Uranus Orbit

 Although not everyone agrees on the exact duration of Uranus' orbit, its Perihelion Precession from AD 1882 to 1996, then projected on to 2050, is as follows:

The extracted data above shows four amounts of Perihelion Precession for Uranus. The first pair are from Horizon Ephemeris in comparison with the OGS15 evolutionary algorithm (orbit-gravity-sim-15.exe) for the second pair. These show that the time between subsequent perihelions is greater than the length of the orbit. The historical amount (1st precession) is about 51 days greater than the duration of the orbit according to Horizon Ephemeris. This is more than 2000 seconds-of-arc, which as an average is about 25.6 as/Ey (arc-seconds per Earth-year).

This calculation used the duration for a sidereal orbit of 84.0169 years (30687.7 days) from Horizon Ephemeris data given here: https://ssd.jpl.nasa.gov/?planet_phys_par

But the NASA fact sheet gives an orbital sidereal duration of 84.0106 years (30685.4 days) obtained here: https://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html

But we can also examine the Horizon Ephemeris data in full detail, and derive another value. Notice that each pair of extracts is a day apart, as Uranus crosses the Y-axis. The start of the orbit is typically described as when an observer on the planet would see the Sun move from the constellation of Pisces into Ares. So the Y-positional value changes from positive to negative in these three pairs of data extracts, like this:

 2378734.500000000 = A.D. 1800-Aug-27 00:00:00.0000 TDB X =-1.830572494374941E+01 Y = 2.126596468880682E-03 Z = 2.387978424459388E-01 2378735.500000000 = A.D. 1800-Aug-28 00:00:00.0000 TDB X =-1.830576412120087E+01 Y =-1.992298195068668E-03 Z = 2.387829491983334E-01 daydiff = 30693 = 84.035 years 2409427.500000000 = A.D. 1884-Sep-08 00:00:00.0000 TDB X =-1.829574976296597E+01 Y = 3.025797242494421E-03 Z = 2.380139599346975E-01 2409428.500000000 = A.D. 1884-Sep-09 00:00:00.0000 TDB X =-1.829578603662717E+01 Y =-1.096643151321898E-03 Z = 2.379991317371774E-01 daydiff = 30689 = 84.024 years 2440116.500000000 = A.D. 1968-Sep-17 00:00:00.0000 TDB X =-1.829680044094919E+01 Y = 3.639375536665729E-03 Z = 2.374792495390383E-01 2440117.500000000 = A.D. 1968-Sep-18 00:00:00.0000 TDB X =-1.829683213041257E+01 Y =-4.828250409043095E-04 Z = 2.374643827331723E-01 do the sums: average day difference = 30691 = 84.029 years (+-0.002)

So now we have a third value for Uranus' orbital duration: 84.029 years (or 30691 days). Note that the second orbit is four days shorter than the first. We can thus say that strictly according to the Horizon Ephemeris data, (rather than their tables) that Uranus has a Perihelion Precession of 24.12 arc-seconds per Earth-year. But if we use the fact sheet data (84.0106 years or 30685.4 days) then the amount is a little more: 25.64 as/Ey.

 The website utexas.edu and many others claim that there is an observation of Uranus' Perihelion Precession being only 3.34 as/Ey. This can only be the years 1882-1966. Horizon Ephemeris yields a result of between 24 and 27 as/Ey for that Perihelion Precession which is entirely different to the alleged observation from utexas.edu (detailed quote in the Introduction). Now if we take the other commonly quoted date for the length of orbit for Uranus, as being 84.323 years then that would be 30799.5 days which would result in Uranus' perihelion receding for the years 1882-1966. That commonly quoted amount of 84.323 years for Uranus' orbit is actually more widely quoted than the given NASA values. It is commonly used by www.astronomy.org, www.astronoo.com and hundreds of others. My own value is between those amounts. The details are fairly intricate, but if I use a value of 84.02 years for the duration of the orbit, then the date for the perihelion shifts to May/03/1882. When 84.13 is used then a more agreeable perihelion is obtained of Mar/28/1882, which is just 4 days difference from Horizon Ephemeris Mar/28/1882. This may seem a bit abstract. But when you compare these large discrepancies to my values on Jupiter it becomes clearer. Recall that with Jupiter the margin of difference between OGS15 and Horizon Ephemeris of 237 years of evolution is just 4 minutes of time. With Uranus' orbit being 7 times longer than Jupiter, we would expect an inaccuracy 7 times more. Instead the disagreement is 800 times larger. For the next perihelion of 1966 the discrepancy is 17000 times worse. So we can clearly see that these differences with Uranus are either a consequence of inadequate understanding of 3d-n-body-gravity on the side of Horizon Ephemeris, or inaccuracy in observations, and have nothing to do with Einstein's formulae. This is clear because Jupiter should be the easiest to calculate due to its vast mass being far less swayed by the other planets. Jupiter does not get its orbit distorted by Jupiter's own gravity like the other planet's do. Whereas Einstein's formula for accelerations towards light, time dilation, distance contraction and gravity moving at light-speed should cause similar proportions of disagreements across all planets. I see no record that anyone else has even noticed that perihelion and aphelion both fluctuate negatively and positively by considerably greater amounts than the alleged 'observation'. The graphs to follow now show the aphelion, followed by perihelion:

 Whilst there is some pattern obvious in the aphelion graph above, showing cycles of 11 orbits, or 913 years; at no point does a really clear pattern arise for Perihelion Precession. Once more we can see that it would have been far wiser to measure aphelion, rather than perihelion as the standard. This is because variation between peaks and troughs for perihelion are as much as five times more than aphelion, and perihelion is 100 times more than any given average. Any claim of observational average is quite meaningless. This is because since its discovery Uranus has only passed perihelion twice, in 1882 AD and 1966 AD. So there could only ever have been one measurement of a change to its perihelion. Even using the 913 year average does not work here. The first 11 orbits result in an average movement of of 9.2 as/ey for aphelion and 16.4 as/Ey for Perihelion Precession. The 33 orbit cycle gives better results for both of 2739 years.

 . Perihelion Precession average for Uranus: 4.2  arc-seconds per year .

 Historical methods claimed an expectation of 2.72 as/Ey for perihelion and an observational 'average' of 3.34 as/Ey. (See utexas.edu quote in the Introduction). Since Uranus has only yielded a single pair of observable perihelions since its discovery, the historical 'observation' has to be considered most likely the result of experimenter-bias in favor of theoretical estimates. As can be seen in the opening data extract, regardless of differences between Horizon Ephemeris and OGS15, the results are of similar proportion for that one Perihelion Precession from 1882 to 1996. Horizon Ephemeris gives 25.6 as/Ey, whereas OGS15 evolves 30.8 as/Ey. These are nowhere near the 2.72 as/Ey expectation and observation of 3.34 as/Ey from utexas.edu - But! These are still the only attempts I found after extensive searching to give full detail to the Perihelion Precession of all the planets! As it is I am a little hesitant at my own results, but not for reasons of formula - only for accuracy of process which is a consequence of entry-level computing power to a lesser extent, but more greatly for the accuracy of the source data which begins the formulaic process. My formula, being evolutionary and not statistical, has a 100% internal logical consistency with itself. The formula is free and entirely transparent here: N-body-gravity Algorithm. All other methods are opaque. But although Horizon Ephemeris is the most complete resource I have found, how reliable is the Horizon Ephemeris data in terms of internal logical consistency? I have found only one other in-depth analysis of their vector data. Bernard Burchell:

Its vital to appreciate that the Horizon Ephemeris primarily offers positions of the planets for astronomical reasons, and is almost never used for velocity-vectors. It claims that these velocity-vectors have been 'computed', but it is entirely evasive as to the formulae and gravity theory being used.

So let us take a closer look to verify Bernard Burchell's claims of the problems with velocity errors in the Horizon Ephemeris. We will use Uranus' position 1 day apart. Then we simply calculate if the given velocity will result in the given position for the next day.

Here is a sample from NASA's Horizon Ephemeris of Uranus' orbit on 2 separate days. This data was extracted in June 2018, the data itself claims to be last updated in 2013:
.
 2429652.500000000 = A.D. 1940-Jan-24 00:00:00.0000 TDB X = 1.218024646632164E+01 Y = 1.536490011176794E+01 Z =-1.011567620040021E-01 VX=-3.115080497393145E-03 VY= 2.268599762922680E-03 VZ= 4.887062818369996E-05 LT= 1.132427003882362E-01 RG= 1.960736576176021E+01 RR=-1.576235738063593E-04 2429653.500000000 = A.D. 1940-Jan-25 00:00:00.0000 TDB X = 1.217713113999823E+01 Y = 1.536716840671393E+01 Z =-1.011078892038513E-01 VX=-3.115572127171412E-03 VY= 2.267990104227816E-03 VZ= 4.887497174495546E-05 LT= 1.132417899526494E-01 RG= 1.960720812472497E+01 RR=-1.576504986240305E-04

 We use 3D Pythagoras such that v = sqr (vx^2 + vy^2 + vz^2). The xyz positions used are in astronomical units from the Sun. RG = AU = 149 597 870.7 km So on 24 January 1940, it is claimed that Uranus had a velocity of 0.00385391 miles per second or 6.20227475 meters per second. Then 1 day later (86400 seconds) at that given velocity it would be expected to move 535 876 km away - as the space-crow flies. But alas, when the positional data is examined Uranus is now placed 576 540 km away. Of course there is a tiny orbital curve involved, so we do expect a very little difference. We have effectively compared an orbit to a polygon with more than 30 000 sides. Even an 8-sided polygon differs by only 2.5% when comparing the curved circumference to the straight-line polygon. A proportional difference between those two distances above being 1.07588 is therefore a gross error of over 7.5% in the Horizon Ephemeris velocity vector data. Thus Bernard Burchell is possibly correct. It seems that the Horizon Ephemeris could have distorted the planetary velocities by over 7.5% to try and 'confirm the predictions' of General Relativity. There is a difference between using velocity and position, in comparison to the Sun; and then velocity and position, referencing the barycenter of the solar system. This will reflect a 0.1% difference due to the effects mostly from Jupiter being 0.1% the mass of the Sun. That has been taken into account anyways. It is thus not the cause of the 7.5% problem at all. The only other possibility I can see is that a NASA-mile is 7.5% longer than an Earthling mile. The error is so huge that it is similar to the type of problem that results in spacecraft crashing into planets due to somebody making a typo and confusing miles with km. Never mind the confusion between real science like Newton's theory, and the sheer illogical sophistry of Relativity.

 One issue we must consider. If the alleged perturbation of the orbit of Uranus gave rise to the discovery of Neptune in the early 1800's, and the given duration of Uranus' orbit is so widely varied depending on which resource one looks at, then we have to conclude that the pencil-and-paper mathematics of the astronomers of that glorious bygone era could be vastly superior to our computations today. How much does Neptune effect the orbit of Uranus in comparison to these discrepancies? A 3-way comparison follows between (1) Horizon Ephemeris, and OGS15, with (2) Neptune and without (3) Neptune:

 Two significant features here: Firstly the effect Neptune has on Uranus' orbit is just 0.001 year (0.36 days). Whereas the variety of given durations to Uranus' orbit we saw earlier from within NASA differ by 6 times that (2.3 days). In comparison the Horizon Ephemeris is 6 days different, whereas the widely quoted value of 84.323 years for Uranus' orbit is a duration 14 days longer than NASA's shortest value. So it is perhaps a popular myth that variations to Uranus's orbit resulted in the discovery of Neptune. After all, Galileo clearly could see Jupiter's Galilean moons, with Europa having a visibility magnitude of about 5.6, whilst Uranus itself has a visibility magnitude of, also 5.6! They may simply not have noticed Uranus for the two centuries between Galileo and the discovery of Uranus. The problem here is that the effect of Uranus on Saturn is of similar proportion to the effect of Neptune on Uranus. But Uranus was said to be simply noticed, not predicted, like Neptune was. But the various opinions on the duration of Uranus' orbit, as well as the theoretical filibuster which comprises Einstein's formula suggest that its not just a decision as to whether current understanding of gravity is weaker than that of the 1800's. The widespread acceptance Einstein's pseudoscience alone is proof of the degeneration of academic process. The discovery of Neptune could simply have been as a result of angular displacement to Uranus, not actual distances or durations of the orbit. But that claim may simply have been to bolster academic territory and perceived value of mathematical process over the comparatively simpler astronomical observation. With Uranus potentially visible to telescopes for 200 years or so before its official discovery, we should be skeptical about such claims; however widespread they have become. Thus it may be true that their maths was superior at least to that of the 20th century; and it may also be a myth that Neptune was discovered by calculations on Uranus' orbit. It could very easily be a myth as to who discovered of Uranus too. Academia is rife with opportunist claims. Such speculation is of course only the first step to proof anyways. But the radical various claims as to the parameters of Uranus' orbit leave much to be desired, and open the door to such speculation. I do calculate a variation of 15 days over numerous centuries to the various future orbits of Uranus. But the orbit 1800 to 1884 I get at 30727 days. From 1884 to 1968 the duration is 30723 days, a shrinking of only 4 days in the only 2 orbits of Uranus ever observed - that we know of. This is identical the Horizon Ephemeris data earlier which, also showed the orbit contract by four days between those two orbits, even if the other parameters differ. So if we marginally disagree on the duration of the orbit and the dates of perihelion and aphelion, the proportional difference of 4 days between orbits is not different between models - if we have correctly evolved the gravitational alteration of the other planets to Uranus's orbit. So the disagreements in perihelion and aphelion dates can only be a result of them using statistical and not evolutionary processes. After all, the OGS15 starting position and direction of the velocity vectors comes directly from their database. The second interesting feature of the table depicted previously, is that when I exclude Neptune completely from the calculation of the Perihelion Precession of Uranus, the result is virtually identical to that in the Horizon Ephemeris data: 26 arc-seconds per Earth-year! Make of that what you will, but I am only completely certain of one thing: my formula for 3d-n-body-gravity is logically correct within itself. Everyone else does not even publish their methodology and formulae. The 26 as/Ey extracted from Horizon Ephemeris depends on the largely varying question as to the duration of Uranus orbit. But with OGS15 I simply take the angle between Uranus and the Sun at the two perihelions in radians. Those values are generated for the user next to the label 'Theta' in the 'data-drift.txt' database should you wish to run the algorithm and double check the math. Then I subtract one angle of the perihelion from the other, and convert it into the standard units of measurement. That result is a 100% correct angular geometry because it has nothing to do with the duration of the orbit. It is situations like this that have made this particular analysis so vital. It is simply assumed by the public that the famous organization is flawless, knows it all, and never lies because it has an 'official' name rubber-stamped on it. As a logical positivist, the imperative is to take nothing at face-value. The primary method is to simply examine claims according to their own internal logical consistency ... or lack thereof. But it is certainly clear the Horizon Ephemeris is not an evolutionary n-body-gravity model, because the velocity vector should be the principle cause of the next position in a proper evolutionary process. I deal with this issue in more detail in the section: Sorting Horizons, which demonstrates similar calculations regarding Mercury's orbit. So this section on Uranus serves only to show up the inconsistencies in available data and theory. The published data at NASA varies within that organization by 0.018% for the duration of Uranus' orbit which is an amazing 1.35 million kilometers. Neptune only alters the position of Uranus by 0.2 million kilometers in that orbit. Other sources increase that error-margin to over 8 million km; 40 times the effect of Neptune. The orbit of Neptune itself, however, is certainly going to be even less accurate.

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 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 11