Re: 1905 Relativity is sufficient to support GPS function

From: Rafael Valls Hidalgo-Gato (valls_at_icmf.inf.cu)
Date: 03/25/05 

Date: 24 Mar 2005 16:32:56 -0800

"Harry" <harald.vanlintel@epfl.ch> wrote in message news:<42428991$1@epflnews.epfl.ch>...
> "Koobee Wublee" <kublai@cox.net> wrote in message
> news:_It0e.74$ZV5.34@fed1read05...
> >
> > "Rafael Valls Hidalgo-Gato" <valls@icmf.inf.cu> wrote in message
> > news:33d06fe2.0503221850.4b7a7390@posting.google.com...
> > > "The GPS is a remarkable laboratory for applications of the concepts
> > > of special and general relativity".
> > > http://www.livingreviews.org/Articles/Volume6/2003-1ashby/
> > >[...]
> >
> > It looks like Ashby does not agree with you. It would take GR to explain
> > GPS. However, since it is the 1st order effect of GR that determines
> within
> > the precision as measured by today's technology, any theory of gravity
> > should have no problem meet. That is because any theory has to be
> downward
> > compatible with Newtonian physics, and the 1st order effect is what
> > determines the Newtonian mechanics. For excample, from the spacetime
> > equation in polar coordinate with Schwarzschild metric, we can write down
> > the observed energy of a planet orbiting the sun as follows. Note that
> any
> > other metric (or solution to Einstein's field equations) would have a
> > different equation.
> >
> > E = m c^2 sqrt(1 - 2 U) / sqrt(1 - B^2)
> >
> > Where
> >
> > ** E = observed energy
> > ** m = rest mass of the planet in flat spacetime
> > ** c = speed of light in vacuum
> > ** U = G M / c^2 / r = gravitational potential
> > ** B^2 c^2 = (dr/dt)^2 / (1 - 2 U)^2 + (r cosT dG/dt)^2 / (1 - 2 U) + (r
> > dT/dt)^2 / ( 1 - 2 U)
> > ** r = radial distance
> > ** T = lattitude
> > ** G = longitude
> >
> > For (U = 0, flat spacetime), we have the familiar equation
> >
> > E = m c^2 / sqrt(1 - v^2 / c^2)
> >
> > For (1 >> 2 U) and (1 >> B^2), we have
> >
> > E - m c^2 = m v^2 / 2 - m U c^2
> >
> > The above equation is what you are talking about the total energy is the
> > kinetic energy plus the potential energy with
> >
> > ** m v^2 / 2 = kinetic energy
> > ** - m U c^2 = potential energy
> > ** E - m c^2 = total energy you are familiar with
> >
> > Newtonian mechanics is an approximation to
> >
> > E = m(v, U) c^2
> >
> > Where
> >
> > ** m(v, U) = a function of v and U
> >
> > As you can see, what you and Hatch are talking about where
> >
> > E = m(v) c^2 - m(U) c^2
> >
> > Does not make much sense. Energy, even under the concept of GR, is an
> > observed parameter. It is just as Einstein (and pointed out by you) had
> > said
> >
> > (observed) energy = (observed) mass
> >
> > The interesting thing is to ask does the equation
> >
> > E = m c^2 sqrt(1 - 2 U) / sqrt(1 - B^2)
> >
> > Predict the observed Mercury's orbital anomaly? This is going to separate
> > the truth from BS. It is the 2nd order effect that determines the
> observed
> > anomaly to Mercury's orbit. In 1,915, Einstein was able to calculate out
> > this 2nd order effect with only the 1st order tools (without a complete
> set
> > of field equations and the Schwarzschild metric). This should have sent
> an
> > alarm through out the academic communities. I am sure Hobba is going to
> > quote BS which he does not understand that explains how any one could
> > measure down to 0.01" with a ruler only having 1" scale.
>
> That sounds interesting, apparently you are good in explaining this subject.
> Please elaborate on Mercury's anomaly and your last intriguing remark.
> Harald

Hi Harald. Are you interested in Mercury's anomaly? Very easy. To
calculate it (with same accuracy as with GR) just consider the
variation of the unit of mass in Mercury location owed to the Sun's
gravity, using the factor (1+GMs/rc^2) that I derived already from
1905 Relativity (making use of rest mass measuring potential energy).
Ms is Sun's mass. Apply then Newtonian stuff and that's all. The
acceleration of Mercury is then
Am=GMs(1+GMs/rc^2)/r^2. Of course, to justify this procedure I need a
little more space.

Best regards,
RVHG

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