Newtonian-Planck Gravity

Newtonian-Planck gravity differs sleightly from purely Newtonian gravity. For Newton, time was infinitely divisible as is used in Calculus. But infinitely divisible time is now replaced by quantum time. The general idea of quantum time had actually been demonstrated in ancient Greece by Zeno's paradox.

The essential nature of quantum time is most clearly demonstrated in evolutionary n-body computer algorithms.
All orbits are thus best calculated as many-sided polygons. At its most accurate, Mercury would have well over 10^50 sides to its polygon-orbit. But because of limits in computational power, the number of sides is reduced in the algorithms. A polygon-orbit of about 50 million sides will be accurate to 0.025 arc-seconds of angle for the perihelion and aphelion positions. Such an angular quantity for Mercury amounts to about 0.15 seconds of time per quanta. This is the computational accuracy of Scenario [41] of the algorithm OGS15 (orbit-gravity-sim-15.exe).

Having calculated the Newtonian origin of Perihelion Precession in the OGS15 algorithm of a planet such as Mercury, it is clear that deviations to the extremities of individual orbits vary considerably. Some orbits precede by over +80 arc-seconds per century whilst other orbits recede by lower than -40 arc-seconds per century.

This natural flux to the major axis is certainly caused by Newtonian-Planck-gravity due to the varying positions of the other planets - for the most part. Though it is possible, but unlikely, that there exists any law other than Newtonian-Planck-gravity in effect. The essential differences between a purely Newtonian orbit and a Newtonian-Planck orbit are for the most part smaller than the error margins, and thus it can be taken for granted that the two terms are virtually synonymous unless otherwise specified within this article.

So an entire century of orbits for Mercury will often yield a deviation (natural flux) to the total over 120 arc-seconds per century averaged; just depending on which orbit is selected as the starting orbit. All the other widely published theories on the matter only give the crude average, and fail to note that some perihelion and aphelions recede, while others precede.

Running the Newtonian-Planck algorithms at sub-optimal speed, so that the jumps of quantum-time are too big; will cause a quantum-error-margin. Interestingly, this variation as well as the natural flux to the major axis, can be ironed out by simply letting the evolution take place over numerous amounts of orbits with positive and negative error-margins eventually canceling each other out.

But it is vital to note the natural flux to the major axis varies for each planet. This amount is least for Mercury due to the eccentricity of its orbit, but it can often be over a full degree (3600 arc-seconds) for the orbits of other planets such as Venus and Saturn. For Neptune it can even occasionally be a full 18 degrees. As has been presented in the section Jupiter+Saturn, a  59-year sample is better than the crude 100 year sample for an average because of the synchronicity of the orbits of Jupiter and Saturn. Although the convention is still to express these amounts per century or per year.

years yields a very good average for inner planets, and 913 years is virtually optimal. But there is no absolutely ideal sample-length, which is why the OGS15 algorithm offers a wide variety of Scenarios across various dates and rates of computation for all the major planets.

Comparing aphelion and perihelion is just another check. Had other studies used both aphelion and perehelion in analysing Mercury's orbit properly, they would have realized that the aphelion actually has a natural flux half of the perihelion, and thus they would have improved their results by 100% had they used the aphelion as the benchmark instead.

Over the years, there have been numerous attempts to observe and model Mercury's Perihelion Precession. These almost always have only managed a crude average due to the detail required being too vast for non-computational mathematical models. As can be seen in the table below, it is proved that including the Z-axis in gravity evolution decreases the Perihelion Precession by an average over 60 arc-seconds per century.

But we also need consider the way in which the angle is measured after the evolution itself. Are we measuring the angle on the flat 2D ecliptic plane, or is the angle measured in terms of the 3D orbit itself? Using either of these two methods can yield about a 5% difference as a result.

A table of Mercury's Perihelion Precession in arc-seconds of angle per century:

Claimed Observation
in model
of angle
UC Riverside
Le Verrier
Bernard Burchell
Horizon Ephemeris
measure angle in 3D
2D or 3D?
Horizon Ephemeris,
angle on ecliptic 2D
2D or 3D?
OGS13 algorithm 2D
OGS15 algorithm 3D
angle on ecliptic 2D
OGS15 algorithm 3D
measure angle in 3D

The difference between the observation and theoretical model has been widely assumed to be proof of Einstein's theory of Relativity. Einstein predicted that Newton's theory would yield a shortfall of 43 arc-seconds per century in comparsion to observations. With gravity evolving on the Z-axis accounting for 60, and the natural flux of individual varying perihelions being 120, neither of which have been noted historically, nor considered for in the 2D ring-planet models, it can easily be seen how any historical claims are dwarfed by the unseen error-margins within their own methodology; several times over.

The second item on the list expresses the 43 arc-second per century difference attributed to Einstein's theories. However it also gives an amount that is about 10 times more than the others. Miles Mathis reports that Einstein claimed these amounts himself.

In the section Precession of the Equinox we unraveled how this discrepancy was said to be caused by the Earth's axis rotating. Importantly this is not the rotation of the Earth on its axis, but the observation that axis itself is rotating about every 26000 years.

There are various issues here because all the numerous other articles quoted and researched have not properly explained how that large discrepancy (from Riverside and Einstein) was precisely arrived at. My first assumption is that it was just the local spatial movement of the observer on the Earth which was effecting the observation. But this gives an amount far smaller than required.

My next analysis was that it was caused by using a tropical year as a universal measurement of time, rather than the more apt sidereal year. This resolved the problem by realizing that Riverside and Einstein were using an incorrect temporal measurement. The next section
Sidereal Year or Tropical Year  explains that detail.

Most vitally when examining all the planets we can see that the theoretical amounts do not all fall short of the observational accounts. If Einstein's Relativity was valid, an amount equitable with the 43 arc-seconds per century attributed to Mercury's Perihelion Precession would also be in evidence for the other planets. Nowhere could be found any formulaic result or even numerical detail for the other planets as regards Relativity. Yet it is a fair point of basic logic that if the Relativistic claims are valid then the amounts observed should at least all be above the the prediction. They are not:

The next table includes the previous data, as well as my own, and also some data from Horizon Ephemeris. For reasons of method the primary focus is on Mercury. Where two values are given for Mercury it is due to two different standards of measurement. See the section on Mercury for that explanation. These scenarios often take weeks or months to evolve, and I will update this table when the results come in.

Aphelion and Perihelion Precession
latest update: March 2020
(exact details for the planets are available on their various pages)
measured average in arc-seconds of angle per century:

567 or
483 or
483 or
36 !!

~0 ?

*Not Averages.
For the outer planets the sample from Horizon Ephemeris and some of my algorithms have a small orbital count, and are not effective averages. Thus these amounts will be distorted by individual fluctuations of orbits being vastly different to any crude average. These quantities still deserve quotation because they are the only values that could form part of a realistic observational time-frame. Thus it is clear that averages are a fairly weak way of trying to ascertain if there are any non-Newtonian principles effecting Perihelion Precession for the outer planets; at least in the current era. Specific orbits are required to evaluate the outer planets.

Note that Jupiter's Aphelion Precession is calculated to be 7.86 as/Ey for the years 1900-2835, (77 orbits) but by 4661 AD (after 231 orbits), it will have increased to 8.27 as/Ey as the orbit gets less eccentric.

The results computed can be improved by existing Scenarios in the OGS15 algorithm but for which my little computer is just to slow to complete in an effective time-frame. Should you wish to participate, you can help obtain these results by simply running the algorithm for a length of time then post your results on my Cosmology forum:

Saturn's orbit is also circularizing like Jupiter. Starting in 1900 AD, the Aphelion Precession for Saturn will be 20.86 (31 orbits), but after the evolution of 93 orbits will become 21.83 as/Ey.

!! It is not possible for any observations to have been made of the Perihelion Precession for Neptune as it has only passed perihelion once since its discovery!

Also note that references to Earth, should in effect only be describing the Earth-Moon barycenter in the context of trying to ascertain the effect of gravity on Aphelion or Perihelion Precession. Other text may simply use the term 'Earth' in that regard.

The essential code of the 3D-n-body-gravity-algorithm operating in OGS15 is freely available here as an act of good faith on my part: How to Build N-body-gravity Algorithm
You can also download the algorithms for free here: Download

Some Speculation:
Regardless of the hard details in the computation, the mind always wants to jump ahead, to see the patterns in the data, and use them to inductively predict way beyond the data. I have two models in mind as to what awaits the future evolution of the solar system, and these two models are quite at odds with one another. I would need radically improved processing power to figure which one is correct. The orbit of Mars being the prime example of proof; that same Martian orbit which Horizon Ephemeris will not predict even 500 years into the future. Thus it is likely that they are also in two minds.

The first model is a stable system. As the Perihelion of Mars approaches Earth's orbit, so the gravity of the Earth drags Mars forward, speeding it up. This pushes Mars outwards, and its orbit becomes more circular thereafter. As the aphelion of Mars gets nearer to Jupiter, so Jupiter slows down Mars, and again, the orbit is pushed away, becoming more circular. This occurs because Mars is slower than Earth, but faster than Jupiter.

So all the planetary orbits regulate one another in a similar manner. I have certainly read words similar to this elsewhere. In a previous chapter, I demonstrated this principle in an algorithm, although it was not to any specified scale - not describing any particular planets, just a general trend observed fairly frequently.

Orbital eccentricity over about 86% of pure circularity does certainly increase circularity. This is a context dependant value, not absolute. But it serves all the planets of the solar system. (% = distance of perihelion over aphelion x 100).

The second model is dynamic. And the most striking information supporting it is statistical. Looking at the details in the orbital evolution, both from my algorithms and Horizon Ephemeris, it is just a fact that the two most eccentric orbits, Mars and Mercury, are also the two smallest masses, and these two orbits are both becoming increasingly more eccentric. Whereas all the other heavier bodies have quite circular orbits by comparison, and all of these are in a process of becoming more circular still. Mars is 83% eccentric, Mercury is just 66%.

The dynamic model also has algorithmic evidence supporting it. OGS16 is still under construction. Its purpose is to attempt to show how retrograde moons are bodies which are actually alternatively shared between planets. So the outermost moons of Jupiter and Saturn get pulled away from their parent body by the gravity of the Sun. They then move into a spiral orbit which is unstable, and are then captured by the nearest planet. Often this results in a moon with a retrograde orbit. This can occur. But the only algorithmic proof I have is also not to scale for the solar system. But it does have a specified scale quite close, involving a pair of hypothetical planets about 3 times more massive than Jupiter, in orbits similar to Jupiter and Saturn. I'll follow this up hopefully in future chapters in more detail.

So the algorithmic evidence is more accurate for the dynamic model over the stable model. Albeit not conclusive proof. It seems possible that Merury could end up as a moon of Venus. Which raises the question as to where Mercury originated from?

I have already published a video ( which demonstrates the algorithms that prove that at one point in time all the inner planets were once moons of Jupiter. The theoretical speculation of Velikovsky may be methodologically weak, but the inductive intuition of his as to potential movements around the solar system is certainly a fairly good one.

So Mercury would be a more recent lost moon of Jupiter because both Earth and Venus have very stable orbits. And these orbits which are becoming increasingly stable. It may be that we should not consider Mars and Mercury to be 'proper planets'. Instead they could be termed 'radical' planets due to their unstable orbital dynamics. Of course Mercury would have had to pass by the orbits of Venus and the Earth to reach its current position. Those dynamics require precision way beyond my current equipment.

But another interesting question arises. The orbits of Jupiter, Saturn, Uranus, Earth, Venus, and Neptune are all certainly becoming more circular. So what caused them to be less circular before now? If we postulate the hypothesis that such dynamics eventually result in orbits that are almost circular, then some fairly recent event must have distorted them to their current eccentric elliptical shape.

If we look at the details in Saturn's orbit, we see that over the next 3000 years Saturn's aphelion will decrease by a total of about 10 million kilometers. Its Perihelion will increase at the same rate. Saturn's aphelion and perihelion are about 1500 and 1350 million kilometers respectively. Which means the orbit will reach circularity in just 20 thousand years.

So inductively we have to conclude that several thousand years ago something large enough to significantly disturb Saturn and all the other planets passed within the solar system.

Neptune being very circular was least effected, as was Venus. It is possible that this unknown rogue body dislodged Mars and Mercury from their original orbits as Moons around any of the major planets. But they could have departed their parent body (most likely Jupiter) simply as a result of the Sun's gravity in more ancient times too.

Mars may well become a second moon of Earth in less than 200 thousand years! There are many potential scenarios with very subtle differences resulting in a variety of outcomes. Any of the three bodies: Earth, Moon and Mars could collide.

But the most likely scenario I can reckon is that because Mars moves slower than Earth, it will fall behind the Earth's orbit at its nearest rendezvous. This will slow the Earth down which will cause a greater orbital eccentricity to develop for the Earth - and solar seasons to come into effect. Where will the moon be? Likely the Moon will be effected by Mars most dramatically when the Moon is also behind the Earth. Thus the Moon will either be dragged away completely, becoming a rogue body itself, or a moon of Mars. I do guess that it is most likely that the Moon will just settle into a wider orbit. But it could even disintegrate into a ring system.

This dynamic is thus also a possible cause of any of the rings in the solar system forming from disintigrating moons during the encounter with the rogue body that certainly seems to have distorted Saturn's orbit quite profoundly. I will have to name it sometime.

So where does Mars go next? Certainly it could go back outwards as it is sped up by Earth. But the dynamic is so volatile that Mars could end up a Moon of Venus, or even cause more disruption to Mercury's orbit. Mars could even disintegrate into an asteroid belt as it is a fairly beaten up little planet already. Apologies! My imagination is running ahead quite excitedly.

In both the stable and the dynamic models, the 6 major planets stabilize one another. But it is the radical planets, Mercury and Mars that are open to question in the dynmaic model. Saturn must have come very close to going rogue itself as its orbital eccentricity is only a few percentage points closer to circular than Mars is.

When analyzing Mercury's Perihelion Precession I extracted data from Horizon Ephemeris for Mercury's perihelion from 1774 to 2011 AD. Now compare that data to how Mercury evolved in the OGS15 algorithm. We just want to look at the distance from the sun for those 2 perihelions separated by 237 years or 984 Mercurial orbits:

The comparison between Horizon Ephemeris and OGS15 are more accurate than I had hoped for! Just 8 km discrepancy over 237 years of evolution, which is a rate of just 8 meters per orbit of Mercury.

Recall that with Jupiter the difference was about 4 thousand km over the same time frame. But with Jupiter the timing discrepancy was just 4 minutes (1 second per year). Whereas with Mercury OGS15 is 9 hours short for the Perihelion date, but my orbital duration average is about 2.5 hours longer (9 seconds per orbit).

It is quite surprising that there is good agreement between OGS15 and Horizon Ephemeris data for the years 1773 and 2011. But for there is a wider disagreement with their data for the years 1900 to 1940.

But more to the point of the evolution of the solar system, is the change to Mercury's Perihelion as a matter of distance. Both models agree on Mercury's perihelion getting nearer the Sun at a rate of 13 km per year. I then infer that my data for aphelion is good enough and that Mercury will be getting closer to Venus at about 11 or 12 km per year. (You may want to double-check with Horizon Ephemeris on their aphelion values yourself).

With Mercury and Venus being only about 30 million km apart, its an easy sum to see that there is a very good likelihood of Mercury going into orbit around Venus in less than 3 million years. This amount is an approximation, with the effective gravity of Venus getting larger as Mercury gets closer, the true arrival will be much sooner than that. (Or in the stable model, Venus slows Mercury, which effectively pushes it away.)

If Mercury goes into orbit around Venus, this will cause Venus to experience a fairly radical shake-up. Its magma will likely go liquid due to magma tides forming from the gravity of its new moon. With the core of Venus going molten, iron within it will start to generate a magnetic field. The atmosphere will be altered in a way which I hazard to guess. But its not overly wild to suggest that trapped oxygen, hydrogen and other gasses will be pushed outwards from the planet core by this grinding effect. Very similar the way a centrifuge purifies substances into layers.

Well, I don't want to over-speculate. This thesis is about gravity, not really planetology. OGS16 awaits. Although I may jump ahead to see what occurs when Mars decides to pay the Earth-Moon system a visit in less than 200 thousand years time. Processing power permitting. Detail for the orbit of Mars' increasing its eccentricity as extracted from Horizon Ephemeris is available here: Mars+Jupiter+Earth.

The paradox is that if the stable model is correct, and Mars evevntually gets pushed away from the Earth, then we have to accept that the statistics are telling us something else out of sheer coincidence. There is less than 1% chance that all eccentric orbits can be reshaping with increasing eccentricity, whereas all circular orbits are getting more circular. When we consider that it is the bodies with least mass that are eccentric, then the coincidence becomes 0.01%.

However! My intuition is nagging me to put to test the famous 38mm per year that NASA reckon they have observed the Moon departing from the Earth. I am quite certain that the natural fluctuations to the moon's orbit are going to dwarf that amount hugely. Even though I am in agreement that the Moon should be departing from the Earth to some extent, purely due to the gravity of the Sun. That anyone believes this is caused by the oceanic tides shows the extent of ignorance on the matter. The Earth's magma has tides way more than the ocean, so if such effects were even possible, the ocean would have negligible influence. Never mind that it is clear to my mind, that such ideas are yet more science of the gaps.

Those who think I have my fingers in too many pies, cannot see where my toes are going!

For all the important planets: Jupiter, Earth, Mars and Mercury, I have found that discrepancies between OGS15 and Horizon Ephemeris are smaller than those within the various NASA documents. The vital difference in method being that my formula is transparent: Newtonian.

As I am not an observer, but an analyst, I have to simply pass this dialectic back to the astronomers and wait for a response. You, the reader have an important role to play. Because the dialectic of the logical-positivist method relies on another hidden part of the epistemology, and that is: the communicator.

The ordinary reader should act as the go-between, to ensure the dialectic keeps vibrant. This is an essential element that keeps honest the relationship between analyst and astronomer. Due to the introverted nature of analysis and observation, it is the extroverted nature of the common reader who needs to actively pass on the message. That often is the most neglected, and thus the vital role.

The full details will take some years to compute with better and better precision. This page will be updated periodically. But for now the results are so vital and clear that publication must proceed as widely as possible.

Please feel free to run the algorithm for more accurate results, then let me know at this forum here:

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