On Sunday, October 8, 2023 at 1:05:45 AM UTC-3, Bill wrote:
On Saturday, October 7, 2023 at 8:04:33 PM UTC-7, Richard Hertz wrote:
All the data is based on Kepler/Newton, without a trace of relativity...
From the technical report on that site:
"This section presents the dynamical models of the planetary and lunar ephemerides... The point-mass interaction between planetary bodies is governed by the parameterized post-Newtonian (PPN) formulation (Will and Nordtvedt, 1972; Moyer 2003)
[Equation 27, the general relativity post-Newtonian formula]
where the summations are over all bodies, and beta and gamma are the Eddington-Robertson-Schiff parameters representing the measure of nonlinearity in the superposition law for gravity and the amount of space curvature produced by a unit rest mass,
respectively, and are constrained to unity as predicted by the general theory of relativity (GTR)."
This site represents the value of TRUE SCIENCE...
Indeed.
https://ssd.jpl.nasa.gov/planets/approx_pos.html
Approximate Positions of the Planets
Lower accuracy formulae for planetary positions have a number of important applications when one doesn’t need the full accuracy of an integrated ephemeris. They are often used in observation scheduling, telescope pointing, and prediction of certain
phenomena as well as in the planning and design of spacecraft missions.
Approximate positions of the planets may be found by using Keplerian formulae with their associated elements and rates. Such elements are not intended to represent any sort of mean; they are simply the result of being adjusted for a best fit. As such, it
must be noted that the elements are not valid outside the given time-interval over which they were fit.
High precision ephemerides for the planets are available via the Horizons system.
.......
Formulae for using the Keplerian elements
Keplerian elements given in the tables below are
1. semi-major axis [au, au/century]
2. eccentricity
3. inclination [degrees, degrees/century]
4. mean longitude [degrees, degrees/century]
5. longitude of perihelion [degrees, degrees/century]
6. longitude of the ascending node [degrees, degrees/century]
***********************************************
This SIX Keplerian elements are the basis for the entire construction of the algorithms built in the Horizons software.
The formulae to generate them are based on the developments explained in the same page, and have been used for MORE THAN 200 YEARS!
QUOTE:
In order to obtain the coordinates of one of the planets at a given Julian ephemeris date, T_eph,
1) Compute the value of each of that planet's six elements:
2) Compute the argument of perihelion, w , and the mean anomaly, M.
3) Obtain the eccentric anomaly E, by recursion.
4) Compute the planet's heliocentric coordinates in its orbital plane, x', y', z'.
5) Compute the coordinates, (x_ecl, y_ecl, z_ecl) , in the J2000 ecliptic plane, with the x-axis aligned toward the equinox.
6) If desired, obtain the equatorial coordinates in the "ICRF" or "J2000 frame", (x_eq y_eq, z_eq)
END QUOTE
FAQ QUOTE:
Q: I want to write my own solar system "calculator". Where do I find the relevant equations?
A: The following books provide fundamental equations used in celestial mechanics.
“Explanatory Supplement to the Astronomical Almanac”, ed. P. K. Seidelmann, 1992, University Science Books.
“Fundamentals of Astrodynamics”, R.R. Bate, D.D. Mueller, J.E. White, 1971, Dover Publications, Inc.
“Fundamentals of Celestial Mechanics”, J.M.A. Danby, 1992, Willmann-Bell.
“Methods of Orbit Determination for the Micro Computer”, D. Boulet, 1991, Willmann-Bell.
“Orbital Mechanics”, J.E. Prussing, B.A. Conway, 1993, Oxford University Press.
“Orbits for Amateurs with a Microcomputer”, D. Tattersfield, 1984, Halsted Press.
“Spherical Astronomy”, R. M. Green, 1985, Cambridge University Press.
“Vectorial Astrometry”, C.A. Murray, 1983, Adam Hilger Ltd.
END QUOTE
I've used these formulae TO VERIFY Horizons data IN THE OSCULATING MODE (classic) and made its conversion to STATE VECTORS (position, velocity).
Then, I compared each result with the OUTPUT of the Horizons database for 3 orbital periods, with 1 hour resolution (more than 6,300 lines of data), in
the OSCULATING PARAMETERS mode. Then I compared equal amount of data in the STATE VECTORS mode, with a 100% match.
These parameters, generated by Keplerian/Newtonian math, are used by thousands of observatories (in high resolution mode) and hundred of thousand
amateurs and professional in almost every country of the world, as it's the most complete online ephemerides data resource that exist.
What you wrote about, which I couldn't find in the site, is probably an alternative source of information FOR RELATIVISTS.
NASA depends on JPL to obtain data for its projects, based on Kepler-Newton.
As you can see, not a trace of GR DERIVED PPN in the four types of outputs:
1. Observer Table
2. Vector Table
3. Osculating Orbital Elements
4. Small-Body SPK File
Why don't give it a try, and also make a fact-check? It's fun, but no GR/PPN ANYWHERE (sorry for that).
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