OFFSET
45,2
COMMENTS
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 = E_1*E_2/(F_P*r^2), where E_1 and E_2 are the energies of the bodies.
EXAMPLE
F_P = c^4/G = 8077608713062490229263800746151696 (m^4/s^4)/(6.67384...*10^-11 (m^3)/(kg*s^2)) ~ 1.2103...*10^44 (kg*m/s^2), where c is the speed of light in vacuum and G is the Newtonian constant of gravitation.
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Omar E. Pol, Sep 26 2013
EXTENSIONS
a(49) corrected by Ivan Panchenko, May 21 2019
STATUS
approved