Perihelion of Mercury with classical mechanics ?

"Paul Schlyter" wrote in message
...

[snip]

Thanks, Paul, for saving me the trouble of replying with all
the details. You hit the nail on the head.

Cheers.

wrote in message
ups.com...
Greg Neil wrote:
No amount of fiddling around with classical mechanics can
produce the correct result.

Now that's for sure at least an exaggeration, as I know for fact that
in 1898 Paul Gerber derived from Newtonian mechanics the same equation
as Einstein for the perihelion, and that he calculated c from it with
high accuracy. But I don't have his paper so I don't know the details
of how he did it. I only have a copy of the original end part as
printed in the book Einstein plus two, and Gerber found c = 305500
km/sec.

I believe that Gerber's derivation was shown to be incorrect,
even though he arrived at the correct answer.

Greg Neil wrote:
No amount of fiddling around with classical mechanics can
produce the correct result.
SNIP
I believe that Gerber's derivation was shown to be incorrect=AD,
even though he arrived at the correct answer.

As your belief led to your strong statement above, I would like to know
what his error was - especially as Petr Beckman repeated his derivation
in a slightly different way with the same result.

Thanks,
Harald

wrote in message
oups.com...
Greg Neill wrote:
No amount of fiddling around with classical mechanics can
produce the correct result.
SNIP
I believe that Gerber's derivation was shown to be incorrect*,
even though he arrived at the correct answer.

As your belief led to your strong statement above, I would like to know
what his error was - especially as Petr Beckman repeated his derivation
in a slightly different way with the same result.

Here's a link that may help:

http://www.mathpages.com/home/kmath527/kmath527.htm

Nicolaas Vroom wrote:

"Greg Neill" schreef in bericht
. ..
"Nicolaas Vroom" wrote in message
...

[...]
Newton's theory assumes that gravity act instantaneous.
However if you take into acount that the speed of gravity is
not infinite but equal to 300*c you can correctly simulate
the perihelion precession of Mercury.

Unfortunately, this leads to the problem of the
energy of the orbit changing due to the non-central
nature of the resulting force.

Can you be more spefic what you mean.
Does this mean that the distance (to the Sun) increases ?
What is magtitude of this effect ?

See problem 12.4 of Lightman et al., _Problem book in relativity
and gravitation_, for a simple derivation. For a speed of gravity
of 300c within Newtonian gravity, the Earth's orbit is unstable
enough that it would have been at the edge of the Sun about
120,000 years ago.

Laplace considered the effect of a finite speed of gravity in
Newtonian mechanics in 1805, and showed that observations of the
orbit of the Moon required a speed of at least 7x10^6 c.

Steve Carlip

Greg Neill wrote:
No amount of fiddling around with classical mechanics ca=ADn
produce the correct result.
SNIP
I believe that Gerber's derivation was shown to be incorr=ADect=AD,
even though he arrived at the correct answer.
Here's a link that may help:
http://www.mathpages.com/home/kmath527/kmath527.htm

Thanks, I had not thought of looking there! Note however that that site
is less sure than you are; and for the moment I have not yet seen a
strong argument against the validity of the first paper that I cited.
Cheers,
Harald

Nicolaas Vroom:
Newton's theory assumes that gravity act instantaneous.
However if you take into acount that the speed of gravity is
not infinite but equal to 300*c you can correctly simulate
the perihelion precession of Mercury.
For details go to my home page:
http://users.pandora.be/nicvroom/
and study the e-book:
The Reality Now and Understanding.
http://users.pandora.be/nicvroom/now.htm

Hey Nicolaas, that's an interesting site! And I look forward to use and
(if I can manae) to adapt your programs so as to include the attraction
of the sun by Mercury.

Cheers,
Harald

PS I have feedback on your Twin problem, but I suppose that has been
sorted out by now

wrote in message
...
Nicolaas Vroom wrote:

"Greg Neill" schreef in bericht
. ..
"Nicolaas Vroom" wrote in message
...

[...]
Newton's theory assumes that gravity act instantaneous.
However if you take into acount that the speed of gravity is
not infinite but equal to 300*c you can correctly simulate
the perihelion precession of Mercury.

Unfortunately, this leads to the problem of the
energy of the orbit changing due to the non-central
nature of the resulting force.

Can you be more spefic what you mean.
Does this mean that the distance (to the Sun) increases ?
What is magtitude of this effect ?

See problem 12.4 of Lightman et al., _Problem book in relativity
and gravitation_, for a simple derivation. For a speed of gravity
of 300c within Newtonian gravity, the Earth's orbit is unstable
enough that it would

have had to

have been at the edge of the Sun about
120,000 years ago.

to be at it's present position, today.

{I don't have a copy of Lightman at hand. But I presume that Lightman is
competent in wielding the aberration argument -- #3, below.}

Laplace considered the effect of a finite speed of gravity in
Newtonian mechanics in 1805, and showed that observations of the
orbit of the Moon required a speed of at least 7x10^6 c.

Steve is being deliberately dishonest, here. He is attempting to "motivate"
you, so that you don't "waste your time" with theories that Steve does not
support. (This is not inadverntent. He has done it before, and been called
on it, several times.) In this immediate response, Steve has mixed two
counteracting forces (aberration: Lightman, and drag: Laplace) in such a way
as to make you think that they are addressing the same force.

There are five components to this deliberate distortion.

1) Steve is not telling you the name or type of the gravitational theory
that Laplace was addressing. The theory is called Le Sagian gravity, and
was proffered by Georges Louis Le Sage, in 1782. This theory derives
Newton's gravitational law (actually it derives the weak-field limit of GR)
from the partial absorption of 'ultra-mundane corpuscles' by mass. {A
search on Le Sage or Lesage will bring up quite a few recent discussions on
the theory.}

2) The 'drag' effect mentioned by Steve is based on the drag of a matter
body as it moves through a *medium.* It is not the speed of gravity -- per
se -- that would cause the Earth to shrink its orbit; it is the impact of
those 'ultra-mundane corpuscles.'

3) The effect that arises in *any* gravitational theory with a finite speed
of gravity (including GR) is gravitational aberration. And gravitational
aberration will tend to *increase* the radius of an orbit. Steve did a
paper on just this effect -- to try to save GR from the issue.

4) Laplace (and just about everyone since, including Feynman and Poincare)
determined their "requirement" for high speed on the basis of drag, alone.
And never considered the potential balancing of the two forces. In fact,
Steve will tell you that the aberration term will *always* overpower the
drag term (for the Earth).


Steve will likely tell you that such is done simply to avoid "confusion."

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

"Nicolaas Vroom" wrote in message
...

"Greg Neill" schreef in bericht
news
"Paul Schlyter" wrote in
message
...

[snip]

Thanks, Paul, for saving me the trouble of replying with all
the details. You hit the nail on the head.

Cheers.


Because Paul did all this good work
as a token of appreciation why don't you give
your opinion about my latest posting in the
news groups sci.astro.research or sci.physics.research:
"How important is GR in order to calculate
the precession of Mercury"
I would really appreciate that.

I'm afraid I haven't seen that posting. Perhaps it's
my newsreader acting up.

However, in answer to your question, "How important is GR in order
to calculate the precession of Mercury", I would say that it is
essential if one wishes to consider a theoretical approach that
agrees with all available data.

greywolf42 wrote:
wrote in message
...

[...]
Laplace considered the effect of a finite speed of gravity in
Newtonian mechanics in 1805, and showed that observations of the
orbit of the Moon required a speed of at least 7x10^6 c.

Steve is being deliberately dishonest, here. He is attempting to "motivate"
you, so that you don't "waste your time" with theories that Steve does not
support.

That is not true.

[...] In this immediate response, Steve has mixed two counteracting
forces (aberration: Lightman, and drag: Laplace) in such a way
as to make you think that they are addressing the same force.

This is simply wrong. Go back and read Laplace, _Celestial Mechanics_,
section X.VII.22. It's true that elsewhere in X.VII, Laplace deals with
drag. But this section, which contains the limit that I quoted, deals
*explicitly* with aberration, *not* drag.

There are five components to this deliberate distortion.

Of which you list four?

1) Steve is not telling you the name or type of the gravitational theory
that Laplace was addressing. The theory is called Le Sagian gravity, and
was proffered by Georges Louis Le Sage, in 1782. This theory derives
Newton's gravitational law (actually it derives the weak-field limit of GR)
from the partial absorption of 'ultra-mundane corpuscles' by mass. {A
search on Le Sage or Lesage will bring up quite a few recent discussions on
the theory.}

It may be that Laplace had LeSage in mind. I don't know. In particular, I
have been unable to find any reference to LeSage in section X.VII of Laplace's
_Celestial Mechanics_. Perhaps it's elsewhere -- I haven't read the whole
book. Would you care to provide a specific citation?

2) The 'drag' effect mentioned by Steve is based on the drag of a matter
body as it moves through a *medium.* It is not the speed of gravity -- per
se -- that would cause the Earth to shrink its orbit; it is the impact of
those 'ultra-mundane corpuscles.'

That is incorrect. The issue in this thread has been the effect of finite
propagation speed in Newtonian gravity, and that's what I addressed. I did
not say, or imply, anything about "drag." Contrary to your claim, the limit
I quoted from Laplace also had nothing to do with drag, but came from the
effect of putting a finite propagation speed into Newtonian gravity.

3) The effect that arises in *any* gravitational theory with a finite speed
of gravity (including GR) is gravitational aberration. And gravitational
aberration will tend to *increase* the radius of an orbit. [...]

Right. That's what I said. "For a speed of gravity of 300c within Newtonian
gravity, the Earth's orbit is unstable enough that it would have been at the
edge of the Sun about 120,000 years ago." That's an increase in the radius
of the orbit, right?

4) Laplace (and just about everyone since, including Feynman and Poincare)
determined their "requirement" for high speed on the basis of drag, alone.
And never considered the potential balancing of the two forces. In fact,
Steve will tell you that the aberration term will *always* overpower the
drag term (for the Earth).

Once again: Laplace, _Celestial Mechanics_, section X.VII.22, is about finite
propagation speed, not drag.

Steve will likely tell you that such is done simply to avoid "confusion."

No, I will say that greywolf wrote a fictional account that had nothing to do
with what I said. Unlike him, I will not charge "deliberate distortion" or
accuse him of "deliberate dishonesty." He may have misremembered Laplace,
or only read someone else's description, and leapt to conclusions without
actually paying much attention to the post he was responding to.

Steve Carlip