In the double surface model Bohr radius expressed in the units of Compton wavelengths of the electron is deduced from the average path on the elliptic and hyperbolic side of the orbit:

From the relation (3) and (4) is seen that the radius of the elliptic side of the double surface is greater than Bohr radius only once, i.

Since the uniform circular motion of an electron is in opposition to Heisenberg's Uncertainty Principle (actually [DELTA]r = 0 and [DELTA]mv = 0), my correction to special relativity allows me to consider that when the electron tends to stop, it oscillates around the origin of the x-axis with an amplitude equal to the

Bohr radius and it moves (on average) with twice the minimum speed.

0], the

Bohr radius, gives the scale of the interaction and [gamma] is the relativistic correction factor.

For a single charge atom like hydrogen and lowest spin level corresponding to n = 1, we get the

Bohr radius r = [r.

Interestingly, the gravitational Bohr radius derived from this gravitational Schrodinger equation yields prediction of new type of astronomical observation in recent years, i.

Furthermore, as we discuss in preceding paper [4], using similar assumption based on gravitational Bohr radius, one could predict new planetoids in the outer orbits of Pluto which are apparently in good agreement with recent observational finding.

3 A new type of redshift from gravitational Bohr radius.

In this regards, we use gravitational Bohr radius equation:

we can derive a gravitational equivalent of

Bohr radius from generalized Schrodinger equation [4].

In the field of a vortical torus, with

Bohr radius of the charge, r = 0.

EM] observed at the scale of the

Bohr radius [[alpha].