Horizon Ephemeris Sorted

The Horizon Ephemeris has good 3D planetary positions; in addition to velocity-vectors, which consist of a combination of both historical and predicted values. It operates according to a theory on gravity which is rather opaque. It is said to be based on Kepler's ellipses but variations to the perihelion and aphelion are also in operation. They give no direct formulae, instead offering a list of books as their sources, and then qualifying that by saying that this list is not complete. So they're just not telling!

There is a great degree of consensus between the Horizon Ephemeris and the 3D-n-body-gravity algorithm OGS15
(orbit-gravity-sim-15.exe) regarding deviations to Jupiter's perihelion and aphelion. The dates of perihelion for Jupiter's barycenter evolved from 1773 to 1999 with an accuracy of 4 minutes and 4113km. Improvements beyond that not being viable for with my current equipment. Accuracy for the distances of Mercury's Aphelion and Perihelion evolved an average difference of just 8m per orbit between Horizon Ephemeris and OGS15 over a similar time frame of 237 years. (See sections on Mercury & Jupiter for more details).

The algorithm can improve on this if executed on a faster computer. The accuracy to within 4 minutes for Jupiter is especially good because the duration between various perihelions can differ from the duration of the Jovian year, by often as much as 17 days. There is however essential disagreement about the Perihelion Precession of Mercury which is the crux of this thesis.

Nevertheless, it has been detected here that all the Horizon Ephemeris velocity-vectors, contain a gross error regardless of agreement with their positional data as they express that data in comparison with the center of the Sun. This problem is agreed upon by a blind corroboration with Bernard Burchell, (alternativephysics.org) following from his analysis. As an example, in order to make Horizon Ephemeris' data consistent with their given average orbital duration of Jupiter being 11.86178 years, it was required that their given velocity of Jupiter had to be multiplied by 1.073880766.

So this 7.4% increase in their velocity values was necessary so that Jupiter's position starting 18 December 1773 @ 11h53, reached agreement with the 1999 perihelion of May 20th. Scenario [25] of the algorithm OGS15 puts the time for that particular perihelion at 10h18, whereas Horizon Ephemeris has it at 10h14.

However the given velocity-vectors are still in proper proportion for the orbits for any set of data. Thus the multiplying factor varied from 1.073 to 1.078 for various planets and various orbits. But that value could be applied equally to the X, Yand Z axes for any position in space and time for any major planet, in order to reach consensus for the duration of the orbits.

It may be considered that this difference might occur because OGS15 begins with positions referencing the center of the Sun, and thereafter gives the Sun equal but opposite momentum. But the velocity of the Sun is only 0.1% of Jupiter. Of course 0.1% is not 7.5%. And the other planets will reflect amounts varying by +-1%. So even the fluctuation in the value between 7.3% and 7.8% cannot be reconciled. For this reason it may be prudent to make your model using the barycenter of the solar system. Their data for that might bypass this issue. It is not clear which data Bernard Burchell used.

The average duration of an orbit is taken to be the most reliable parameter reported by astronomers due to it being a comparatively simple observation. The dates of perihelion and aphelion being also direct observations are thus the second parameter of reference. Estimates of distance to the Sun are derived from calculation and theories on gravity, and thus have a greater chance of inaccuracy.  But the duration of the orbits must vary from  one orbit to the next, due to the gravity of the other planets. This is the essence of the question being here resolved with the OGS15 algorithm.

Their is a strong blind corroboration with Bernard Burchell (alternativephysics.org) that the velocity-vectors have been 'tweaked' by Horizon to agree with General Relativity, whereby they cease to have agreement with themselves, and with the very principles of geometry and logic. But this does not seem to effect Horizon's positions of the planets, which are still good and consistent with the Newtonian-Planck-computational paradigm here proposed.

But it is clear that Horizon Ephemeris are not using an evolutionary 3D-n-body algorithm. Instead they are likely using a statistical process which is mathematically more complex, but lacks internal congruence. This is such that their calculations result in 7%+ errors in their velocity vectors. It is clear at least that Mercury's orbit is short by a day between 1940 and 1999, and that could not occur in an evolutionary process. (See Mercury)

The exact and corrected velocity values that I reverse engineered from the Horizon Ephemeris' postional data and orbital durations, are given for the major planetary bodies, together with the exact formula for 3D n-body-gravity in the section:
How to Build N-body-gravity Algorithm

Proof of gross errors in Horizon Ephemeris for velocity-vectors is as follows for Mercury's aphelion of 1940/Apr/10, using their data (extracted June 2018).
here starting at 08:50 are 5 minutes apart:
2429729.868055556 = A.D. 1940-Apr-10 08:50:00.0000 TDB
X =-1.034953498461351E-01 Y =-4.542388824691579E-01 Z =-2.755589694986220E-02
VX= 2.178768614554590E-02 VY=-4.820175512435458E-03 VZ=-2.396538876799911E-03
LT= 2.695401531796818E-03 RG= 4.666943081325449E-01 RR= 1.340741503276090E-06

2429729.871527778 = A.D. 1940-Apr-10 08:55:00.0000 TDB
X =-1.034196963423474E-01 Y =-4.542556112181828E-01 Z =-2.756421778178096E-02
VX= 2.178873190870961E-02 VY=-4.815583897754233E-03 VZ=-2.396260294393365E-03
LT= 2.695401548957475E-03 RG= 4.666943111038205E-01 RR= 3.707132819103774E-07

2429729.875000000 = A.D. 1940-Apr-10 09:00:00.0000 TDB
X =-1.033440392087653E-01 Y =-4.542723240238078E-01 Z =-2.757253764625372E-02
VX= 2.178977690712820E-02 VY=-4.810992114093735E-03 VZ=-2.395981627885495E-03
LT= 2.695401546665300E-03 RG= 4.666943107069427E-01 RR=-5.993149475160505E-07

The sample above is in text format, so you can highlight and copy-paste the values into any calculator to check the arithmetic fairly easily. Or go and obtain any other values for any other planet from the Horizon Ephemeris using their 'vector' option.

Using 3D-Pythagorus the first XYZ co-ordinates (in black) yield a difference to the second position 5 minutes later.

So d = sqr (dx^2 + dy^2 + dz^2).
Where dx is the difference between the two X values (ditto dy & dz for Y and Z).

This amount, d, is converted from Astronomical Units, so that the straight-line difference between the times of 8:55 and 9:00 is: d = 11657 km.

Using a similar formula for 3D-Pythagorus, the velocity-vectors (blue in sample) are expected to be in miles per second, which converts to an amount of 36.118 km/s. Multiply by 300 seconds = 10835 km.

This 5 minutes of Mercury's orbit should not result in a curve that much different in distance from the straight-line between the two points. Their given velocity is thus about ~7.5% too slow.

The problem perhaps being that nowhere are actual units of measurement designated by Horizon Ephemeris for their velocity vectors. But I am not aware of any unit of velocity measurement that is 1.07588 times less than a mile/second. This proportion varies a little throughout varying between 7.3% and 7.8%.

Multiplying by these amounts ensured that the orbital duration was as reported: 87.969 days for Mercury. The discrepancy of Jupiter's orbit being from 11.861776 to 11.862615 years was insignificantly small in compassion to the ~7.5% error in their velocity vectors. See the section on Jupiter for more details on this.

This process of multiplying the velocity by 7.5% needed to be repeated for every one of the many hundreds of such data extractions I have used in constructing my algorithms. So just to double-check it, please observe the other detailed example here: Uranus.

The only possibilities for the ~7.5% velocity-vector problem being a typing error in the calculations by Horizon Ephemeris; or the data has been 'relativized' as Bernard Burchell suggests. Einstein's Relativity certainly fogs up matters one way or another.

However, no formula or result from any calculation for a single Jupiter orbit in Special Relativity is anywhere more than 1 part in 2700 million different from its Newtonian counterpart. Although a gravity delay in General Relativity results in 1 part in 1 million different from one Newtonian orbit. (See previous chapter: Sum General Theory).

Despite this, Horizon Ephemeris is still the best source I have found for XYZ positions of the planets in numerical format, so long as one takes the trouble to adjust their velocities by ~7.5%. Fortunately the XYZ vector velocities are still in good proportions to one another for any particular reading! And that is still crucially useful information for which there is no better resource. I am still trying to prove that this may be a misconception of mine, but to no avail thus far.

As for their theories on time being according to General Relativity, its a small argument to point out that Earth-dates are only applicable and useful to people on Earth. Thankfully they seem to have completely ignored Special Relativity's deplorable but less effective adjustment to time.

The Horizon Ephemeris' aphelion for Mercury 1940/Apr/10 = 69 813 570 km from Sun. But for the 3D algorithm OGS15 (orbit-gravity-sim-15.exe) = 69 802 219 km for Scenario [62] which starts in 1900 which is a difference of -0.016% .

It is no coincidence that the 2D algorithm OGS13 results in 69 816 466 km for 1940/Apr/10. If we compare that to Horizon's aphelion distance being 69 813 570 km, then this yields a much closer difference of just 0.004% with Horizon Ephemeris.

It is therefore fairly likely that Horizon is using an orbit of Mercury which is from a 2D model that has then simply been tilted. The amount of gravitational effect on Mercury caused by the other planets in a 3D model will be significantly less than a 2D model. And it is this Z-axis in the n-body-gravity adjustment that the Horizon Ephemeris has not accounted for. See detail in the section on Mercury where we saw other reasons suggesting Horizon Ephemeris simply tilted the orbit and did not evolve it. There has to be calaculations in their process, it cannot be entirely observed; due to Earth, Moon and Sun obscuring the view periodically.

Nevertheless its a classical mistake to assume that there is only one inaccuracy.

It has to be considered that these differences in distance of aphelion of Mercury could be partly attributed to variations in G with Horizon's most recent update (2018) claiming to be in agreement with CODATA which is G=6.67408. Previously Horizon used G=6.67259. However their vector data has a date of last revision July 13, 2013 which is not in keeping with their claims that it has been updated to CODATA's G in 2018.

Their list of astronomical constants also offers the old value of G. This has also not been updated (https://ssd.jpl.nasa.gov/?constants). Any change to G is equatable with adjustments to planetary mass anyhow, so this is unlikely the central problem; albeit here is certainly further evidence of a lack of consistency in their process.

Altering G and the masses of the planets and Sun can yield zero change to orbital parameters if G and mass are kept in fair proportions to one another. What is untenable is to use data where some values originate with one value of G, whereas other data uses another value of G.

I have to conclude that their data is using the old value of G=6.67259. My own model could thus still use further tuning to the CODATA value, but I can only do this once Horizon update their numbers accordingly (or at least their dating system of their data). But they first need to take into account this thesis in its entirety, or else such dissonance here exposed will accumulate.

My time and energy is 100% available to this task.
Queries can be posted at my Cosmology forum: cosmology.africamotion.net

In order to extract the dates and positions for perihelion and aphelion from Horizon Ephemeris, I wrote a small app which picks the least or greatest distance from one of their wonderful databases. I have deployed it here, as it may be useful:

(52 kb vb6 application)

Extracting data from the Horizon Ephemeris vector option would be fairly arduous without this. You first need to download a database, place it in the same folder as this application, then run the application and follow the instructions on the screen. (Unless you are terrified of .exe files.) I have found the Horizon Ephemeris to be the most vital asset in this thesis and I am eternally grateful that it is offered freely... aside from the errors, whoever owns them.

Sections of this Article by web-page


n-body gravity from www.flight-light-and-spin.com