Newton's constant of gravitation - a physical constant too difficult to measure?

College Best Publication Award for ‘Improved Determination of G Using Two Methods’

Article by Professor Clive Speake

G-Figure-v2Professor Clive Speake and coauthors recently published results of a determination of the value of Newton’s constant of gravitation, G (Physics Review Letters 111,101102, 2013). There is much controversy about the actual value of this oldest fundamental constant of nature, with experiments of claimed accuracies of tens of parts per million (ppm) disagreeing by up to some 500 ppm. The new result, which itself came from two largely independent measurements agreed with the value that the collaboration had published in 2001, despite a rebuild and significant improvements to the apparatus. It would seem that the difficulty of determining or, perhaps, even defining G continues!

 

Modern physics has been extremely successful in developing our understanding of the sub-atomic world. However our understanding of the force of gravity is very basic. Gravity is the force that dominates on the scale of the Universe but the forces between objects that can be held in one’s hand are extremely weak. The force of attraction between two people is some ten powers of ten weaker than the force that they require to resist the gravitation force of the Earth (their weight). 

The first universal equation that characterised a force of Nature was Newton’s inverse square of gravitation which stated that the force acting between two spherical objects in proportional to the product of their mass values and inversely proportional to the square of the distance between their centres. In order to determine the magnitude of the force we also need to define a constant of proportionality which is referred to as Newton’s constant of gravity, G, or ‘Big G’ (as opposed to ‘little g’ which is reserved for the acceleration due to Earth’s gravity). Despite Newton’s law of motion being formulated in the 17th century, we still don’t have a reliable value for G. The first professor of physics at University of Birmingham, John Henry Poynting famously weighed the Earth with a bullion balance at the end of 19th century. Today G remains, however, the least well-known constant of nature. There is a spread of some 500 parts per million (ppm) in recent measurements, despite most of them having uncertainties close to 20 ppm or even less. As a result, the ‘accepted’ value (evaluated by the CODATA group) has an uncertainty of 120 ppm. This compares with the uncertainty on the Rydberg constant (that characterises the optical spectra of atoms) which is at the level of parts per billion. 

In our paper published in Physical Review Letters (PRL) we present the result of our latest measurements of G. Our new result is some 240 ppm above the CODATA value but is in close agreement with the value that we published in PRL in 2001. All the recent results are derived from mechanical devices that are simple in concept, such as torsion balances, common balances or simple pendulum suspensions. 

Over a period of some twenty years we have developed techniques that have enabled us to make two essentially independent measurements of G. In one method we rediscovered the torsion ‘strip’ balance to avoid the problems associated with internal damping in the metal from which the strip is constructed (a materials problem which we ourselves highlighted). In the other approach we developed a novel electrostatic torque generator which was used to calibrate the measured torque due to gravity.  

 

The approach is unique: No previous research team has successfully attempted to determine G in independent ways, and so the strength of our work lies in the use of a torsion balance having two different modes of operation with the two results being statistically consistent but essentially statistically independent. In addition we rebuilt and improved the experimental apparatus which we used for the 2001 result and the new apparatus gave a new result that agreed with the previous result but with a reduced uncertainty.