# RE: Doppler freq. shift

```Dear Paul,

You are too slick! That was a GREAT analysis on Doppler!!!

73,

Dave / W6TE

-----Original Message-----
From: owner-AMSAT-BB@AMSAT.Org [mailto:owner-AMSAT-BB@AMSAT.Org] On
Behalf Of Paul Williamson
Sent: Tuesday, April 27, 2004 9:50 PM
To: Bill Bruno
Cc: amsat-bb@AMSAT.Org
Subject: Re: [amsat-bb] Doppler freq. shift

>I need some help understanding the Doppler freq shift on the sat's
>downlinks.  My understanding of Doppler is the freq rises as the object
>approaches and decreases as it moves away.

That sounds almost right, but it's stated in a confusing way. Let me
try to clarify. This would be easier with a blackboard or a napkin.
Try to visualize.

When the object is approaching (range is decreasing) the Doppler
shift is a frequency increase, proportional to the speed of closure.
Likewise, when the object is receding (range is increasing), the
Doppler shift is a frequency decrease, again proportional to the rate
of change of the range. We say "range-rate" as a shorthand for this
speed along the line from you to the object.

Now think about the geometry of a LEO pass. Let's make it an overhead
pass for simplicity. At the beginning of the pass, the satellite is
near the horizon, and rushing toward you. It turns out that the
range-rate is highest at this moment. As the satellite gets closer to
you, it rises in the sky, and more and more of its orbital speed is
perpendicular to the line between you and the satellite. That is, the
satellite is moving faster across the sky but not getting closer as
fast as before. Because the range-rate is now lower, the Doppler
shift is proportionately lower.

When the satellite is exactly overhead, it is moving across the sky
but not getting any closer to you or any further away. That is, the
range is momentarily constant. The Doppler shift is thus zero, and
you hear the downlink on the exact frequency it was transmitted on.

After the satellite passes through overhead, it begins to move away
from you. More and more of the orbital speed is parallel to the line
between you and the satellite, until it reaches a maximum value as
the satellite disappears over the horizon. So during this time, the
Doppler shift (now negative) increases to a maximum.

So, the Doppler shift is always falling. It starts out at a big
positive value, goes through zero as the satellite goes overhead, and
then ends up at a big negative value at LOS. That's why you see the
frequency decreasing throughout the pass.

For "overhead" you can substitute "time of closest approach" for a
non-overhead pass, and everything above is still true. It's just a
little harder to visualize that way.

I specified LEO because with a high elliptical orbit it is possible
to get other Doppler curves, because the rotation of the Earth
becomes a significant factor.  A LEO satellite always describes a
beautiful S-curve in frequency. The Doppler shift is big but nearly
constant near the ends of the pass, and changes quickly but smoothly
in the middle, passing through zero at the time of closest approach.
Plotting this curve from observations and finding the slope of the
steepest part of the curve is a good way to measure the orbit; it's
possible to derive your own Keplerian elements from several of these
observations.

Any clearer now?

73  -Paul
kb5mu@amsat.org
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