Mercury's perihelion precession and the reason why GR is badly wrong
- From: Albertito <albertito1992@xxxxxxxxx>
- Date: Fri, 13 Jun 2008 04:01:27 -0700 (PDT)
The observation of the precession of the equinoxes is
a main point here. It is known that precession is about
5025 arcseconds per century. So, that means that if an
orbit of a body in solar system is seen preceding by
exactly that amount, then that orbit can be regarded
as stationary (its perihelion does not precedes).
Mercury's orbit is seen preceding about 5600 arcseconds
per century, so it means its perihelion precedes about
5600 - 5025 = 575 arcseconds per century.
Now, suppose we have at hand a correct post-newtonian
gravity theory that can predict the contribution of each
planet to the total precession observed by Mercury's
perihelion. Say, we compute on N-body problem. Call f
total gravitational force per unit of mass, defined as
a sum of vector
f = f_1 + f_2 + f_3 + ... + f_N
where f_i is the contribution of each body
It follow that
r f'/f = (r/f)(f_1' + f_2' + f_3' + ... + f_N'),
where
r is radial distance to the center of masses, and
' stand for derivative wrt r
Then, the apsidal angle \psi is
\psi = (- pi/2)( r f'/f) =
= (- pi/2)(r/f)(f_1' + f_2' + f_3' + ... + f_N'),
Define now f_n, as total newtonian force per unit of mass,
and f_ni as the newtonian force per unit of mass exerted
by body i. We get an apsidal Newtonian angle as
\psi_n = (- pi/2)( r f_n'/f_n) =
= (- pi/2)(r/f_n)(f_n1' + f_n2' + f_n3' +
+ ... + f_nN'),
Thus, the perihelion advances by
\delta\psi = \psi - \psi _n =
= (- pi/2)( r f'/f - r f_n'/f_n).
Any clever buddy would realize that the precession starts
to be contributed from the first body 1 to the last N. IOW,
there are no second or higher order terms that contribute
alone to the perihelion advance, but all the terms, from the
first to the last, are contributing. What does it mean in
the case of Mercury's perihelion advance? If the observed
precession is 5600 arcseconds per century, and 5025 arcseconds
per century are due to the precession of the equinoxes, then
5600 - 5025 = 575 arcseconds per century is total perihelion
advance. Newtonian gravity can account for 532 arcseconds
per century, but a correct post-newtonian gravity theory
could account for all those 575 arcseconds per century, so
there would be no remaining. GR can account for the extra
575 - 532 = 43 arcseconds per century,but this means that
GR leaves 532 arcseconds per century to be explained only by
Newtonian gravity. That's a wrong assumption, since the precesion
must start to count from the first to the last body, without room
for any extra bizarre phenomenon. You can't claim that 532
arcseconds per century are explained by Newtonian gravity and
the extra 43 arcseconds per century are accounted for by GR.
In order to prove that GR can predict the correct Mercury's
perihelion precession, you must solve at least a 5-body problem
under GR. The Sun and Planets Venus, Earth and Jupiter are
contributing to Mercury's perihelion precession (other body
contributions can be neglected). The question is, can you solve
a 5-body problem under GR? There is no simple analytical solution
to a 5-body problem in Newtonian gravity, even under GR you can
hardly solve a simple 2-body problem. Anyway, under Newtonian
assumptions, you can use computational techniques, developed by
Lagrange, Laplace (among others), to determine that the effects
of all the other planets should contribute an additional 532 arc
seconds per century to the precession of Mercury's orbit. So,
under a correct post-newtonian gravity theory, you will be able
to determine the complete 575 arcseconds per century, with no
room for bizarre phenomena, like spacetime curvatures. Had
Newtonian gravity been a more accurated theory of gravitation,
able to predict those 575 arcseconds per century, GR wouldn't have
slipped in, because there wouldn't have been room for bizarre
speculations.
Now, the question is, can we repair the damage caused by GR and
all those bizarre relativistic corrections along more than one
century of absurdities? Fortunately, the answer is yes. Here is
the solution,
f_ij = - (G m_i / r_ij^2) cosh(v_ji/c),
where
f_ij is the post-newtonian gravitational force per unit of mass
exerted by body i on body j, with i /= j ,
m_i is mass of body i,
r_ij is the distance between body i and body j,
v_ji is tangential speed of body j wrt body i,
c is finite speed of gravity, and
cosh stands for hyperbolic cosine.
The post-newtonian gravitational force F_ij is then expressed
as
F_ij = - (G m_i m_j / r_ij^2) cosh(v_ji/c).
.
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