Jun 24 2014

## Macroscopic vs. Atomic G

Dan Fordice sent me two articles about newer experiments that were set up to measure the gravitational constant.  One of the articles referenced a paper by Tino et al. where the constant is determined using one mass type of hundreds of kilograms of tungsten, and the other being laser cooled rubidium atoms.  The apparatus involving the tungsten masses looks like it may be the same apparatus as was used for the Schwarz et al. experiment from 1998 [1].  The Tino et al. value for G is given as 6.667 x 10-11 m3kg-1s-2 [2] with statistical uncertainty and systematic uncertainty given in the paper.

When we have a macroscopic mass where atoms are chemically bonded, and masses are held together by various means, a gravitational field acting on one atom can have a component of force on another atom that is chemically bonded to it.  A single atom free of bonding to other atoms, on the other hand, has fewer instantaneous electron orbital path vectors than a macroscopic mass of several kilograms when we consider it as a whole.  Therefore one would expect that the value of G when measured on individual atoms would be lower than a conventional value of 6.672 x 10-11 m3kg-1s-2 [3].

The gravitational constant based on one third the mass of the proton is 6.6807 x 10-11 m3kg-1s-2, but does it ever get this high in reality?  Planets in orbit around the sun would get close to this value.

G = 6.672 x 10-11 m3kg-1s-2 is probably still a good value to use when considering macroscopic masses on the surface of the earth, or in the atmosphere, or in orbit around the earth.

[1]  Schwarz, Robertson, Niebauer, Faller, “A Free-Fall Determination of the Newtonian Constant of Gravity”, Science, 282, 2230-2234; 1998: http://www.ngs.noaa.gov/PUBS_LIB/BigG/bigg.html

[2]  G. Lamporesi, A. Bertoldi, L Cacciapuoti, M. Prevedelli, G.M. Tino, “Determination of the Newtonian Gravitational Constant Using Atom Interferometry”, http://arxiv.org/abs/0801.1580, 2013

[3]  Tipler, Paul A., Physics, Worth Publishers, Inc., 1976, inside back cover