Einstein's cosmologicas constant divided by energy density x c^4= Newtons gravity constant.?

Question

Did Newton know about that but refused to elaborate an explanation?

Answer 1

L = 8pi G rho/c^4 is the definition of the cosmo constant L (1/m^2); where c = light speed and rho is the energy density of the known universe in a vacuum.

F = GmM/r^2 is the equation for the attraction force F between two masses m and M, r distance apart.

L was created by Einstein to make his equations come out right. By that, he meant the universe should be spherical (not flat or saddle shaped). His original results showed a flat universe, and he just "knew" that was wrong; so on came L to fix the shape problem.

F was the result of experiments by Newton. Through observation, he found that the attractive force between two bodies was proportional to the inverse square of the distance between them and to the product of the magnitudes of the two masses. That is, F varies as (~) (mV/r^2).

Whenever there is a proportionality, as in F ~ mM/r^2, there has to be a constant of proportionality. In this case Newton called it G; so that F ~ mM/r^2 becomes F = GmM/r^2 when the constant is inserted.

The G in both equations is the same constant. But Sir Newton came upon it long before Einstein found it could be used in his equations and the calculation of L. So there is no way that Newton (1642-1727) could know about Einstein's (1879-1955) use of it much later.