has good 3D planetary positions; in addition
to velocity-vectors, which consist of a combination of both
historical and predicted values. It operates according to a
theory on gravity which is rather opaque. It is said to be based
on Kepler's ellipses but variations to the perihelion and aphelion
are also in operation. They give no direct formulae, instead
offering a list of books as their sources, and then qualifying
that by saying that this list is not complete. So they're just
There is a great degree of consensus between the Horizon Ephemeris
and the 3D-n-body-gravity algorithm OGS15
(orbit-gravity-sim-15.exe) regarding deviations to Jupiter's
perihelion and aphelion. The dates of perihelion for Jupiter's
barycenter evolved from 1773 to 1999
with an accuracy of 4 minutes and 4113km.
Improvements beyond that not being viable for with my current
equipment. Accuracy for the distances of Mercury's Aphelion
and Perihelion evolved an average difference of just 8m
per orbit between Horizon Ephemeris and OGS15
over a similar time frame of 237 years. (See
sections on Mercury
& Jupiter for
The algorithm can improve on this if executed on a faster computer.
The accuracy to within 4 minutes for Jupiter
is especially good because the duration between various perihelions
can differ from the duration of the Jovian year, by often as
much as 17 days. There is however essential
disagreement about the Perihelion Precession of Mercury which
is the crux of this thesis.
Nevertheless, it has been detected here that all the Horizon
Ephemeris velocity-vectors, contain a gross error regardless
of agreement with their positional data as they express that
data in comparison with the center of the Sun. This problem
is agreed upon by a blind corroboration with Bernard Burchell,
(alternativephysics.org) following from his analysis. As an
example, in order to make Horizon Ephemeris' data consistent
with their given average orbital duration of Jupiter being 11.86178
years, it was required that their given velocity of Jupiter
had to be multiplied by 1.073880766.
So this 7.4% increase in their velocity
values was necessary so that Jupiter's position starting 18
December 1773 @ 11h53, reached
agreement with the 1999 perihelion of May 20th.
Scenario  of the algorithm OGS15
puts the time for that particular perihelion at 10h18,
whereas Horizon Ephemeris has it at 10h14.
However the given velocity-vectors are still in proper proportion
for the orbits for any set of data. Thus the multiplying factor
varied from 1.073 to 1.078
for various planets and various orbits. But that value could
be applied equally to the X, Yand
Z axes for any position in space and time for any major
planet, in order to reach consensus for the duration of the
It may be considered that this difference might occur because
OGS15 begins with positions referencing the
center of the Sun, and thereafter gives the Sun equal but opposite
momentum. But the velocity of the Sun is only 0.1%
of Jupiter. Of course 0.1% is not 7.5%.
And the other planets will reflect amounts varying by +-1%.
So even the fluctuation in the value between 7.3%
and 7.8% cannot be reconciled. For this reason
it may be prudent to make your model using the barycenter of
the solar system. Their data for that might bypass
this issue. It is not clear which data Bernard Burchell used.
The average duration of an orbit is taken to be the most reliable
parameter reported by astronomers due to it being a comparatively
simple observation. The dates of perihelion and aphelion being
also direct observations are thus the second parameter of reference.
Estimates of distance to the Sun are derived from calculation
and theories on gravity, and thus have a greater chance of inaccuracy.
But the duration of the orbits must vary from one orbit
to the next, due to the gravity of the other planets. This is
the essence of the question being here resolved with the OGS15
Their is a strong blind corroboration with Bernard Burchell
(alternativephysics.org) that the velocity-vectors have been
'tweaked' by Horizon to agree with General Relativity, whereby
they cease to have agreement with themselves, and with the very
principles of geometry and logic. But this does not seem to
effect Horizon's positions of the planets, which are still good
and consistent with the Newtonian-Planck-computational paradigm
But it is clear that Horizon Ephemeris are not using an evolutionary
3D-n-body algorithm. Instead they are likely
using a statistical process which is mathematically more complex,
but lacks internal congruence. This is such that their calculations
result in 7%+ errors in their velocity vectors.
It is clear at least that Mercury's orbit is short by a day
between 1940 and 1999, and
that could not occur in an evolutionary process. (See Mercury)
The exact and corrected velocity values that I reverse engineered
from the Horizon Ephemeris' postional data and orbital durations,
are given for the major planetary bodies, together with the
exact formula for 3D n-body-gravity
in the section:
How to Build N-body-gravity Algorithm