Saturn Orbit

Saturn's Orbit

The orbit of Saturn is notorius for its peculiarities. Estimates for its distance of aphelion vary by close to 1%, with NASA's 'fact sheet' giving a maximum distance 15014.5 million km, whilst NASA's Horizon Ephemeris offers 15005 million km. Unfortunately the Cassini misshap resulted in that spacecraft being unavailable to give us a clear measurement because it crashed into Saturn for questionable reasons. That the Cassini spacecraft was cruelly murdered half a year before Saturn reached aphelion was an epic tragedy from this philosopher's perspective.

But its not just the distance of the extremities of Saturn's orbit which vary so much. The duration of the orbit being 10759 days is just an average; with individual orbits fluctuating by as much as a dozen days either side of that amount. But the times between perihelions and aphelions vary even more than the duration of the orbit itself. The wild swings to the angle of the major-axis of the orbit make it almost meaningless to give any overall average to its orbital parameters. Such averages should only ever be defined in terms of a particular sample of orbits.

The data extracted from Horizon Ephemeris above shows quite a number of interesting aspects of Saturn's orbit. There is a distinct duality to Saturn's orbital structure. The last column shows that individual alterations to Satuarn's perihelion (and thus its major axis) can easily vary by over one and a half full degrees of angle. This wild two-faced behaviour is clearly mostly due to Jupiter and Saturn having a 2:5 orbital duration ratio. (Though a ratio of 31:77 is more accurate).

In the Introduction we were informed that Saturn was observed to have an average Perihelion Precession of 19.5 as/Ey (arc-seconds per Earth-year) by utexas.edu. even though no specific dates for particular orbits were offered. With Saturn only completing a mere 8 orbits since the discovery of Uranus we would certainly be hard-pressed to achieve a meaningful observational average to fluctuations of Saturn's major axis.

The average Perihelion Precession for Saturn is:

20.01

arc-seconds per year

Scenario [26] of the OGS15 algorithm begins in 1773, but because we need 9 orbits to get 8 fluctuations to the major axis, the average Perihelion Precession is:

orbit #	Average Perihelion Precesion as/Ey	Perihelion shift for orbital pair as/Ey	from 1797 AD to
7	4.06	-190.23	1973
8	29.05	+178.98	2003
9	3.38	-176.27	2032
31	29.50	+328.20	2681
32	20.01	-264.75	2710

Once more we see how an unqualified average is easily warped by the individual orbit fluctuations being 10 times larger than the average itself. So even our 8th orbital pair (orbit #9) will given a meaningless average (3.38 as/Ey) over the sample that closely synchronizes the 8:20:3 ratio with respectively: Saturn; Jupiter; Uranus. Only the 913 year average makes any sense. The better ratio is: 31:77:11

The pattern is clear that the variations to Saturn's aphelion are becoming greater individually as well as for its average. While in the previous section we saw how those amounts for Jupiter were diminishing individually, but increasing on average.

The important point here is that taking an average is only meaningful if that average fits into an amount that is divisible by the cycles in the graph. For both Jupiter and Saturn follow the same cycle 913 years: 31 orbits for Saturn and 77 orbits for Jupiter. Is it possible that observational data is reliable on that time-frame? Maybe not for us, but detail of this study could become relevant 700 years from now.

The following table is divided into two sections, the first 3 samples showing variations against the average, whereas the second 3 samples show the better averages in the 913 year cycles. This is the same data used to make the graphs above, from Scenario [66] of OGS15 beginning 1900 AD.

orbit	precesion average as/Ey	orbit average in days	duration 1 orbit in days	perihelion average mil-km	perihelion 1 orbit mil-km	aphelion average mil-km	aphelion 1 orbit mil-km
1	-	-	10754.7	-	1350.4	-	1503.0
7	-29.7	10753.7	10749.3	1349.6	1350.5	1504.3	1503.5
16	7.3	10757.0	10770.5	1349.0	1347.7	1505.7	1507.9

31	20.7	10759.2	10756.1	1349.9	1352.7	1505.1	1502.1
62	21.5	10759.3	10757.1	1352.2	1357.3	1502.8	1497.6
93	21.8	10759.3	10757.8	1354.9	1362.1	1500.4	1492.9

As you can see, the average perihelion increases its distance, whereas the average aphelion decreases its distance. This clearly shows that the orbit of Saturn must be in a process of circularizing.

Remember NASA's 'fact sheet' gave a maximum distance 15014.5 million km, whilst NASA's Horizon Ephemeris offers 15005 million km. We need to be mindful that there is a difference between the average maximum, and the ultimate maximum.

However in Scenario [26], Saturn begins its first aphelion of August 1782 at a distance of 1509 million km and never again reaches that far out, with aphelion getting closer to the Sun. From 3609 AD the aphelion is always below 1500 million km up until to my last calculation 5423 AD, showing that the orbit is getting less eccentric. This is also clear in the graph because the perihelion is increasing its distance over this time-frame.

Its not suprising to me that the detail of Saturn's orbit is so inconsitent in NASA's published data, yielding that difference of 10 million km (1%) to the aphelion. This is because Saturn yields very few orbits in any given time-frame, and is also radically effected by Jupiter. So because nobody else is using a genuine 3D-n-body-gravity evolutionary algorithm, that lack of understanding will result in a substantial errors in such predictions.

We also need realize that whenever we see an 'average' distance from the Sun; or an average for distance of Perihelion or Aphelion; or an average for Perihelion Precession - or indeed the Aphelion Precession - then it should always be qualified by the number of orbits, and also the specific starting orbit. Those averages vary considerably - and in effect there is no overall average.

As we can see from the individual samples in the graph, the duration of Saturn's year varies by more than 20 days. This is over 2400 arc-seconds for the orbit or 80 arc-seconds per year of Earth. Jupiter really plays havoc with Saturn's orbit. So its no surprise that there are such radical discrepencies in measurements of Saturn's orbit. If you look at the last column on the graph above you can see that individual samples vary by at least by 15 million km as regards Saturns aphelion.

We get s similar problem with Jupiter when trying to determine if any post-Newtonian theory is affecting either orbit. The observation for Saturn is given as 19.5 as/Ey whereas the least Newtonian prediction from my algorithm averages 20.66 as/Ey. Relativity is supposed to increase that Newtonian prediction, not decrease it! So once more the data has to be counted as proof against any Relativistic prediction.

however, our source data (see Introduction) claims that the Newtonian prediction should be 18.36 as/Ey. But that was not calculated by an evolutionary process that uses a 3d-n-body-gravity algorithm. That was a 2D numerical process. So we need to compare Horizon Ephemeris and OGS15 to see the amount of agreement.

Its a fairly close comparison. Bare in mind that these are all measurements of Saturn's barycenter. With my current equipment I just do not have the processing power to improve the accuracy beyond this. But this is fair enough for computing the fluctuations to perihelion and aphelion.

The biggest problem being that the Horizon Ephemeris, still have not rectified their ongoing velocity vector problem. And that problem has absorbed half the effort in this study. Because all the velocities they offer need to be multiplied by over 7% to begin to approximate the positional data. For the given velocity of Saturn on 2 January 1900 @ 00h08 the velocity needed to be multiplied by 1.073890795 to reach an average orbital duration of 10759.22659 days by 3718 AD, 62 orbits later.

That 7% error also fluctuates from planet to planet and position to position. Their error varying by 7.3% to 7.8% with no obvious pattern accounting for the 0.5% variation within that amount. So it is not just a matter of inaccuracy or even subtle laws of physics, but it is a categorical error in their statistical process. That could never happen in a genuine 3d-n-body algorithm. Their error is now outlined in precise detail in the next section.

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