There is a problem with the validation of the concept which accounts for the 43 " per century in the motion of Mercury.The table of figures given below by Ohanian and Ruffini goes on to support the validation but a major problem in principle emerges as the 'observed' precessions of the Earth and Mercury are matched.
In basic terms it would be required to subtract the value given for Earth from the value given to Mercury to get the true value of the advance of Mercury but the table of figures, while adopting the principle that both Earth and Mercury are partaking in the same system of rotation around the Sun and the gravitational solution is dictated locally by the Sun,manage to treat the figures seperately as though the 3.85 minutes given for Earth had nothing to do with the 43 " given for Mercury.
The values given in Ohanian & Ruffini are:
PLANET OBSERVED PRECESSION PREDICTED PRECESSION
Mercury 43.1 +/- 0.1 arcsec/century 42.98 arcsec/century
Earth 3.85 3.84
The predicted perihelion advance of Mercury as 43 " was taken without knowing what the advance for Earth is,only one other participant in the sci.forums recognised the problem and sought admirably to at least bridge the gap but ultimately it fails, for if you alter the figure for Mercury you are obliged to alter it for Earth,therefore you cannot reduce the value of Earth to 0 and thereby isolate the advance of Mercury and certainly not as 43".
The other participant,Nicolaas Vroom,tried to simulate the motion of Mercury while including a value for Earth but again,this method generates a paradox rather than a validation insofar as it is impossible to derive a figure for Mercury where the initial figure for Earth is not known.For you headache inducing benefit ,here is the original attempt by Mr Vroom to resolve the issue.
"I am not behind everything what "Oriel36" is claiming
but let me try to explain why I think that everything is more
complicated as someone might think.
Consider a three body system consisting
of the Sun, the planet Mercury and our Earth.
With a computer simulation program based on Newton's
Law I calculate the observed positions of the Sun and
Mercury over a period of 100 years at random moments t.
This computer simulation is based around the following
parameters : Initial positions and velocities of Sun, Mercury
and Earth at t0. The masses of Sun, Mercury and Earth.
t0 is not part of the set of observations at t.
My first question is:
is it possible to calculate the parameters based
on the observations ?
You can use the same simulation program as part of
IMO what you have to do is to guess those parameters
and calculate an error value with the observations.
Try n other guesses and calculate n error values.
The guess with the smallest error is your first answer.
You continue etc etc until error becomes "zero".
That is your final answer.
Your answer on this question can be that the parameters
can not be calculated based on lack of information.
If that is the case "You" should indicate which information
is missing in order to solve this exercise.
It is important to remark that Mercury in this 3 body example
also shows a perihelion shift which is explained as
as influenced by Newtonian gravitation.
However this shift is not eqaul to 531"
but only equal to 93" in one century.
With your final answer you can demonstrate this.
This finishes exercise one..
Exercise one is not subject of the 43" angle explained by Einsteins
theory of Relativity.
Exercise two is almost identical as exercise one
Starting point are the same calculated observed positions
of the Sun and Mercury over a period of 100 years at
random moments t as mentioned above.
With one exception that ALL the observed positions of
Mercury are modified with a value as a function
of the famous value 43" and the time since t0 as
of that observation.
That means for an observation at t1 the position of Mercury
is modified with a value: (t1-t0)*43/100
My second question is:
Calculate the same parameters as previous based on
observations using Newton's Law.
i.e. initial positions and velocities at t0 and the masses
of Sun, Mercury and Earth.
Your first quess should be the final answer of exercise one.
Which this quess you should calculate an error value0.
This error value0 should be non zero.
(i.e. larger as final error value of exercise one)
Try n other guesses and calculate n error values.
Search for the smallest error valueX
(In fact you should repeat this process to find THE
smallest error valueX but this value will never be zero)
The real issue is now to answer the question if
error valueX is smaller than error value0
If that is the case than you have find a set of parameters
which better describe the observations as the initial
set of parameters (i.e. the parameters of exercise one)
Which that set of parameters you should also calculate
the perihelion shift of Mercury (in exercise one this value
was the value 93")
In fact that value is the observed perihelion shift.
That value in principle can be any value between
93" and 93+43 = 136"
a. If you find a value very close to 136 than it means
that you can describe the describe the positions solely
based on Newton's law and you do not need Einsteins Theory
b. If you find a value like 120" than you know that Newton's
Law those not fully describe the positions and you need
also something else.
c. If you find a value close to 93 than that is "prove"
that you also need Einstein's theory in order to explain
the missing 43" shift
and to describe the positions of the 3 bodies accurately.
My point is that in case you find someting inbetween (120")
than you should write a new simulation program solely
based on Einsteins Theory and which that theory
you should also calculate positions at random moments t
and find after n tries a final error value
That final error value (after n tries) should be close to zero.
If that is the case than you know that Einsteins theory is better
than Newton's theory.
In short you should not mix the two theories in order to prove
which one is better."