We created and analyzed a citation history of papers covering measurements of Newtons constant of gravity from 1686 to 2016. Interest concerning the true value of the gravitational constant was most intense in the late 90s to early 2000s and is gaining traction again in the present. Another network consisting of the same papers was created using citations from databases to display the prominence of papers on Newtons constant in the wider scientific community. In general, papers that were important in one network remained important in the other while papers that had little importance in one network remained unimportant in the other. The US contributes the most to literature on the topic both in where journals were published and where the work was done; however, many other countries, such as China, Russia, France, Germany, Switzerland, and the UK also provide many papers on Newtons G. Work done within certain countries tends to be considered more important and cited more often within that country. Recent efforts promoting international collaboration may have an impact on this trend.
In 1789, Henry Cavendish was to use the first torsion balance to measure the strength of gravitational interaction. After his initial success, many others explored methods of measuring the gravitational constant, either by modifying his experiment or seeking better ones. However, even with experimentation and concern for finding the true value of the constant over the past few centuries, Newton's constant remains elusive. It is by far the least well known of the fundamental constants of physics. Measurements from a handful of differing experiments -even more recent measurements -have discrepancies of up to .05%, leading to large uncertainty in the true value of the constant. Researchers agree on at most the first three significant figures, or that 𝐺 = 6.67 × 10 -11 N × m 2 /kg 2 .
The uncertainty associated with Newton’s gravitational constant is concerning because gravity is the most easily experienced and most recognizable fundamental force of nature. A very precise value could be a hint of some physics beyond general relativity. It is notoriously tricky to measure for of three reasons. First, gravity is an extremely weak force compared to other measured forces such as electromagnetic or nuclear forces. For a proton and an electron, the ratio of the electromagnetic to the gravitational force is given by
, where 𝑒 is charge on the electron, G is Newton’s constant, 𝑚 𝑝 is the mass of the proton, and 𝑚 𝑒 is the mass of the electron. Second, G is not tightly coupled in with the constants of electromagnetism and quantum mechanics in the way that the mass and charge of an electron are. And third, all measurements of Newton’s gravitational constant have had to be done very close to a large, interfering mass -Earth.
In 2016, the National Science Foundation began a quest for a more precise value of “Big G.” They convened a workshop at NIST (National Institute for Standards and Technology) to propose and discuss novel measurement techniques to resolve discrepancies and lead to a more precise value for G. One of us, Virginia Trimble, was a participant.
In this paper, we explore the relationship between papers searching for or discussing the importance of Newton’s gravitational constant. Dating from Newton in 1686 to efforts in 2016, the citation map created shows some of the most important relationships between literature published on Newton’s constant within the past few centuries and the resources those papers used for inspiration. The citation map helps identify which papers are the most influential within the community. We aim to discover whether members within this community are receiving the credit they deserve or if other members are overrepresented. We also intend to see if countries in which the work was done or journals in which the papers were published in affect the amount of influence a paper has.
Katelyn Horstman thought of looking for correlations with gender but discovered that the use of initials often made this impossible to determine and we suspect that there are very few women authors in this network.
Stephan Schlamminger, a physicist at the National Institute of Standards and Technology (NIST), kindly gave Virginia Trimble a flash drive consisting of the papers he deemed important concerning Newton’s gravitational constant. She concluded that some sort of citation analysis, grouping publications and using citations from outside the group, would be useful. We created the citation analysis using around 220 of the roughly 300 original papers from the flash drive. The 80 or so papers not used did not help build the network as they either did not cite papers within the list or consisted of papers with no citations at all. We created another network consisting of the same papers, but each paper’s graphical representation was based the number of times it was cited within the scientific community.
We used an excel spreadsheet to document and cite the papers within the network. Each paper in the network either cited another paper within the network or was cited by another paper within the network. We formatted the sources and their citations to establish relationships between papers then uploaded the created relationships to a citation analysis program called Gephi. Gephi created a citation network graphically showing the relationship among papers.
Each paper was assigned a number, listed in the Appendix, and then ordered chronologically on the diagram. Lines connecting different numbers show which papers cited other papers and the direction is indicated with small arrows pointing toward the paper that was cited.
The larger the number appears in the diagram, the more times that paper was cited. In addition, most frequently cited papers are purple, moderately cited papers are yellow, and least frequently cited papers are white. The network shown displays the relationship between various methods of calculating Newton’s gravitational constant and other papers documenting its importance or history.
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