In the fastidious hunt for G, remembering gravity’s gradient

Of the four fundamental forces known to humankind, gravitation was the first to be studied in detail even though it is the weakest. This is because the effects of the other three – electromagnetic, strong nuclear and weak nuclear forces – are distinctly apparent only at subatomic scales. Gravitation on the other hand is the mover of stars. So, is there any irony that the gravitational constant among all the forces’ constants is the one known with the least precision?

Since the Chimborazo and Schiehallion experiments in 1749 and 1774, respectively, the Cavendish experiment in 1798, and a cameo by Marie Alfred Cornu and Jean-Baiptistin Baille in 1873, people have tried to measure the strength of Earth’s gravitational pull – first in an attempt to prove Isaac Newton right, then in attempts to judge if Albert Einstein was right. Nonetheless, the value of the constant, G, involved in the calculations has been known only to within 100 parts per million.

Measuring G is is tricky because the gravitational force is apparent at all times, and isolating an experimental setup from its effects is impossible. This means the focus is more on the apparatuses than on the experimental method itself, and small changes in design often manifest as irreconcilable values of G. Moreover, researchers have been able to argue that it might not be the same for every type of particle using measurements of helium abundance in the early universe.

In June 2014, a team of Italian scientists added another measurement and it was in the same breadth but for one crucial difference. For the first time, they had measured G using ultracold atoms instead of the motion of heavy weights. In January 2015, they extended the same technique to measure the rate at which Earth’s gravitational force weakens across a particular distance, i.e. its gradient.

Even if their contribution didn’t bode well for the search for the absolute value of G (6.67191×10-11 m3kg-1s-2, 150 parts per million), the measurement of the gradient and the apparatus used to do so present exciting opportunities for new applications.

Various measured values of the gravitational constant, G.
Various measured values of the gravitational constant, G. Image:

Their experimental apparatus is deceptively simple. As Philip Ball writes in APS Physics,

… the team launched three clouds of ultracold atoms to three different heights inside a meter-long vertical pipe. Surrounding the top half of the pipe was 516 kg of tungsten alloy weights, to increase the variation in the gravitational field. Near the peaks of their trajectories, the atoms were irradiated with a rapid series of laser pulses from the top and bottom of the pipe.

The apparatus used to measure the curvature of Earth's gravity using atomic interferometry.
The apparatus used to measure the curvature of Earth’s gravity using atomic interferometry. Image:

This is where the fun starts. The laser pulses provide a momentum boost to some of the atoms in the cloud but not others. The boosted atoms fall through a different distance in the same time the atoms in the ground state do. When all the atoms in the cloud recombine, there is an interference effect whose extent is determined by the effect of the gravitational force on the momentum-boosted atoms.

As a result, they calculated the average curvature of Earth’s gravitational pull to be 1.4×10-5 s-2m-1. Knowing the value of the gradient, the Italian team’s apparatus can be inverted and used to measure how mass distribution varies within Earth. In fact, because we are aware of the density of oil and other minerals, the apparatus can be used by prospectors to look for deposits as well as inexpensively study their density profiles from the surface. Moreover, future experiments can resolve higher-order derivatives of Earth’s gravitational force, helping scientists arrive at a more accurate value of G.