Oh my God, the Pioneer Anomaly again?

J. G. Waller

I think it would be a fine tradition to resume Pioneer
Anomaly Discussions at this season. I'm not going to explain
here what Pioneer Anomaly is, there is a lot of literature
concerning this issue in internet, try some googles,
or John Baez Open Question in Physics
(http://math.ucr.edu/home/baez/open.questions.html)

Let me propose my own insight about this famous problem:
A. The so-called anomalous acceleration, a_p, detected in
Pioneer 10/11 spacecrafts, is a real acceleration towards
the solar system barycenter.
B. The "mysterious mechanism" accounting for it is the
precession of open orbits, such as hyperbolic orbits!!!!!.

We know that elliptical orbits exhibit periapsis precessions,
but we assumed that open orbits, like hyperbolic or parabolic
orbits were unable to exhibit those precessions, with orbital
bodies keeping their trajectories stationary on their initial
orbital curves. General Relativity (GR) Model shows us how
spacetime is curved by gravitational systems, and how precessions
can be accurately addressed. Anyway, the question is, can GR account
accurately enough for any kind of orbit precession?. In the case
of planet Mercury's anomalous precession, GR was success in the
prediction, but in cases like hyperbolic orbits, it is not so
clear how GR could accurately predict precessions, as there are
few experimental data about evolution of hyperbolic orbits, along
meaningly high time intervals. Maybe, a serious Quantum Gravity Theory
could account for Pioneer Anomaly, and, of course, for other open
questions
in physics too. The galaxy rotation problem is tightly related to
Pioneer
Anomaly, both issues must really be the same phenomenon, that is,
orbit precesion effects.

So, if we assume hyperbolic orbits exhibit precessions, then there
must exist an extra centripetal acceleration, in such a way that
an hyperbolic orbit is no longer hyperbolic along time, but a kind
of hypotrochoid curve. That extra centripetal acceleration would be
the famous anomalous acceleration a_p observed in Pioneer Probes.
It has been observed that acceleration is of order a_p = -cH,
where H is Hubble constant and c speed of light in the vacuum.
We must say that experimental value has been observed for positions
beyond Jupiter and Saturn encounters. How can we interpretate that
a_p = -cH value?. One interesting solution would be any value of order
±cH must be a lower bound for any acceleration. Values of order ±cH
have
been found in different scenarios, and at different scales,
for example, the centripetal acceleration of solar system around
the Milky Way is about that order. That would be the lower measurement
uncertainty for any acceleration, and here is when Quantum Gravity
might
play its role. Symmetrically, an upper bound, a_h, for any
acceleration,
must be a_h = ± c/ t_p, where t_p is Planck time.