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From: tomyee3@gmail.com (ProkaryoticCaspaseHomolog)
Newsgroups: sci.physics.relativity
Subject: Re: Weakness in the results of the three tests of GR shown in rhe lasr
 century,.
Date: Sat, 2 Nov 2024 04:41:46 +0000
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On Fri, 1 Nov 2024 16:45:35 +0000, rhertz wrote:

> The site was developed in order to be used by AMATEUR ASTRONOMERS
> (hobbysts). The data CAN'T BE USED FOR ANY SERIOUS CALCULATION.

"JPL planetary ephemerides are generally created to support spacecraft
missions to the planets." That's pretty serious calculation, in my
opinion.

"The JPL Horizons on-line ephemeris system provides access to solar
system data and customizable production of accurate ephemerides for
observers, mission-planners, researchers, and the public, by
numerically characterizing the location, motion, and observability of
solar system objects as a function of time, as seen from locations
within the solar system."

In other words, it's a general purpose system that outputs a variety
of different ephemerides for different purposes *besides* planetary
exploration. Yes, they *do* cater to amateur astronomers *as well as*
to mission planners and professional astronomers.

If I, an amateur astronomer, want to generate an "Observer Table" so
that I can plot the retrograde motions of Mars as observed from Dallas,
I can do so. If I, writing a simulation program, want to generate a
"Vector Table" so that I can get position and velocity of a particular
planet at a particular time, I can do so. If I wanted to get
"Osculating Orbital Elements" for Ceres so that I can rapidly generate
an approximate orbit over a particular span of time, I can do so.

Lower accuracy formulae for planetary positions are also available:
https://ssd.jpl.nasa.gov/planets/approx_pos.html

Other ephemerides and toolkits for managing them are available:
https://ssd.jpl.nasa.gov/planets/eph_export.html
The data are available in ASCII format as well as in machine-dependent
binary.

> Watch this extract for Mercury, with 16 digits numbers. Only a very
> retarded asshole can take them literally.

NOBODY is intended to "believe" that the output is accurate to 16
figures. The numbers are merely the best possible ASCII representation
of the binary output of the ephemeris-generating program.

I understand where you are coming from. You are taking the rules of
"significant figures" in rather too narrow a fashion.

For five years, I taught technical mathematics (pre-calculus and
calculus) for an online college. They were a bit desperate due to
death of their principal instructor, so I stepped in as a substitute
teacher, even though my PhD is in molecular biology. I got such high
ratings from my students that my temporary stint as a substitute kept
getting extended year after year until one year, the college did a
general review of their curriculum for accreditation purposes, at
which point they discovered that they had to limit me to teaching only
my main course, introductory biology. My teaching hours and
compensation went down so much that I quit.

The point is, I understand about significant figures. The purpose of
rounding final results to an appropriate number of significant
figures is so that YOU DO NOT DECEIVE OTHERS of the precision and
accuracy of your results. And yes, I understand about precision
versus accuracy.

When performing an extended calculation, however, you do not round
*intermediate* results prematurely, but instead retain as many
significant figures as practicable. You round only when ready to
present your FINAL results to others. If you round prematurely, your
calculation will accumulate "dirt", and depending on the nature of
your mathematical manipulations, your final results can potentially
be very far off due to "catastrophic cancellation" or "loss of
significance".
https://en.wikipedia.org/wiki/Catastrophic_cancellation

The designers of the Horizons system do not know to what uses their
numerical outputs will be used, nor is it designed to provide its
numbers with appropriate statistical brackets. Since their outputs
may be used as starting points for other calculations, it is only
reasonable that the outputs be presented as the best possible ASCII
representation of their program's results.

Does that make sense to you?