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Re: Where Does Doppler Occur?

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 

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
with apparently way too much time on my hands

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