Thank you all for these explanations.
Gysbreght: I don't understand yours:
"Therefore, if the difference between red and blue line is almost zero, the calibrated BFO is almost zero, and hence the north-south component of the airplane groundspeed is almost zero, i.e. the track is almost due east or west."
IMHO, no Doppler between a/c and sat happens when a/c and sat have parallel pathes and same speed, or concentric pathes and speeds proportional to the pathes radii.