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Re: Where Does Doppler Occur?



Good explanation!  I'm reminded of a saying that go something like, "Every
observer in the universe can measure the universe with equal right and
equal accuracy."  

If we were to capture a signal from outer space being emitted from a
radiation source not associated with an atomic standard, etc.  Lets say a
CW beacon signal from some distant AMSAT type organization somewhere in the
universe, we would not have any idea of whether the signal we were hearing
was being doppler shifted or not.  If the source were traveling directly
toward us we would not hear any "drifting" of the signal at all.  It would
be a steady, on frequency, non-drifting carrier.  However the signal could
be doppler shifted a considerable amount from the frequency observed on the
vehicle.  We would have no way of knowing this without precise location
observations.  To an observer located well off to one side of this path of
travel the signal would be drifting.  But to us there would be no drift. 
We both would be correct. 

Paul Williamson wrote:
> 
> At 10:34 AM 12/1/2001 -0600, James Alderman, KF5WT wrote:
> >I have been wondering...we all observe Doppler shift when we monitor a
> >downlink signal from a satellite.  But where precisely does it occur?
> 
> The question is more or less meaningless. Doppler shift arises due to
> relative motion. The *only* thing that matters is the rate of change of the
> distance between the two stations. Where does that change occur? There's no
> good answer to that question.
> 
> As a thought experiment, consider a very short transmission from the
> satellite, say one microsecond in duration. At lightspeed in a vacuum, that
> transmission is about 300 meters long (or about 300 meters "thick" if you
> think about it as a spherical shell expanding around the transmit antenna,
> but let's be one-dimensional and think about it only along the line between
> the two stations). If the distance between the two stations is 300 km, the
> transmission is in transit for a millisecond. We can think of the
> transmission as a sort of object traveling from the satellite to the ground
> station. During that time, what is the frequency of the wave?
> 
> My question is meaningless, too, without a reference frame. In the
> reference frame of the satellite (neglecting its orbital acceleration) the
> frequency is exactly the frequency it was transmitted with. In the
> reference frame of, say, the Sun, it's something else. And of course in the
> reference frame of the ground station it's some other value. Which of these
> is the "real" frequency? They are all equally real. This is starting to get
> philosophical.
> 
> For most practical purposes, we can set aside all this confusing relativism
> and just pick a convenient reference frame for all our calculations. For
> this example, let's pick the reference frame in which the mass center of
> the Earth is fixed. (We'll neglect gravitational accelerations due to the
> Sun, Moon, and other celestial bodies.) That's a convenient reference frame
> for computation of the main effects on a satellite -- satellite tracking
> programs use it.
> 
> In this reference frame, both the satellite and the ground station are
> moving. The satellite is zooming around in its orbit, and the ground
> station is moving with the rotation of the Earth (unless it's on the North
> or South Pole). At any given instant, you can think of each motion as a 3D
> vector measured against our chosen reference frame. Or, in our
> one-dimensional world along the line between the two stations, each motion
> is a 1D vector, or in other words a signed speed.
> 
> Now let's get back to that microsecond pulse, and place it in our
> one-dimensional world. It starts out at the satellite's position and
> travels toward the ground station's position. While it's in motion, you can
> think of it as "knowing" the satellite's speed, but not the ground
> station's speed. If the ground station's motion suddenly changes, that has
> no effect on the wave in transit. Likewise, if the satellite's motion
> suddenly changes after it emits the transmission, that has no effect
> either. The satellite's motion matters during the microsecond of
> transmission, and the ground station's motion matters during the
> microsecond of reception.
> 
> In that sense, if you were going to assign a location to the occurence of
> Doppler shift, and if you think of the Doppler shift as an inherent
> property of the signal, I think you'd have to say that the shift due to the
> satellite's motion occurs at the satellite, and the shift due to the ground
> station's motion occurs at the ground station. If you assign the locations
> anywhere else, you'd have a spooky action-at-a-distance that's not
> necessary here.
> 
> A purist with a better understanding of Einstein than mine (which wouldn't
> be saying all that much) would find some holes in my argument, but I think
> it's basically sound and applies well enough in practice.
> 
> >At first I wondered
> >if it was occurring on some linear scale over that path between the
> >satellite and me.  But I have abandoned that theory ...
> 
> That theory would require that the signal somehow "knows" where it will be
> received while it's still propagating. Even if the spookiness of that
> doesn't bother you, you'd still have to explain how it could work for
> multiple receiving stations (all with different relative motions). I think
> you were correct to abandon that theory.
> 
> >I'm convinced that the shifting occurs at the moment the signal strikes my
> >antenna and is converted from an electromagnetic wave into voltage.
> 
> Depending on your precise definitions, that could be considered correct,
> too. If you don't think of Doppler shift as inherent in the signal itself,
> but instead as an artifact of its reception, then of course you'd have to
> think of it as occurring at the receiver.
> 
> However, I find that way of thinking to be less useful. Perhaps it captures
> something "true" about where the measurement takes place, but it separates
> the effect (Doppler shift) from one of the causes (motion of the satellite
> and motion of the ground station). Indeed because a LEO's motion is faster
> than the ground station's motion (most of the time), it separates the
> effect from the dominant cause. I think it's more useful to think about
> where the causes are located than about where the measurement takes place.
> 
> For our practical purposes, it doesn't matter which you choose. Both
> stations are moving smoothly (without any abrupt changes in speed) and the
> propagation delay is generally negligible compared to the time it takes
> either station's speed to change enough to matter. It wouldn't be easy to
> measure any difference between the theories.
> 
> 73  -Paul
> kb5mu@amsat.org
> with apparently way too much time on my hands
> 
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-- 
73, Roy

Internet: w0sl@amsat.org
Home Page: http://home.swbell.net/rdwelch
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