Earth's Orbit: Aphelion and Perihelion Precession

 The major difficulty with the Earth's orbit is the Moon. Of course our Moon is the largest in the solar system proportional to the parent planet. So typically there is plenty of data available for Earth's Perihelion and Aphelion. But it is the data for the Earth-Moon barycenter that is meaningful for understanding gravity in the context of this algorithm. Note that references in this particular study referring to 'Earth' are normally referencing the 'Earth-Moon barycenter' unless otherwise specified. You should be able to clearly see that Earth's Perihelion Precession coincides with the orbits of Jupiter roughly every 12 Earth-years. With fluctuations varying by 1000 Arc-seconds per pair of orbits, the average error-margin would clearly deviate by +-1 arc-seconds after 500 years of observation. So it would be pretence to suggest that even after 250 years of observation the average could have a meaningful error-margin better than +-2 as/Ey. However, by properly understanding the cycles of the inner planets as they aggregate against the orbits of Jupiter and Saturn, we can attain useful averages despite this.

 All historical studies use the weak methodology of 100 year samples. But with a single deviation of +-500 as/Ey, the average jumps so much, that the idea of a meaningful observational average is going to be woefully inaccurate unless we use 237 orbital pairs. This can be seen in the following data where the highlighted average varies widely between individual years, altering that average considerably depending on which is the starting and ending orbit.

 The 59th orbit gives a somewhat similar average to the 238th orbit because these numbers aggregate fairly evenly with the durations of the orbits of Saturn and Jupiter. Those details are discussed in the section Jupiter+Saturn. Note that the optimal sample to measure the average Perihelion Precession for Earth is 237 pairs of orbits. However, because we need 2 orbits to get a single reading, the 238th orbit (2137 A.D.) yields the optimal average for those 237 orbital pairs.

 Note that in the 2 samples above, error-margins are different as well as the starting dates, as well as measurements to respectively Perihelion Precession, and then aphelion. And yet the results are very similar after 237 orbital pairs. These amounts are thus greater than the values quoted at the Introduction. The observation of 11.45 as/Ey and theoretical value of 11.87 as/Ey that was there quoted from utexas.edu do not specify which orbits are evaluated. As I am an analyst, not an astronomer, I can only take their observation at face-value. Though I am certain that the Newtonian Perihelion Precession of the Earth-Moon barycenter is more than the observation regardless of whether we use their model or my algorithm. But in both their and my analysis, the answer is still contrary to Relativity which predicts that Newtonian gravity theory should be less than the observation. See the sections on Mercury and Mars for a far deeper analysis of that. However, even for the Earth, the 237 year cycle is still not perfect. The fluctuations of Perihelion Precession between individual orbits are fairly radical in this sample size as should be clear in the extracts either side of the 237th orbital pair (238th orbit). The next scenario runs for the larger 913 year sample, as well as other selected dates. Though its doubtful that observational data will be reliable going back in time, future generations will benefit from this in the centuries to come.

 The data above is interesting for quite a few reasons. Orbit #914 is the 913th orbital pair of Perihelions and is extremely close to the theoretical amount quoted from utexas.edu being 11.9 as/Ey. The other highlighted amounts are optimized every 237 years. The 474th orbital pair is very close to the observed value from utexas.edu, being 11.5 as/Ey. (See their details in the Introduction). There is thus no room here for any theory other than Newtonian gravity having any effect. Also note that the celestial New year advances by about 1 day every 70 years, from 17 March 1774 to 30 March 2722 AD. This shows that the algorithm is correct for the difference between tropical year and sidereal year caused by Axial Precession. In this section: Cause of Precession of the Equinox, there was an unexpected and extraordinary theoretical conclusion as to why this occurs. In the bottom left of each sample you can see how the duration of the year averages alternatively above and below the required amount, reflecting an accuracy of a fraction of a second over most of a thousand years. With individual orbits varying by as much as 12 minutes due to n-body-gravity interactions, that is as good as it gets with Scenario [23]. Scenario [33] is 10x more accurate, but 10x slower to execute. But most interesting, is how the Earth's orbit will consistently circularize in this time frame. The extremities of the 'ellipse' moving closer to each other by the massive amount of about 100 000 km over the given thousand years. (I'll get back to this in a wider context a bit later). It is visible that the Earth-Moon barycenter will advance by about 3 degrees per thousand years in these extracted graphic images from the OGS15 algorithm:

 . So the average precession for the major-axis of the Earth-Moon barycenter is in the region of: 11.5   to   12.6 arc-seconds per year .

The problem being that the observational data could not satisfy the requirements for the effect on the Earth-Moon barycenter of Uranus. We would actually need a sample 924 years for Uranus, but is more closely aggregated to 913 years to properly account for Jupiter and Saturn. And that is outside any observational time-frame. But notice that in the earlier example that started at 1900, the 59 year average is very close to the 237 year sample that began at 1773: 12.5 arc-seconds per year (as/Ey).

Scenario [49] is in 1500 second quanta. This causes a computational error-margin of about 0.26 as/Ey over the 237 orbits of Earth. Scenario [33] and scenario [53] are 10 and 100 times more accurate respectively. The latter would take a 40-day process to evolve full-time on my 1.5 gHz
Windows 10 glorified pocket calculator, so you could get better results than me when using my software.

If you do extract better Perihelion Precession data from OGS15, please let me know by contacting me here: cosmology.africamotion.net. Though you may want to first see how to operate the algorithm here:
Orrery.

I  prefer to openly express the uncertainty in the quantities, because an open methodology always offers transparent room for improvement. This is a process of increasing accuracy, never a final answer. It is dialectic methodology, not dogma.

The Earth's orbit is becoming more circular. This is true also of Jupiter, Saturn, Uranus and Neptune. Mercury and Mars, the least massive bodies, and the most eccentric orbits, are however becoming more eccentric by contrast. Mars' orbit is analyzed in detail in the next section:

 see also: — Earth & Relativity

 Sections of this Article by web-page N-body-gravity Algorithm Introduction Mercury Perihelion - Perihelion Precession - Precession of the Equinox Mercury - Venus - Earth - Mars - Jupiter - Saturn - Uranus - Neptune Jupiter+Saturn - Mars+Jupiter+Earth - Orrery Download - How to Build N-body-gravity Algorithm - Sorting Horizons Newtonian-Planck Gravity - Sidereal Year or Tropical Year Cause of Precession of the Equinox - The Scientific Method Discussion Forum : cosmology.africamotion.net page 7