RE: [amsat-bb] Doppler freq. shift

["David Smith" <w6te@xxxxxxxxxxx>]

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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