**Acknowledgements**

best pendulum clocks ever realized [13] were probably not differentially stable better than 10−9 at the target 104 s averaging time, which means that 60 dB improvement is necessary. Although this is granted on paper by projected S/N and *Q*, actually achieving it is still a big challenge. On the positive side, it is worth pointing out here that energy-induced amplitude changes [11] do not affect frequency if operation is kept at the minimum period isochronous point and that an approach to oscillation support aimed at overcoming pulse stability problems by moving to a sine-wave excitation system similar to that employed in high-stability

**Table 1.** Accuracy budget projection based on 1-m-long 4 μm tungsten fibres, 6-mm-diameter suspension cylindrical profiles, a swing amplitude of 0.01 rad, and a 5 mm tungsten bob. The position of field masses' gravity center is assumed

This said, it can be seen in **Table 1** that most geometrical contributions to uncertainty impose quite loose requirements at the target accuracy level of 10−5, with the sole exception of size and positioning of field masses, which must be guaranteed at high accuracy. While other contributions enjoy relaxed specifications granted by parabolic minima which are specific of this configuration, the latter do not and must comply with specs which are similar to any other big G experiment. However, the expectation that accuracy on G may be limited by control on this single geometry contribution ushers the possibility of doing even better than 10−5 if resources were to become available to improve the accuracy of field masses. A summary of such uncertainties is reported in **Table 1**, as listed in Ref. [1], where the reader can find more details and

A new experiment was presented for the determination of the Newtonian constant. It is based on a time and frequency metrology approach consisting in the measurement of the small frequency difference between two freely oscillating pendulums via their time delay rate of change. A system of dense field masses is moved back and forth between the two, alternately increasing one frequency and reducing the other and vice versa. The increase in resolution by averaging is fast in this case because the limiting noise is white delay noise, which yields *σ<sup>y</sup>*

quartz oscillators will remove one of the worst contributions to instability.

**Effect Relative bias Uncertainty Conditions**

Field masses' density 0 5∙10−6

known with <300 nm uncertainty.

70 Metrology

Shift at bob's vertical position 6.7∙10−4 <10−6 < 50 μm uncertainty in *a*, w Bob's vertical position 0 2∙10−6 0.2 mm full tolerance Bob's lateral position 0 1.7∙10−6 0.2 mm full tolerance

Non-isochronism −1.8∙10−5 < 10−7 Operation at minimum period

Spacing between twin masses 0 6∙10−6 0.4 μm gap uncertainty Field masses' dimensions 0 6∙10−6 1 μm uncertainty

a deeper discussion on accuracy.

**7. Conclusions**

The author wishes to thank for encouragement and discussions Robert Drullinger, Stephan Schlamminger, and Bill Phillips of NIST and Valter Giaretto, Mario Lavella, and Lamberto Rondoni of the Politecnico di Torino. Special thanks go to Luca Maffioli for his master's thesis on the pendulum analysis and to Meccanica Mori of Parma for the TIG welding of the thin steel tubes to the experimental chamber. The author also wishes to acknowledge the support of the US Department of Commerce and NIST through the Precision Measurements Grant Program, Award ID number 70NANB15H348.
