Origin of the Gravitational Red Shift in Newtonian Dynamics

This can be worked out with one of the equations I remember from school:

u squared – v squared = 2 g r

Now drop an object to earth from a distance r above the earth, with initial velocity u = 0, final velocity v. Thi is an inertial phenomenon with radial but no angular part to the velocity. The acceleration g due to gravity is conventionally

g = – MG / r squared

from the equivalence principle. So

v squared = 2 MG / r

In special relativity the Lorentz factor is

gamma = (1 – v squared / c squared) power minus half

= (1 – 2 MG / (r c squared)) power minus half

~ MG / (r c squared)

= dtau / dt

which is the gravitational time delay, QED. Nothing to do with the old and incorrect Schwarzschild metric or the old and incorrect Einstein theory. The starting equation comes from the work integral, and I will explain this in note 265(1). For an elliptical orbit:

v squared = MG ( 2 / r – 1 / a)

and this must be used in the expression for the gravitational time delay. The difference is that the orbit contains an angular as well as a radial contribution to v. Here a is the semi major axis of the ellipse. In a precessing ellipse v squared is modified as in UFT264 to contain x, and the gravitational time delay will also be a function of x.


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