On the common ZPE origin of quark force, Pioneer anomaly & flat stellarrotation curves in galactic halos

I add a few more details.

First delete

"Obviously, if the attractive force is constant, like for the quarks,
the orbiting speeds of the stars will not depend upon their distance
from the center of the galaxy."

The correct statement is below and is in my book Super Cosmos. I
misremembered what I did.

The Skeptics like to debunk zero point energy as "psychoceramics"
(Visser's "Lorentzian Wormholes") well let's see who has the last laugh
now? ;-)

I forgot to mention that essentially this same simple idea also explains
the flat stellar rotation curves in the galactic halos.

Three at a blow

1. Quark Force

A Zee in "Quantum Field Theory in a Nutshell" says that the quark-quark
effective potential inside the hadron in the IR long wave limit ~ r
(their separation). Therefore, there is a constant attractive force
between them so it costs more and more work-energy (linearly) to
separate them.

2. NASA Pioneer Anomaly

Same thing on a much bigger scale. The anomalous constant force on the
two probes is

g = cH

H is Hubble parameter

g ~ 1 nanometer per sec^2 - observed number


3. Flat stellar rotation curves in dark matter galactic halo.

Same idea. Imagine a circular orbit, the radial inward acceleration is f^2r

If the gravity force were from a compact object, r outside it then

GM/r^2 ~ f^2r

f^2 = GM/r^3

f ~ 1/r^3/2

v = fr ~ 1/r^1/2

disagrees with observation

On the other hand, if the star is moving through an exotic vacuum of
positive pressure.

The radial inward force is from

V = -c^2/\r^2

g = -dV/dr = 2c^2/\r = f^2r

2c^2/\ = f^2

c/\^1/2 = f

v = fr = c/\^1/2r

Therefore

/\ ~ 1/r^2

in that case.

Not quite the same as

/\ ~ 1/r for quark force and Pioneer anomaly, but essentially the same
mechanism with a steeper fall off.