The curious case of the gravitational constant

Abstract

More than 200 years after it was first measured, this fundamental property of our universe continues to confound In 1763, surveyors Charles Mason and Jeremiah Dixon set off from Philadelphia to demarcate the border between Pennsylvania and Maryland. On the other side of the Atlantic, British scientist Henry Cavendish worried about the effect of the Allegheny Mountains on Mason’s and Dixon’s measurements, which would eventually establish the famous Mason–Dixon line. Cavendish reasoned that the gravitational attraction of the mountains would pull at the theodolite plumb-bob that Mason and Dixon were using, enough to throw off their measurements of local latitudes by as much as 200 meters (1). Fig. 1. Physicists have had a surprisingly difficult time calculating the gravitational constant, Big G, one of the most fundamental measures in all of physics. Image courtesy of Dave Cutler. Such analysis set Cavendish down a path to performing one of the first high-precision experiments in physics. Using a newly designed device called a torsion balance, Cavendish measured the almost-infinitesimal gravitational attraction between two spheres of lead. His experiment allowed physicists to calculate a value for the gravitational constant—often called Big G to differentiate it from little g, the acceleration due to gravity—for the first time since Isaac Newton wrote down his law of gravity approximately a century earlier. Cavendish’s brilliant insights are more obvious in light of modern experiments. More than 200 years and 350 experiments later, scientists know the gravitational constant to a precision only about 1,000-times better than could be calculated from Cavendish’s data. “For any other experiment in physics, this would be a real surprise or shame,” says physicist Guglielmo Tino of the University of Florence in Italy. That’s because the majority of physical constants are known with extreme precision—often out to 9, 10, or even 12 digits. But G …