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Doppler Tracking via the Transit System

The discussions of determining locations using Doppler shift got me reading 
about the old Transit military navigation satellites.  From my research on 
the Web, it looks like you determine your position by knowing the exact time, 
frequency and orbit of the satellite.  That data was dowlinked to the 
receiver from the Transit satellite.  I imagine you determine your latitude 
by computing where the satellite is when your receiver frequency equals the 
satellite frequency, i.e., no Doppler shift.  I don't see how you determine 
your longitude with this system.  I imagine there are formulas that will 
enable you to triangulate how far to the side you are from the satellite by 
noting the reduced Doppler shift.  If the pass were near the horizon it would 
be obvious if you were to the West or east of the satellite since your 
ballistic missile submarine would either be in the Atlantic or in Kentucky.  
If the pass were near overhead, how would you determine which side of the 
satellite you were on?  Also, how did the receivers circa 1964 compute this 
information?  Automatically or did the operator use a slide rule and maps?  I 
would really like to hear from anyone with some specifics on this system.




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