On Wed, 05 Jun 2013 23:33:47 +0200, "Paul B. Andersen"
wrote:

On 05.06.2013 01:02, Henry Wilson DSc. wrote:
On Tue, 04 Jun 2013 22:52:47 +0200, "Paul B. Andersen"
wrote:

On 04.06.2013 12:20, Henry Wilson DSc. wrote:

What amazes me is that nobody ever discusses why planet Mercury precesses at
all. How many different factors are responsible for planetary precession in
general?

What doesn't amaze me is your ignorance.

The main reason for the precession of the perihelion of Mercury
(NOT the precession of Mercury) has been known for centuries;
it is simply the tug from all the planets in the Solar system.
Relativity hasn't changed that.

Maybe they all got it wrong.

Not likely. Remember that Le Verrier calculated the Newtonian
prediction back in the mid 19. century (without computer. Impressive!),
and since then a lot of people have repeated it with better precision,
lately with the aid of computers.

Multi body calculations like this are very complex to do analytically,
but shouldn't be very hard to simulate on a computer, which
I am sure is done.

I think the Newtonian prediction is very well established.

In the frame of mercury, all the planets move in ellipses that appear to be
precessing because of their own orbital motion. Right?
Why should that have a nett force on Mercury over a long period of time?

It isn't the _motion_ of another planet (say Jupiter) that is
'pulling' Mercury. A ring of tiny stationary planets with
the same total mass as Jupiter would do the same job.
Since we are talking of a tiny precession, Jupiter will make
thousands of orbits before the precession becomes 360 degrees.
The (Mercury) annual precession will vary depending on Jupiter's
position, but the long term average precession will be as if Jupiter
were distributed in a continuous ring with the same mass as Jupiter.
This 'ring' will perturb the gravitational potential around
the Sun, so it isn't quite proportional to -1/r, and the speed
of Mercury at the aphelion will be a bit higher than it should
be according to Kepler's laws. This will have the effect of
rotating the (somewhat perturbed) ellipse a little.

Consider this:
Solar system seen from 'above'.
S - Sun, M - Mercury at aphelion. J - Jupiter

S M J
M's speed is higher than if Jupiter weren't there.
(The ellipse is distorted)

J S M
M's speed is lower than if Jupiter weren't there.

But since the distance to J is bigger, this doesn't
quite cancel the former case, so the average is
that M's speed at aphelion is higher than it would
have been without J.

According to that theory, the orbit should be continually expanding and
changing eccentricity as well.

What is wrong with this counter argument?

Mercury orbits around the J-S centre of gravity.

Over time, any consequent change in the direction of the major axis should be
balanced, clockwise and anti-clockwise. Any precession should be cyclical,
averaging zero.


Also, what effect would a finite speed of gravity have on the overall picture?

It will have an effect, and many anti-relativists have tried
to explain the anomaly with a modified Newtonian gravitation
with retarded gravity. None has been successful.

Remember that this 'modified Newtonian gravitation' also must
be able to explain the orbits of all planets and satellites,
you can't have a modified theory that works for Mercury only.

As you know, the precession of other planets is almost immeasurable small.

According to Newton, the precession should be 5557 arc seconds
per century. However, when the precession of the perihelion
of Mercury's was measured by Le Verrier in 1856, he found that
Newton's prediction was not exactly right, it was 38" per century
too small. Later more precise measurements have shown that the
precession of the perihelion of Mercury is 5600 arc seconds
per century, so the discrepancy is 43" per century. This is called
the anomalous precession of the perihelion of Mercury, and its
cause has indeed been discussed since Le Verries's time.

(Ever heard of the planet Vulcan?)

Le Verrier needed another planet to account for the anomaly.
Maybe an Earth twin was hiding behind the Sun?

It is this anomalous precession that is explained by GR.
GR predicts 43" per century in addition to the tug from the planets.

Only after Einstein added the infamous factor of 2 after he found his original
prediction was wrong.

A bit confused? :-)
We are not talking about gravitational bending of light.

And Einstein never "added a factor of two" to anything.
GR correctly predicts the gravitational bending of light.
Period.

His 1911 prediction for the bending of light was plain
wrong, because he basically used "falling light", and thus got
the same wrong answer as Newtonian gravitation gives.
And the Newtonian prediction happens to be wrong by a factor 2.

The bending of light by the sun has not been measured accurately enough to
deterimine whether the factor of 2 exists or doesn't exist.


See above.

That you don't understand it right away doesn't mean that it
doesn't add up.

What's your point anyway?
Are you claiming that since you don't understand it, Newton
doesn't predict a precession of the perihelion of Mercury? :-)

Henry Wilson DSc.