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# AMSAT An educational endeavor (-bb) for a 501(c)3

```Right here is the answer to the question about AMSAT's mission and
qualifications as a 501(c)3
IF THIS ISN'T AN EDUCATIONAL EFFORT, I DON'T KNOW WHAT WOULD BE!
Thanks all.
Gunther Meisse
W8GSM

-----Original Message-----
From: owner-AMSAT-BB@AMSAT.Org [mailto:owner-AMSAT-BB@AMSAT.Org]On
Behalf Of Paul Williamson
Sent: Saturday, December 01, 2001 9:21 PM
To: James Alderman, KF5WT
Cc: amsat-bb@AMSAT.Org
Subject: Re: [amsat-bb] 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
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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