[amsat-bb] Re: Doppler and direction calculation?
Joe Fitzgerald
jfitzgerald at alum.wpi.edu
Wed Jan 10 07:27:39 PST 2007
n3wwn at futuretek.cx wrote:
>
> How can I calculate the doppler shift and direction of travel of a
> satellite accurately?
>
The key is to know the magnitude of the velocity of the transmitter with
respect to the receiver.
The following description is one I wrote to calculate Doppler for the
Mars Reconnaissance Orbiter while it was on its way to Mars using data
from the JPL Horizons system.
*****
To get the doppler shifted frequency expected at your station, follow
the directions to get the predictions e-mailed to you. Results will
look something like this:
****************************************************************
Date__(UT)__HR:MN Azi_(a-appr)_Elev delta deldot
****************************************************************
$$SOE
2005-Sep-21 00:00 A 58.3615 20.1819 1.3573313E+07 3.74868
2005-Sep-21 01:00 m 66.0930 30.0251 1.3586801E+07 3.75241
2005-Sep-21 02:00 m 73.5422 40.4658 1.3600337E+07 3.77473
The "deldot" column is the rate at which the range to the spacecraft is
changing, in this case moving away from us. Units here are km per second.
Note that Horizons also has an option to give delta and deldot in
astronomical units, so if you see numbers several orders of magnitude
different than the example above, check your units!!!
So the doppler shift at 00:00 UTC on the 21st is
xmit freq *(deldot/speed of light)
or
437.1 * (3.74868/299792.458) = .00546 MHz = 5.465 kHz
Since the spacecraft is moving away from us, the observed signal will be
lower in frequency, so the expected receive frequency is
437.100000 - 0.005465 = 437.094535 MHz
>
>
> I'd also like to find out the direction of travel, relative to the
> lat/lon coordinate system (90 if travelling east, 180 if south, 270 if
> west, etc).
>
> Can anyone help me out here with some equations or point me in the right
> direction?!
>
There is a nice series of articles at http://www.celestrak.com/columns/
Good luck!
-Joe KM1P
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