The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10 and 6.674484 × 10 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

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By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295  μm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59  μm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300  μm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160  μm.

We present evidence for the cooling of normal-metal phonons, in addition to the well-known electron cooling, by electron tunneling in a superconductor-normal-metal-superconductor tunnel junction. The normal-metal electron temperature is extracted by comparing the device current-voltage characteristics to the theoretical prediction. We use a quantitative model for the heat transfer that includes the electron-phonon coupling in the normal metal and the Kapitza resistance between the substrate and the metal. It gives a very good fit to the data and enables us to extract an effective phonon temperature in the normal metal.