Justification for a new doppler radar formula
in [Physics]
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From: PD on 23 Feb 2010 09:23 On Feb 22, 8:55 pm, Surfer <n...(a)spam.net> wrote: > On Mon, 22 Feb 2010 12:33:02 -0800 (PST), PD > > <thedraperfam...(a)gmail.com> wrote: > >On Feb 20, 9:08 pm, Surfer <n...(a)spam.net> wrote: > >> Suppose a frame of reference is identified in which the one way speed > >> of light is 'truely' isotropic, referred to below as the 'isotropic > >> frame'. > > >Filippas and Fox showed experimentally that this is not the case. > > I found. > > Velocity of Gamma Rays from a Moving Source > T. A. Filippas and J. G. Fox > Phys. Rev. 135, B1071B1075http://prola.aps.org/abstract/PR/v135/i4B/pB1071_1 > > That tested the idea that photons might travel at speed c relative to > the source from which they are emitted. > > But what I wrote above is quite different. Not really, unless you assume that the laboratory was at rest with respect to the aether for every single run that they did, just by fortuitous accident.
From: Surfer on 23 Feb 2010 11:08 On Mon, 22 Feb 2010 20:02:11 -0800, eric gisse <jowr.pi.nospam(a)gmail.com> wrote: >Surfer wrote: > >> On Mon, 22 Feb 2010 11:25:29 -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. >>>> >>>> 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) >>> >>>I showed you that deriving this formula is a simple exercise in SR. >>>The above formula is confirmed by experiment. >>> >> >> I don't believe experiments performed so far have been accurate enough >> to detect a difference. > >Is that belief based on the results of an actual literature search? Or a >guess? > A bit of both. This paper reports: Radar Verification of the Doppler Formula Irwin I. Shapiro, Michael E. Ash, and Menasha J. Tausner*,� Phys. Rev. Lett. 17, 933�935 "Frequencies of radar echos from the planets Mercury and Venus have recently been measured to about 1 part in 10^10 at times when the line-of-sight component of the relative velocity between the Earth and target was as large as 10^-4 c....." For comparison here are the two formula again. Fr1 = (c+V)/(c-V) Ft (1) (c + vi) (c - vi + V) Fr2 = --------------- ---------------- Ft (2) (c + vi - V) ( c - vi) As it happens, while the orbits of Mercury and Venus lie close to the ecliptic plane, the direction of 3-space flow is almost perpendicular to that plane. Since (2) is a scalar formula, vi needs to be set equal to the line of sight component of 3-space velocity between the Earth and target. Here are some values: From: http://arxiv.org/abs/0906.5404 Galactic flow speed = 486000 m/s Angle between flow and ecliptic pole = 12 Degrees So, Maximum component of flow in ecliptic plane = galactic flow speed * sin(12 Degrees) = 101045 m/s This is the maximum possible line of sight component of 3-space velocity between the Earth and targets in the ecliptic plane and so is the maximum possible value of vi for Doppler radar measurements of Venus and Mercury. From the above paper by Shapiro et.al. Maximum value of V = 10^-4 c Ft for Venus radar measurement = 1295 MHz. Plugging the above values into (1) and (2) gives as a maximum value, (Fr2 - Fr1)/Ft = 1.598 * 10^-11 So the maximum possible difference is less than the stated accuracy of 1 part in 10^10. However for targets outside the ecliptic plane, such as spacecraft performing earth flybys, vi can be much larger. Eg repeating the above calculations using 486000 m/s for vi gives, (Fr2 - Fr1)/Ft=4.93 * 10^-10 -- Surfer
From: Dono. on 23 Feb 2010 11:21 On Feb 23, 8:08 am, Surfer <n...(a)spam.net> wrote: > On Mon, 22 Feb 2010 20:02:11 -0800, eric gisse > > > > <jowr.pi.nos...(a)gmail.com> wrote: > >Surfer wrote: > > >> On Mon, 22 Feb 2010 11:25:29 -0800 (PST), "Dono." <sa...(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. > > >>>> 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) > > >>>I showed you that deriving this formula is a simple exercise in SR. > >>>The above formula is confirmed by experiment. > > >> I don't believe experiments performed so far have been accurate enough > >> to detect a difference. > > >Is that belief based on the results of an actual literature search? Or a > >guess? > > A bit of both. > > This paper reports: > > Radar Verification of the Doppler Formula > Irwin I. Shapiro, Michael E. Ash, and Menasha J. Tausner*,â > Phys. Rev. Lett. 17, 933â935 > > "Frequencies of radar echos from the planets Mercury and Venus have > recently been measured to about 1 part in 10^10 at times when the > line-of-sight component of the relative velocity between the Earth and > target was as large as 10^-4 c....." > > For comparison here are the two formula again. > > Fr1 = (c+V)/(c-V) Ft (1) > > (c + vi) (c - vi + V) > Fr2 = --------------- ---------------- Ft (2) > (c + vi - V) ( c - vi) > I don't know why you persist in your idiocy but I challenge you to solve the two cases I gave you with your formula.
From: Surfer on 23 Feb 2010 12:30 On Tue, 23 Feb 2010 06:23:09 -0800 (PST), PD <thedraperfamily(a)gmail.com> wrote: >On Feb 22, 8:55�pm, Surfer <n...(a)spam.net> wrote: >> On Mon, 22 Feb 2010 12:33:02 -0800 (PST), PD >> >> <thedraperfam...(a)gmail.com> wrote: >> >On Feb 20, 9:08�pm, Surfer <n...(a)spam.net> wrote: >> >> Suppose a frame of reference is identified in which the one way speed >> >> of light is 'truely' isotropic, referred to below as the 'isotropic >> >> frame'. � >> >> >Filippas and Fox showed experimentally that this is not the case. >> >> I found. >> >> Velocity of Gamma Rays from a Moving Source >> T. A. Filippas and J. G. Fox >> Phys. Rev. 135, B1071�B1075http://prola.aps.org/abstract/PR/v135/i4B/pB1071_1 >> >> That tested the idea that photons might travel at speed c relative to >> the source from which they are emitted. >> >> But what I wrote above is quite different. > >Not really, unless you assume that the laboratory was at rest with >respect to the aether for every single run that they did, just by >fortuitous accident. Here is the second postulate of special relativity http://en.wikipedia.org/wiki/Postulates_of_special_relativity "......As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body...." So far as measured speed of photons is concerned, Filippas and Fox should have obtained a result that complies with that. In contrast what I wrote was, ".....Suppose a frame of reference is identified in which the one way speed of light is 'truely' isotropic....." But here I was refering to actual speed of light rather than measured speed of light. Apologies if that wasn't clear. The two concepts are different. The measured speed is found to be isotropic in all frames, but the actual speed can be isotropic in only one frame. -- Surfer
From: PD on 23 Feb 2010 12:52
On Feb 23, 11:30 am, Surfer <n...(a)spam.net> wrote: > On Tue, 23 Feb 2010 06:23:09 -0800 (PST), PD > > > > <thedraperfam...(a)gmail.com> wrote: > >On Feb 22, 8:55 pm, Surfer <n...(a)spam.net> wrote: > >> On Mon, 22 Feb 2010 12:33:02 -0800 (PST), PD > > >> <thedraperfam...(a)gmail.com> wrote: > >> >On Feb 20, 9:08 pm, Surfer <n...(a)spam.net> wrote: > >> >> Suppose a frame of reference is identified in which the one way speed > >> >> of light is 'truely' isotropic, referred to below as the 'isotropic > >> >> frame'. > > >> >Filippas and Fox showed experimentally that this is not the case. > > >> I found. > > >> Velocity of Gamma Rays from a Moving Source > >> T. A. Filippas and J. G. Fox > >> Phys. Rev. 135, B1071B1075http://prola.aps.org/abstract/PR/v135/i4B/pB1071_1 > > >> That tested the idea that photons might travel at speed c relative to > >> the source from which they are emitted. > > >> But what I wrote above is quite different. > > >Not really, unless you assume that the laboratory was at rest with > >respect to the aether for every single run that they did, just by > >fortuitous accident. > > Here is the second postulate of special relativityhttp://en.wikipedia.org/wiki/Postulates_of_special_relativity > > "......As measured in any inertial frame of reference, light is always > propagated in empty space with a definite velocity c that is > independent of the state of motion of the emitting body...." > > So far as measured speed of photons is concerned, Filippas and Fox > should have obtained a result that complies with that. > > In contrast what I wrote was, > > ".....Suppose a frame of reference is identified in which the one way > speed of light is 'truely' isotropic....." > > But here I was refering to actual speed of light rather than measured > speed of light. Apologies if that wasn't clear. > > The two concepts are different. The measured speed is found to be > isotropic in all frames, but the actual speed can be isotropic in only > one frame. Ah, and how would one verify experimentally that the actual speed is isotropic in one frame and anisotropic in other frames, other than by measurement? Or is it sufficient to propose undetectable gremlins because they make so much sense? PD |