Research On Gravity Gradients In Test Of Weak Equivalence Principle With A Rotatable Torsion Balance

The Weak Equivalence Principle means the gravitational and inertial mass of any objet is equivalent. Einstein extended it to the Strong Equivalence Principle as a basic assumption of the General Relativity. But the Weak Equivalence Principle does not apply to the other fundamental interactions. Almost all attempts to unify the gravity to the other three interactions requires the violation of the Weak Equivalence Principle. Therefore, a high accuracy test of the Weak Equivalence Principle has very important scientific significance whether its result is positive or not.No matter which the method used to test the Weak Equivalence Principle, we need to carefully analyse the environmental disturbance factors so as to enhance test accuracy and confidence level. This paper systematically studied on the ambient gravity gradient e?ects in the test of Weak Equivalence Principle using a rotatable torsion balance. First, we estimate the e?ects using the generalized Fourier series expansion. This expansion makes use of the spherical harmonics as the basis vectors to expand the torque which is generated by the gravity gradient acting on the torsion balance. The torque can be written in the form of infinite series, the main contribution in which is the term of the gravity gradient field Q21 coupling to the torsion balance moment q21. Secondly, considering the specific assembly process of the torsion balance, we sort and process the experimental data, then calculate the size, density, center of mass, and attitude of the torsion balance parts, and analyze attitude,center of mass of torsion balance after assembled, then work out the gravity gradient moments and give the corresponding error budget. Finally, we design the source masses to compensate the ambient gravity gradient field Q21. When the compensator masses are in place, they will produce the same size, but in the opposite direction of ambient gradient field component to lower the ambient field. After detailed evaluation and calculation, we find the compensator masses can reduce the ambient gravity field by a factor of 135. The e?ect of residual gravity gradient in the experiment is smaller than ? ? 6 × 10-12. This system work can provide theoretical guidance to improve the accuracy next step.