Geophysical test of the universality of free-fall

We point out that the universality of free-fall can be tested by observing surface-gravity changes of the Earth. The Earth’s inner core is weakly coupled to the rest part of the Earth by mainly gravitational forces. If there were a violation of the universality of free-fall, because of their different chemical compositions and/or of different mass fractions of binding energies, the inner core and the rest part of the Earth would fall at different rates towards the Sun and other sources of gravitational fields. The differential acceleration could be observed as surface-gravity effects. By assuming a simple Earth model, we discuss the expected surface-gravity effects of violations of the universality and experiments to search for such effects by using superconducting gravimeters. It is shown that the universality can be tested to a level of ${10}^{-9}$ using currently operating superconducting gravimeters. Some improvements can be expected from combinations of global measurements and applications of advanced data analyses.

Figure 1

A schematic cross section of the assumed configuration (not drawn to scale). The Earth is fixed and the Sun goes around the Earth in the circular orbit (radius $r$) at the angular frequency ${\omega }_R\approx 2\pi (24\mathrm{h}{)}^{-1}$. The inclination of Earth’s rotation axis to ecliptic is assumed to be 0° for simplicity. The $x\mathrm{\text{−}}y$ plane is set on the Earth’s equatorial plane. The Earth’s inner core oscillates along the $x$-axis. The gravitational influence from Earth’s mantle and crust (not drawn) is negligible because of Newton’s shell theorem (see text).