  • 31,032

2 Answers2

5

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.

John Rennie
  • 367,598
4

how do you measure mass to a few parts per billion without a method to calibrate out the local $g$?

You don't. The local $g$ is an acceleration and it can therefore be measured directly using only access to length and time standards, which ─ given how the meter is defined ─ boils down to an optical experiment with an accurate timing reference.

Thus, as a simplistic approach, you can essentially make do with a ruler and a stopwatch, but if you want reasonable accuracy then you probably want a proper instrument like the FG5 gravimeter that John linked to. Luckily, gravimetry is a very sturdy branch of metrology, because changes in $g$ can be traced to deposits of random stuff like some kinds of rock and decayed plant matter, which for some reason tend to bring huge clouds of money along with them, so there is a lot of (relatively) cheap metrology you can do rather accurately.

On the other hand, if you want to do primary metrology, then the game changes somewhat, because your measurement of $g$ needs to have as many significant figures as your final measurement: you're trying to upstage a ${\sim}50\:\mu\mathrm{g}/\mathrm{kg}$ variation in the existing IPK system, so you want all of those eight significant figures ─ parts per billion ─ in your measurement of $g$. Quoting from

Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram. M. Stock. Metrologia 50, R1–R16 (2013).

this is quite serious business:

The value of the gravitational acceleration $g$ needs to be known at the centre of mass of the test mass, which is inaccessible once the experiment is set up. One technique to achieve this is to establish a map of the variation of $g$ in the laboratory with a relative gravimeter before the watt balance is installed. In addition, the absolute value needs to be known at least at one point. The absolute value of the gravitational acceleration at the centre of mass of the test mass can then be obtained by interpolation. The gravitational acceleration also varies in time by as much as $2.5$ parts in $10^7$ due to tidal forces from external bodies. This needs to be taken into account either by permanent g measurements or by modelling of the tidal effects. A correction needs to be applied for the gravitational effect of the watt balance itself.

That last point is important, because here the $1/r^2$ dependence of newtonian gravity plays against you: the effects of the balance itself are small but nonnegligible, and they are measurable with some variation from the outside of the balance, but their strength and variation increase by squares when you get to the inside of the device.

That said, the actual methods used for those gravimetry measurements do seem to be relatively standard (or at least they are not explained in depth in the review paper and its references) so you likely just need to do the standard thing but a lot more carefully.

Emilio Pisanty
  • 137,480