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%I #40 Mar 21 2023 13:13:28
%S 3,6,2,7
%N Decimal expansion of G*h^2/c^4 in SI units, where G is the Newtonian constant of gravitation, h is the Planck constant and c is the speed of light in vacuum.
%C Also decimal expansion of h^2/F_P in SI units, where h is the Planck constant and F_P is the Planck force.
%C From _Omar E. Pol_, Oct 21 2017: (Start)
%C According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m_1 and m_2), and inversely proportional to the square of the distance, r, between them. Newton's formula is F = G*m_1*m_2/r^2, where G is the constant of gravitation. Using both the Planck force (F_P) and Einstein's formula E = m*c^2, the law of universal gravitation could be written as F = (G/c^4)*m_1*c^2*m_2*c^2/r^2, or, more simply, F = (1/F_P)*E_1*E_2/r^2, where both E_1 and E_2 are the energies of the bodies.
%C Then using the Einstein's formula E = m*c^2 and the Planck-Einstein relation E = h*f, the law of universal gravitation between two photons could be written as F = (G*h^2/c^4)*f_1*f_2/r^2, or simply, F = (h^2/F_P)*f_1*f_2/r^2, or, more simply, F = Q*f_1*f_2/r^2, where both f_1 and f_2 are the frequencies of the photons and Q is this constant. (End)
%F Q = G*h^2/c^4 = h^2/F_P = A070058*A279386/A183001 = A279386*A228818 = A279386/A228817.
%e Q = 3.627... * 10^-111 [kg * m^3].
%Y Cf. A003676, A003678, A070058, A183001, A228817, A279386.
%K nonn,cons
%O -110,1
%A _Omar E. Pol_, Dec 11 2016
%E Updated by _Ivan Panchenko_, May 29 2019
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