E.G. Adelberger, J.H. Gundlach, B.R. Heckel and H.E. Swanson

Three recent remeasurements of Newton's constant G have yielded values¹ that differ by up to 0.7% (52i). A new determination that will resolve this puzzle is needed, preferably by a method that differs from those used previously and that is less susceptible to systematic error sources found or suspected² in previous measurements.

In last year's Annual Report³ we proposed a method based on a continuously rotating torsion balance located in the field of a massive attractor. A feedback system controls the angular velocity of the turntable so that the torsion fiber does not twist. The rate of change of the turntable angular velocity directly yields the angular acceleration of the 'quasifree' pendulum. Expressed in multipole formalism, this acceleration is where q_lm and Q_lm are the multipole moments of the pendulum and attractor mass, respectively. The overwhelmingly dominant torque is . If one uses a flat, two-dimensional pendulum its q₂₂-to-moment-of-inertia ratio becomes a constant i.e., is independent of the density distribution. For a rectangular pendulum with finite thickness, t, and width, w. this ratio becomes

(1)

i.e. it is only weakly dependent on the width and thickness. Furthermore, if the width-to-height ratio satisfies 10h² = 3(w² + t²) then q₄₂=0. The next-to-leading order acceleration, arising from ,m = 6,2 coupling, is analytically calculable and small (₆₂/₂₂ 10^-5). To further reduce higher-order torques, the attractor will consist of 4 spheres located symmetrically on each side of the pendulum. They will be separated azimuthally by 45° ( Q₄ = 0) and vertically by where is the horizontal distance to the torsion fiber ( Q₄₂ = 0). The acceleration can be fitted with a harmonic series in the turntable angle, , to extract G. We will use a quartz plate for the body of the pendulum so that any non-uniformities can be minimized using optical methods. This plate will then be gold-coated so that its faces serve as mirrors for the angle read-out.

The attractor rotates on a second turntable to eliminate gravitational effects of background gravity gradients. To eliminate gravitational forces from the turntable itself, G will be derived from the difference of two measurements where the attractors are rotated by 90° on the turntable.

We have used numerical simulations to find a feedback scheme that most closely tracks the quasifree pendulum. This feedback method was then successfully implemented on our old Eöt-wash balance. From this test and the simulations, and the expected reduced systematic errors, we believe that our technique should permit a measurement to G/G = 10^-5.