[amsat-bb] Re: Doppler and direction calculation?

[Joe Fitzgerald <jfitzgerald@xxxxxxxxxxxx>]

n3wwn@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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