Justification for a new doppler radar formula
in [Physics]
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From: eric gisse on 21 Feb 2010 00:31 Surfer wrote: > On Sat, 20 Feb 2010 19:16:42 -0800 (PST), artful > <artful_me(a)hotmail.com> wrote: > >>On Feb 21, 2:08 pm, Surfer <n...(a)spam.net> wrote: >>> The formula for radar Doppler shift can be derived without invoking >>> Einsteins' theory of special relativity, because all observations are >>> made in the same frame of reference. >> >>No .. because for there to be a shift it has to be adifference between >>what one frame measures to what another measures. You can't have a >>shift when there is just one value >> >>> The result with c as the speed of light, V as the target velocity and >>> Ft as the transmitted frequency, gives the shifted frequency Fr as: >>> >>> Fr = Ft (c+V)/(c-V) (1) >> >>Which is not what we find experimentally >> > > Sorry, you are wrong. > > The above formula works well enough for normal situations. But not for v ~ c situations, which means your formula is wrong. > > It's described here, > http://en.wikipedia.org/wiki/Doppler_radar > > but is presented in the form > > Fr = Ft (1+V/c)/(1-V/c)
From: eric gisse on 21 Feb 2010 00:33 Surfer wrote: > The formula for radar Doppler shift can be derived without invoking > Einsteins' theory of special relativity, because all observations are > made in the same frame of reference. > > The result with c as the speed of light, V as the target velocity and > Ft as the transmitted frequency, gives the shifted frequency Fr as: > > Fr = Ft (c+V)/(c-V) (1) This is observationally wrong. [...] > Then in the frame of the radar system the transmitted signal will have > a speed of > c-vi > > and the reflected signal will have a speed of > c+vi. This is also observationally wrong. [...] > In the radar system frame of reference, let the transmitted signal > have frequency Ft, then the corresponding outgoing wavelength is, > Lt = (c - vi)/Ft This is observationally wrong. > > This signal will impinge on the target with period > T = Lt/(c - vi + V) > or frequency > F = (c - vi +V )/Lt. This is observationally wrong. > > The reflected signal has the same frequency, and so has wavelength > Lr = (c + vi - V)/F, > > and is received by the radar system with frequency > Fr = (c + vi)/Lr. > > Then overall we obtain, > > (c + vi) (c - vi + V) > Fr = --------------- ---------------- Ft . > (2) > (c + vi - V) ( c - vi) Also observationally wrong. [snip rest]
From: Surfer on 21 Feb 2010 02:11 On Sat, 20 Feb 2010 21:16:23 -0800 (PST), "Dono." <sa_ge(a)comcast.net> wrote: >On Feb 20, 7:08�pm, Surfer <n...(a)spam.net> wrote: >> The formula for radar Doppler shift can be derived without invoking >> Einsteins' theory of special relativity, because all observations are >> made in the same frame of reference. > >I don't know what gave you this idiotic idea. > Its self evident. >This is a simple exercise in SR: If one assumes the speed of light is isotropic in the frame of the radar system, the derivation is dead simple without SR. In the radar system frame of reference, let the transmitted signal have frequency Ft, then the corresponding outgoing wavelength is, Lt = c/Ft This signal will impinge on the target with period T = Lt/(c + V) or frequency F = (c +V )/Lt. The reflected signal has the same frequency, and so has wavelength Lr = (c - V)/F, and is received by the radar system with frequency Fr = c/Lr. Then overall we obtain, Fr = c/(c-V) * (c+V) /c Ft = (c+V)/(c-V) Ft =(1+V/c)/(1-V/c) Ft > >1. Since the object is approaching at V, the frequency hitting the >incoming object is > >F_obj=F_source*sqrt((1+V/c)/(1-V/c)) > >2. The object acts as asecondary source approaching the radar detecot >at V, so, the frequence at the radar detecort is: > >F_radar=F_obj*sqrt((1+V/c)/(1-V/c)) > > >So, according to SR: > >F_radar=F_source*(1+V/c)/(1-V/c) > Yes. You get the same result. However, my method of derivation allows me to optionally use light speeds of (c+vi) and (c-vi) and see what difference that makes. Reliance on the SR formulae wouldn't allow me to do that. -- Surfer
From: Surfer on 21 Feb 2010 02:14 On Sat, 20 Feb 2010 21:33:37 -0800, eric gisse <jowr.pi.nospam(a)gmail.com> wrote: >Surfer wrote: > >> The formula for radar Doppler shift can be derived without invoking >> Einsteins' theory of special relativity, because all observations are >> made in the same frame of reference. >> >> The result with c as the speed of light, V as the target velocity and >> Ft as the transmitted frequency, gives the shifted frequency Fr as: >> >> Fr = Ft (c+V)/(c-V) (1) > >This is observationally wrong. > Its the standard formula for radar Doppler shift. Dono just showed how to derive it using SR. -- Surfer
From: Surfer on 21 Feb 2010 02:22
On Sat, 20 Feb 2010 19:27:42 -0800, Uncle Al <UncleAl0(a)hate.spam.net> wrote: > > 1) No aether, by observation, > >http://arXiv.org/abs/0706.2031 >Physics Today 57(7) 40 (2004) > >http://physicstoday.org/vol-57/iss-7/p40.shtml ><http://cfa-www.harvard.edu/Walsworth/pdf/PT_Romalis0704.pdf> > > 2) No Lorentz violation, by observation, > ><http://relativity.livingreviews.org/Articles/lrr-2005-5/index.html> >Phys. Rev. D 81 022003 (2010) >http://arxiv.org/abs/0801.0287 > Reminds me of Mach's problem with atoms. http://en.wikipedia.org/wiki/Ernst_Mach "......Mach opposed Ludwig Boltzmann and others who proposed an atomic theory of physics. Since one cannot observe things as small as atoms directly, and since no atomic model at the time was consistent, the atomic hypothesis seemed to Mach to be unwarranted...." > > 3) Spacecraft comnunication and radar ranging, GPS to Pioneers and >Voyagers, by observation. > But consider, Earth Flyby Anomalies http://arxiv.org/abs/0910.1321 Michael Martin Nieto, John D. Anderson Physics Today {\bf 62} (No. 10 Oct.), 76-77 (2009) "........ Abstract: In a reference frame fixed to the solar system's center of mass, a satellite's energy will change as it is deflected by a planet. But a number of satellites flying by Earth have also experienced energy changes in the Earth-centered frame -- and that's a mystery ........" During an earth flyby space craft speed (and hence energy) is determined using radar Doppler shift. The anomalies could be an illusion caused by use of an inaccurate radar Doppler shift formula. |