> > Here is the cheese, don't get an indigestion !
> >
> > Let Rs = the satellite orbital radius
> >     Re = the Earth radius
> >     (the altitude h of the satellite is thus Rs-Re)
> >     Nu(s) = the frequency of the signal emitted by the satellite
> >     Nu(e) = the frequency of the signal received at the ground level
> >     Me = the mass of the Earth
> >     G  = the gravitational constant
> >
> > 1) The signal will gain a potential energy Ep
> >
> > (cf. Gravitation and Cosmology by St. Weinberg,1972, pp 84, 85)
> >
> > Ep = m(ph) * gm * (Rs-Re), where
> > gm = G * Mearth / (Rs * Re)
> > m(ph) = hNu(s)/c^2
> > (m(ph) = "mass" of a photon of initial frequency Nu(s))
> > Thus Ep = (hNu(s)/c^2) * (G * Mearth / (Rs * Re) * (Rs-Re)
> >         = hNu(s) * (GMearth/c^2) * (1/Re - 1/Rs)
> >
> > As the photon adds Ep to its initial energy hNu(s), its
> > energy at the ground level (at the distance Re from the Earth center)
> > becomes
> >
> > hNu(e) = hNu(s) + hNu(s) * (GMearth/c^2) * (1/Re - 1/Rs), thus
> > Nu(e) = Nu(s) * [1 + (G*Mearth/c^2) * (1/Re - 1/Rs)]
> >
> > 2) But the orbital velociy vs of the satellite must also be taken
> > into account
> > (N.B.: vs^2 = GMe/Rs).
> >
> > For a satellite observer, the signal travels a distance Rs - Re
> > in a time t' = (Rs-Re)/c.
> >
> > For an Earth observer, the signal follows the hypothenuse ct
> > of a right-angled triangle whose other sides are vs*t and Rs-Re = ct'.
> >
> > Hence, c^2*t^2 = vs^2*t^2 + c^2*t'^2, and
> >
> > t' = t * sqrt(1-vs^2/c^2)
>
> We have seen this junk twice before, Marcel:
>   http://groups.google.com/group/sci.physics.relativity/msg/e06dfeef82810893
>   http://groups.google.com/group/sci.physics.relativity/msg/7f8fa2d867f9bfce
> There you started part 2 with the words:
>    | To take into account the SR effect due to the orbital
>    | velocity v(s) of the satellite,

You are stupid, I didn't use SR in my present derivation!

Marcel Luttgens

>
> Perhaps you could have a look at your own website and
> at your posting history on this newsgroup some day:
> There is no length contraction, by M. Luttgens:
>     http://perso.wanadoo.fr/mluttgens/mmx.htm
> "Sapere Aude": Refutations of SR, by G. Walton:
>     http://perso.wanadoo.fr/mluttgens/sapere.htm
> The Lorentz transformation (LT) are false, by M. Luttgens:
>     http://perso.wanadoo.fr/mluttgens/LTfalse.htm
> Mathematical Error in the Lorentz Transformation, by Paul Marmet:
>     http://www.newtonphysics.on.ca/Lorentz/lorentz.html
> The Twin paradox falsifies SR:
>     http://perso.wanadoo.fr/mluttgens/twinpdx1.htm
>
> Marcel Luttgens, fiercely opposing and tragically misunderstanding
> just about every aspect of special relativity, using special relativity
> to demonstrate that we really don't need General relativity, which
> includes special relativity to begin with.
>
> Either you are a sneaky bastard, or you don't understand what you
> have on your website. I put my money on both.
> 
> Dirk Vdm