Energy Density CBR vs MW at 1pc vs MOND

MOND is presented as a modification of gravity that kicks in when the
local acceleration reaches a low value.

I'm wondering whether anyone has noted the coincidence of the following
values.............(and as well, whether I've goofed in the calculations
and or the values I'm using)

According to various plots for MW stellar rotation curves, MOND kicks in
at about a radius of R = 1kpc = 3.086E19 m

The best value I have so far found for the number of stars within that
radius is about N = 12.3E9. inside of radius 1kpc

This yields
L = 4.75E36 J/s and a volume for the sphere of
V = 1.23E50 m^3
If I consider the energy released per

dt = 1.0 second (which is the energy flowing outward through a spherical
shell of radius 1kpc), I find the energy density within the radius R,
per second of energy emission, to be

Rho_E MW = L dt / V = 3.86E-14 J/m^3 = 3.86E-14 Pa

The energy density of the CBR is around Rho_E CBR = 4.16E-14 Pa, which
is essentially the same value

In other words, the radius where the energy density of MW emissions per
second matches the energy density of the CBR happens to be at 1kpc,
where the MOND effect kicks in.

So, at least for the MW galaxy, if I've done the math right, MOND kicks
in at the same place where the energy density of light being generated
within the the interior of the MW galaxy, matches the energy density of
the CBR.

Did I do the math right and or are the values I'm using about
reasonable?

Ross