In the Introduction we noted that Jupiter's Perihelion Precession has been observed by utexas.edu to be 6.55 arc-seconds per Earth-year (as/Ey) whereas their given theoretical (Newtonian) prediction was said to be 7.42 as/Ey. Though it was not clear which particular orbits were observed or predicted. And this vital detail is a particularly glaring omission which is fairly typical to note.

The 3d-n-body-gravity algorithm OGS15 (orbit-gravity-sim-15.exe) offers Scenario [25] which shows individual fluctuations per orbit of Perihelion Precession in the region of +-400 as/Ey. Optimal orbit counts are 20 orbits or 77 orbits to balance this fluctuation caused the gravity of the other planets. From 1785 to 2023 AD the Perihelion Precession of Jupiter yields 9.06 as/Ey as a Newtonian value for the 20 orbits. For 77 orbits the amount is 7.68 ending with the perihelion of 2699 AD.

The following data extracted from Horizon Ephemeris shows how much Jupiter's perihelion deviates from its average orbital duration of 4332 days. Notice the difference in days for each orbit (highlighted) and the last column which is then converted to the standard measurement as arc-seconds per Earth-year. This is mostly caused by the gravity of Saturn.

It should be clear from this graph that oscillations to Jupiter's Aphelion and Perihelion Precession follow a 913 year cycle which is very close to 31 orbits for Saturn in synch with 77 orbits for Jupiter. This is also evident in the section on Saturn which shows a very similar pattern. But it is not very meaningful to give an average to the Perihelion Precession, because one will notice that as the wave-form decreases amplitude, the values decrease individually, but increase as an average. The point being that any such study that does not give the precise years for the average follows weak methodology.

Nevertheless the observations claim to yield 6.55 as/Ey, and the OGS15 Newtonian algorithm yields an amount of at least 7.86 as/Ey for aphelion and 7.68 as/Ey for perihelion. So this is evidence against Relativity, yet again, because Relativity claims that observation should be more than the Newtonian calculation. (See the section on Mercury for details). Even though nowhere is it evident what that shortfall for Jupiter should be; it matters not, because the numbers are categorically in the wrong direction. Of course the Relativists once more demonstrate weak methodology when they only take into account one planet: Mercury.

But we are compelled to notice that to use all-round averages is also bad methodology because individual orbits oscillate by a combined positive and negative value of 100 times more than this average. Only a 913 year cycle is meaningful as an average and our observations are just not reliable over such a time frame extending back to before the invention of the telescope.

That NASA's error-margins are greater than my own is realized when we consider the question of the average duration of Jupiter's orbit. This is given by the NASA fact sheet as being 4332.589 days or 11.86177 years.
https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html

But with individual Perihelions varying by as much as a month different from the average orbital duration, (see extract at top of page) it is vital to know which orbits in particular are being averaged, when offering amounts of such precise decimals with claims to within a single minute of time. Because the crucial sample size and detail information is just not offered, I had to try a variety of samples when using the starting point of perihelion for Jupiter of 18 December 1773 @ 12h53.

Scenario [29] and Scenario [20] of the OGS15 algorithm evolve an average orbit of the given 11.86177 years over 77 orbits and 20 orbits respectively.

Both scenarios are then evolved to the 1999 perihelion for Jupiter.
Now Horizon Ephemeris had given the date for the 1999 perihelion as May 20th.
But the scenario that uses the 20 orbit average gave that date as early on May 19th.
Whereas the 77 orbit average gave that perihelion taking place on May 22nd.

So the 77 orbit average of 11.86177 years will require those first 20 orbits of Jupiter to yield a higher average of 11.86228 years, see?

Now it seems to me that with the orbit fluctuating so much, that the observation of the perihelion date of 20th May 1999 should be the benchmark to aim at. I selected that date because it was widely confirmed as having been observed as Jupiter's perihelion by numerous websites. This historical 'fact' should be confirmed after 20 years of corroboration.

And in order for the algorithm to split the difference and arrive at Jupiter's perihelion on the given date of 20th May 1999, this can only give a 20 orbit average of 11.861917 years, which is 4332.640 days. (Not 4332.589). So that's a discrepancy of about 1 hour over 237 years.

Now its hardly meaningful to go back in time further than 237 years of observation as that amount represents a fair portion since the discovery of Uranus, and also fits with the optimal amount of 8 orbits for Saturn, Jupiter's most significant partner. This is fairly close to 3 orbits of Uranus, and thus this is the only meaningful sample size for an average duration for Jupiter's orbit.

But another fact sheet of NASA:
https://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html
gives Jupiter a 4331 day orbit, which is 11.857 years,
whereas the Horizon Ephemeris is happy with 11.862615
https://ssd.jpl.nasa.gov/?planet_phys_par

My own value fits the given observational date of 20 May 1999 perihelion with an amount in between those two values, so I have to conclude that my algorithm is most accurate at 11.8619179 years for Jupiter's orbit. Thus all my other scenarios starting 1773 therefore use this more accurate value.

Now the difference between those two NASA values is close to 2 days, whereas my algorithm can happily reconcile with the observational data to within 4 minutes. This takes my little laptop 10 hours to compute a quantity of 237 years.

Scenario [39] and Scenario [30] do the same computation as Scenario [29] and Scenario [20] with 10 times better accuracy. But I have never run them due to Windows 10 being a fairly tragic clone 10 times slower than the older more efficient operating systems like good old Windows XP.

Despite this setback, my computational processes seem to quite happily keep up with, and even out-perform all the super-computers at NASA. The formulae I derived for this study on 3d-n-body-gravity is free on this page: N-body-gravity Algorithm. This is of course due to logical positivist methodology.

So once more I say: If you are not building your own 3d-n-body-gravity-algorithm, then you have no right to claim a bona fide understanding of gravity, the scientific method, Newton, or poor old tragic, Albert Einstein. Though he is not as tragic as those that follow his pseudo-science so blindly. As it is, the previous algorithm OGS12 demonstrated that Jupiter should move away from the sun at 800km per orbit if gravity between Sun and Jupiter was delayed to move at the speed of light.
See link: www.flight-light-and-spin.com/simulator/relativity-jupiter.htm

Of course that would make the solar system have to be radically younger than all geological samples suggest. And yet with gravity calculated as instant, all Einstein's formulae given the boot, the result was this accurate:

Scenario [29] and Scenario [20] of the OGS15 algorithm are useful for other comparisons too. How much difference to the Perihelion Precession and the Aphelion Precession will be generated by a difference in orbital duration? How important to such precession is the selection of the orbital sample?

It is thus my conclusion that the algorithm driving OGS15 is the only known logical answer to 3d-n-body-gravity; which represents the best completion of that process of understanding not only of gravity, but the very scientific method itself which began 400 years ago with Newton.

This is especially so because Horizon Ephemeris use statistical models, and not evolutionary algorithms according to laws on gravity as they occur temporally in nature. We can see this because their given velocity vectors, yield an inexplicable error of ~7.5%. This is a consistent problem which required radical overhauling of their given velocity data for every scenario I developed, and for every planet.

Although fortunately, the velocity vectors supplied by Horizon Ephemeris where in correct proportion to one another as regards the X, Y, and Z dimensions. So it is still an immensely useful resource, despite problems with the velocity vectors. This issue was also corroborated by Bernard Burchell. Supplied are details and examples for those velocity vector errors made by Horizon Ephemeris for Mercury in the section: Sorting Horizons, and also in the section on Uranus.

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