It is possible that the Pioneer anomaly can be explained by the existence of non-Newtonian forces: this effect is registered near the boundary of the Solar System, because Newtonian attraction
here decreases (with radial distance), and non-Newtonian attraction
They affect the measured gravity through the variable Newtonian attraction of water masses and through the loading effect as a result of the Earth deformation due to variable loading.
Hydrological effects are caused by hydrological mass changes (quantity and distribution) which affect the gravity due to 1) Newtonian attraction of variable masses, 2) response of the Earth to this surface mass loading.
The Newtonian attraction of this cylinder at the point located on the top plane in its axis is
Of the unknowns, I think my favorite was George Cheyne, a medical reformer who tried to apply principles of Newtonian attraction
to medicine, in a weird construction known as "iatro-mathematics" Cheyne struggled heroically, but mostly unsuccessfully, with problems of diet and alcohol intake, eventually becoming so fat that "a servant had to follow him with a stool so that he could recuperate every few yards"
In the ideal case one would expect the maximum repulsion of the pendulum to occur when the angular momentum constraint is met and its magnitude to be comparable to the Newtonian attraction
An additional gravitational test of QCM would be a laboratory experiment with a slowly rotating attractor mass producing a repulsive effect to counteract the Newtonian attraction
at specific rotation frequencies for the given separation distance to the affected mass.