In this paper, we will derive the following formula for the value of the gravitational constant G: (1). This equation has only 0.81% error compared to the common accepted value [1]. The parameters in the equation are the following: the fine structure constant, qthe elementary charge, the mass of the electron, the permittivity of the free space, ethe exponential function and the relation between a circumference and its diameter. Values attached:[2],
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Mohr, P.J., Taylor, B.N. and Newell, D.B. (2015) The 2014 CODATA Recommended Values of the Fundamental Physical Constants (Web Version 7.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. http://physics.nist.gov/constants
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Bouchendira, R., Cladé, P., Guellati-Khélifa, S., Nez, F. and Biraben, F. (2010) New Determination of the Fine-Structure Constant and Test of the Quantum Electrodynamics. Physical Review Letters, 106, 080801. arXiv:1012.3627Bibcode:2011PhRvL.106h0801B. https://arxiv.org/abs/1012.3627 https://doi.org/10.1103/PhysRevLett.106.080801
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Arndt, J. and Haenel, C. (2006) Pi Unleashed. Springer-Verlag, New York. English Translation by Catriona and David Lischka.
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Shu, F.H. The Physical Universe. And Introduction to Astronomy, 108. https://books.google.es/books?id=v_6PbAfapSAC&pg=PA108&lpg=PA108&dq=range+wavelength+virtual +photon&source=bl&ots=oqrksX7gjD&sig=9nd3Cr5gK7MWDVuYGnLxL1jZ2Ek&hl=es&sa=X&ved=0ah UKEwil29iSsYXPAhVBnBQKHcuiCkcQ6AEIMTAC#v=onepage&q=range%20wavelength%20virtual%20 photon&f=false