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From: hertz778@gmail.com (rhertz)
Newsgroups: sci.physics.relativity
Subject: Re: Weakness in the results of the three tests of GR shown in rhe lasr
 century,.
Date: Mon, 4 Nov 2024 03:06:47 +0000
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On Mon, 4 Nov 2024 1:57:21 +0000, ProkaryoticCaspaseHomolog wrote:

<snip>

> The other point that I made was that the meaning of "10^-10 accuracy"
> is rather ambiguous. For instance, since it has not been too many
> years since the last Venus orbiters and Venus flybys, the current
> positional accuracy of Venus may be known to the 10^-10 level. Does
> that mean that the longitude of perihelion is known to 10^-10? Of
> course not! The orbit of Venus has extremely low eccentricity, which
> makes it difficult to determine this value. So the longitude of
> perihelion is known to only a few tenths of a degree. That is what
> I meant when I wrote that the accuracy depends on "what specific
> parameters one is discussing".


Take the example below, which I extracted for the first three minutes of
today (now). One minute is the best resolution available.

The data, a Vector Table (xyz position and velocity from SSB), would
allow you to compute the orbital path of Venus, if you download the full
data for the orbital period of 224.7016 days (323,571 minutes), if you
ask to generate data for the entire period.


The resolution, as you can see, is about 1 part in 10E+16 (almost
hundred of micrometers).

BUT, THERE IS A CATCH: TO USE THIS DATA (323,571 BLOCKS) FOR POSITION
AND SPEED ///IN A CLOSED ORBIT///, YOU HAVE TO KNOW EXACTLY THE 3D DATA
OF THE PERIMETER OF THE ELLIPSE THAT DEFINE THE ORBIT OF VENUS.

BUT, TILL TODAY, THE PERIMETER OF AN ELLIPSE IS UNKNOWN. ONLY
APPROXIMATIONS EXIST, BEING THE RAMANUJAN ALGORITHM THE BEST.

THEN, IT MEANS THAT THE STATE VECTOR METHOD USING THE DATA THAT HORIZONS
PROVIDES, DON'T LEAD YOU TO A CLOSED ORBIT. IT MEANS THAT THE RESULTS
ARE APPROXIMATED. AND THIS IS EVEN WORSE WITH MERCURY AND OTHERS.

THE ONLY WAY TO HAVE AN ACCURACY OF 10E-10 (NOT TO MENTION 10E-16) WOULD
REQUIRE EXPERIMENTAL MEASUREMENTS FROM A DEDICATED SPACECRAFT ORBITING
VENUS IN A HIGHLY KNOWN ORBIT, WHICH WOULD HAVE TO RELAY STATE VECTORS
DATA TO EARTH WITH VERY PRECISE TIME SLICING, LOWER THAN 1 SECOND. MORE
THAN 19,414,219 BLOCKS OF DATA, AND FOR SEVERAL ORBITS (TO OBSERVE
PERTURBATIONS AND DEVIATIONS).


AFAIK, there is only ONE project to do such measurements for Mercury
(Japan, two spacecrafts, being ready by the end of 2025).

Meanwhile, all the data available IS THEORETICAL, with some corrections
introduced by several spacecrafts in the past. Not now.

And if it is done as it's being thought with Mercury in 2026, you'd be
surprised of the ACTUAL ORBITAL PATH in a long period of time (say one
year or two). There are many perturbations that simplistic models don't
consider, in particular asynchronous perturbations and random anomalies.

Because of the above comments, I would LOWER the expectations of current
accuracy available for the general public. I'm quite sure that JPL has a
model with better accuracy, but they reserve that data for US only.

After all, it's not a matter of giving to other countries such
information FOR FREE, being some of them competitors in the field of
planet ranging (China, India, Russia, EU ESA, Japan, etc.).

Would you help to your competitors for nothing, so they can beat you?



********************************************

https://ssd.jpl.nasa.gov/horizons/app.html#/

Ephemeris Type: Vector Table

Target Body: Venus
Coordinate Center: Solar System Barycenter (SSB) [500@0]
Time Specification: Start=2024-11-04 TDB , Stop=2024-11-14, Step=1
(minutes)4
Table Settings: defaults


FIRST THREE MINUTES (LOWEST RESOLUTION AVAILABLE AT HORIZONS)

2460618.500000000 = A.D. 2024-Nov-04 00:00:00.0000 TDB
 X = 8.090156187452155E+07 Y =-7.238773823901479E+07
Z =-5.677786971194245E+06
 VX= 2.286856341615997E+01 VY= 2.619946432328162E+01
VZ=-9.591151141072860E-01
LT= 3.626086375351044E+02 RG= 1.087073347386800E+08
RR=-3.769001975990773E-01

2460618.500694444 = A.D. 2024-Nov-04 00:01:00.0000 TDB
 X = 8.090293397320572E+07 Y =-7.238616625790673E+07
Z =-5.677844517046656E+06
 VX= 2.286805938787736E+01 VY= 2.619990594365392E+01
VZ=-9.590799661736238E-01
LT= 3.626085621025725E+02 RG= 1.087073121245759E+08
RR=-3.769032744711913E-01

2460618.501388889 = A.D. 2024-Nov-04 00:02:00.0000 TDB
 X = 8.090430604164793E+07 Y =-7.238459425030173E+07
Z =-5.677902060790177E+06
 VX= 2.286755535112288E+01 VY= 2.620034755436062E+01
VZ=-9.590448178838731E-01
LT= 3.626084866694247E+02 RG= 1.087072895102871E+08
RR=-3.769063512155697E-01


Symbol meaning:

    JDTDB    Julian Day Number, Barycentric Dynamical Time
      X      X-component of position vector (km)
      Y      Y-component of position vector (km)
      Z      Z-component of position vector (km)
      VX     X-component of velocity vector (km/sec)
      VY     Y-component of velocity vector (km/sec)
      VZ     Z-component of velocity vector (km/sec)
      LT     One-way down-leg Newtonian light-time (sec)
      RG     Range; distance from coordinate center (km)
      RR     Range-rate; radial velocity wrt coord. center (km/sec)


Distance from Solar System Barycenter (SSB)

RG 2024-Nov-04 (00:00) = 108,707,334,738.680 meters  (EXAGGERATED)

RG 2024-Nov-04 (00:01) = 108,707,312,124.5759 meters  (EXAGGERATED)

RG 2024-Nov-04 (00:02) = 108,707,289,510.2871 meters  (EXAGGERATED)

*********************************************